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MusicTheoryForDummies®,3rdEditionVisitdummies.com/cheatsheet/musictheorytoviewthisbook’scheatsheet.

TableofContentsCoverIntroduction

AboutThisBook

FoolishAssumptions

IconsUsedinThisBook

BeyondtheBook

WheretoGofromHere

PartI:GettingStartedwithMusicTheoryChapter1:WhatIsMusicTheory,Anyway?

UnearthingMusicTheory’sBeginnings

PuttingtheSpotlightonMusicTheoryFundamentals

SeeingHowTheoryCanHelpYourMusic

Chapter2:DeterminingWhatNotesAreWorthMeetingtheBeat

RecognizingNotesandNoteValues

CheckingOutWhole(Semibreve)Notes

HomingInonHalf(Minim)Notes

ConsideringQuarter(Crotchet)Notes

ExaminingEighth(Quaver)NotesandBeyond

ExtendingNoteswithDotsandTies

MixingAlltheNoteValuesTogether

Chapter3:GivingItaRestGettingtoKnowtheRests

ExtendingtheBreakwithDottedRests

PracticingBeatswithNotesandRests

Chapter4:IntroducingTimeSignaturesDecodingTimeSignaturesandMeasures

KeepingThingsEasywithSimpleTimeSignatures

WorkingwithCompoundTimeSignatures

FeelingthePulseofAsymmetricalTimeSignatures

http://dummies.com/cheatsheet/musictheory

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Chapter5:PlayingwithBeatCreatingStressPatternsandSyncopation

GettingaJumponPick-UpNotes

ExploringIrregularRhythms:TripletsandDuplets

PartII:PuttingNotesTogetherChapter6:MusicNotes(AndWheretoFindThem)

MeetingtheStaff,Clefs,andNotes

IdentifyingHalfSteps,WholeSteps,andAccidentals

FindingtheNotesonthePianoandtheGuitar

UsingMnemonicstoHelpRememberNotes

Chapter7:MasteringtheMajorandMinorScalesFollowingMajor-ScalePatterns

DiscoveringAllThatMinorScalePatternsHavetoOffer

Chapter8:KeySignaturesandtheCircleofFifthsUnderstandingtheCircleofFifthsandRecognizingMajorKeySignatures

FindingMinorKeySignaturesandRelativeMinors

VisualizingtheKeySignatures

Chapter9:Intervals:TheDistanceBetweenPitchesBreakingDownHarmonicandMelodicIntervals

LookingatUnisons,Octaves,Fourths,andFifths

RecognizingSeconds,Thirds,Sixths,andSevenths

BuildingIntervals

ShowingMajorandPerfectIntervalsintheCMajorScale

CheckingOutCompoundIntervals

Chapter10:ChordBuildingCreatingTriadswithThreePitches

ExpandingtoSeventhChords

LookingatAlltheTriadsandSevenths

ManipulatingTriadsthroughVoicingandInversion

ExploringExtendedChords

Chapter11:ChordProgressionsReviewingDiatonicChords,ChromaticChords,andMinorScaleModes

IdentifyingandNamingChordProgressions

AddingaSeventhChordtoaTriad

Seeing(AndHearing)ChordProgressionsinAction

ApplyingChordKnowledgetoFakeBooksandTabs

ModulatingtoaNewKey

ReachingaMusicalCadencethroughChordProgressions

PartIII:MusicalExpressionthroughTempoDynamics

Chapter12:CreatingVariedSoundthroughTempoandDynamics

TakingtheTempoofMusic

DealingwithDynamics:LoudandSoft

Chapter13:InstrumentToneColorandAcousticsDelvingintoToneColor

BuildingtheBand:AnAcousticsLesson

PartIV:MusicalExpressionthroughFormChapter14:TheBuildingBlocksofMusic:Rhythm,Melody,Harmony,andSongForm

EstablishingRhythm

ShapingtheMelody

ComplementingtheMelodywithHarmony

WorkingwithMusicalPhrasesandPeriods

LinkingMusicalPartstoCreateForms

Chapter15:RelyingonClassicalFormsCounterpointasaClassicalRevelation

SussingOuttheSonata

RoundingUptheRondo

FiguringOuttheFugue

CombiningFormsintoaSymphony

ObservingOtherClassicalForms

Chapter16:TappingIntoPopularGenresandFormsFeelingtheBlues

HavingFunwithRockandPop

ImprovisingwithJazz

PartV:ThePartofTensChapter17:TenFrequentlyAskedQuestionsaboutMusicTheory

WhyIsMusicTheoryImportant?

IfICanAlreadyPlaySomeMusicWithoutKnowingMusicTheory,WhyBotherLearningIt?

WhyIsSoMuchMusicTheoryCenteredonthePianoKeyboard?

IsThereaQuickandEasyWaytoLearntoReadMusic?

HowDoIIdentifyaKeyBasedontheKeySignature?

CanITransposeaPieceofMusicintoAnotherKey?

WillLearningMusicTheoryHinderMyAbilitytoImprovise?

DoINeedtoKnowTheoryifIJustPlayDrums?

WhereDothe12MusicalNotesComeFrom?

HowDoesKnowingTheoryHelpMeMemorizeaPieceofMusic?

Chapter18:TenKeystoReadingaMusicalScoreTheBasics

LeadSheets

FullScores

MiniatureScores

StudyScores

PianoScores

ShortScores

VocalScores

Tablature

FiguredBassNotion

Chapter19:TenMusicTheoristsYouShouldKnowAboutPythagoras(582–507BC)

Boethius(480–524AD)

Gerbertd’Aurillac/PopeSylvesterII(950–1003)

GuidoD’Arezzo(990–1040)

NicolaVicentino(1511–1576)

ChristiaanHuygens(1629–1695)

ArnoldSchoenberg(1874–1951)

HarryPartch(1901–1974)

KarlheinzStockhausen(1928–2007)

RobertMoog(1934–2005)

PartVI:AppendixesAppendixA:AudioTracksAppendixB:ChordChartAppendixC:Glossary

AbouttheAuthorsCheatSheetConnectwithDummiesEndUserLicenseAgreement

IntroductionWhatdoyouthinkofwhenyouhearthephrasemusictheory?Doestheimageofyourelementaryschoolmusicteachereyeingyoufrombehindthepianopopintoyourhead?Orperhapsyouhaveflashbackstoalaterimageoffellowcollegestudentsintheoryclassesdeterminedlytryingtonotatethereminwhistles?Ifeitheroftheseideasisanythingclosetoyourownperceptionofwhatmusictheoryis,hopefullythisbookwillbeapleasantsurprise.

Formanyself-taughtmusicians,theideaoftheoryseemsdauntingandevenalittleself-defeating.Afterall,ifyoucanalreadyreadguitartabsandplaysomescales,whywouldyouwanttomuddlewhatyoualreadyknowwiththeory?

Eventhemostbasicmusictheorytraininggivesyoutheinformationyouneedtoexpandyourrangeandabilitiesasamusician.Adecentamountofnote-readingabilityenablesyoutoplayaparticulartypeofmusic,whereassomebasicknowledgeaboutchordprogressionscanhelpyouwriteyourownmusic.

AboutThisBookMusicTheoryForDummies,3rdEdition,isdesignedtogiveyoueverythingyouneedtoknowtobecomefluentatknockingoutasolidbeat,readingmusicalscores,andlearningtoanticipatewhereasongshouldgo,whetheryou’rereadingsomeoneelse’smusicorwritingyourown.

Eachchapterisasself-containedaspossible.Inotherwords,youdon’thavetoreadeverysinglechaptertounderstandwhatthenextoneistalkingabout.Readingthechaptersconsecutivelydoeshelp,though,becauseknowledgeofmusicbuildsfromsimpleconceptstocomplexones.

Wecoveralotofterritoryinthisbook,fromdiscoveringthebasicsofnotevaluesandtimesignaturestodissectingleadlinesandaddingharmonytoamelodytostudyingthestandardformsthatmuchofpopularandclassicalmusicfollow.Soifyou’renewtotheworldofmusictheory,paceyourselfwhilereadingthisbook.Readitwhileyou’resittingatyourpianoorwithyourguitarorwhateverinstrumentyou’reworkingwithnexttoyou,andstopeverycoupleofpagestopracticetheinformationyouread.Ifyouweretakingamusicclass,thisbookwouldcoverseveralyears’worthofinformation,soifyoudon’tlearneverythinginoneortwomonths,youshouldrefrainfromself-flagellation.

FoolishAssumptionsWeassumethatifyou’rereadingthisbook,youlovemusic,youwantdesperatelytounderstandmusicandeverythingaboutit,andyou’reanutforthecomplicateddanceofperfecttimingandarrangementoftones.Attheveryleast,weassumethatyouhaveacoupleofbooksofsheetmusiclyingaroundthathavebeenfrustratingyou,oryouhaveanoldpianointhecornerofyourhousethatyou’dliketomessaroundwith.

Thisbookiswrittenforthefollowingtypesofmusicians(which,frankly,coversthegamut):

Theabsolutebeginner:Wewrotethisbookwiththeintentthatitwouldaccompanythebeginningmusicianfromhisveryfirststepsintonotereadingandtappingoutrhythmsallthewayintohisfirstrealattemptsatcomposingmusicbyusingtheprinciplesofmusictheory.BeginningmusiciansshouldstartwithPartIatthebeginningofthebookandjustkeepreadinguntilreachingthebackcover.Thebookisorganizedtofollowthelessonplanthatcollegemusictheoryclassesoffer.Themusicstudentwhodriftedaway:Thisbookcanalsobehelpfulforthemusicianwhotookinstrumentlessonsasachildandstillremembershowtoreadsheetmusicbutwhowasneverexposedtotheprinciplesofbuildingscales,followingbasicimprovisation,orjammingwithothermusicians.Manyfolksfallintothiscamp,and,luckily,ifyoudo,thisbookisdesignedtogentlyeaseyoubackintothejoyofplayingmusic.Itshowsyouhowtoworkoutsidetheconstraintsofplayingfromapieceofmusicandtrulybegintoimproviseandevenwriteyourownmusic.Theexperiencedperformer:Thisbookisalsointendedfortheseasonedmusicianwhoalreadyknowshowtoplaymusicbutnevergotaroundtoworkingouthowtoreadsheetmusicbeyondthebasicfakebookorleadsheet.Ifthisdescriptionsoundslikeyou,startwithPartI,becauseitspecificallydiscussesthenotevaluesusedinsheetmusic.Ifyou’realreadyfamiliarwiththeconceptsofeighthnotes,quarternotes,andsoon,PartIImaybeagoodstartingpoint.Inthatpartofthebook,welayouttheentiremusicstaffandmatchittoboththepianokeyboardandtheguitarneckforeasyreference.

IconsUsedinThisBookIconsarehandylittlegraphicimagesmeanttopointoutparticulartypesofinformation.Youcanfindthefollowingiconsinthisbook;they’reconvenientlylocatedalongtheleft-handmargins.

Thisiconhighlightstime-savingadviceandinformationthatcanhelpyouunderstandkeyconcepts.

Whenwediscusssomethingthatmaybeproblematicorconfusing,weusethisicon.

Thisiconflagsinformationthat’s,well,technical;youcangoaheadandskipitifyouwantto.

Whenwemakeapointoroffersomeinformationthatwefeelyoushouldkeepwithyouforever,wetossinthisicon.

Thisiconpointsoutaudiotracksthatrelatetothetopiccurrentlybeingdiscussedinthebook.Youcanaccesstheaudiotracksatwww.dummies.com/go/musictheory.

http://www.dummies.com/go/musictheory

BeyondtheBookThere’salotofsupplementalmaterialforthebookthatcanbefoundatwww.dummies.com/extras/musictheory.Youcancheckoutmanymusicalexamples,quickreferencematerialthatisperfectforprintingandshovinginyourbackpocketorguitarcasetotakewithyoutoclass,andinterestingfactoidsaboutmusicingeneral.

http://www.dummies.com/extras/musictheory

WheretoGofromHereIfyou’reabeginningmusicstudentorwanttostartagainfresh,plowthroughPartI.Ifyou’realreadyfamiliarwiththebasicsofrhythmandwanttosimplyfindouthowtoreadnotes,headtoPartII.Ifyou’reatrainedmusicianwhowantstoknowhowtoimproviseandbegintowritemusic,PartIIIcoversthebasicsofchordprogressions,scales,andcadences.YoucanalsocheckoutPartIV,whichdiscussesavarietyofmusicalformsyoucanstartpluggingyourownmusicalideasinto.

Relaxandhavefunwithyourquestintomusictheory.Listeningto,playing,andwritingmusicaresomeofthemostenjoyableexperiencesyou’lleverhave.MusicTheoryForDummies,3rdEdition,mayhavebeenwrittenbyteachers,butwepromise,noclock-watchingtyrantswillshowupatyourdoortoseehowfastyou’remakingyourwaythroughthisbook!Wehopeyouenjoyreadingthisbookasmuchaswedidwritingit.Sitback,read,andthenstartyourownmusicaladventure.

GettingStartedwithMusicTheory

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Inthispart…Gettoknowmusictheorybasics.Understandnotesandrests.Readtimesignatures.Figureoutbeatpatternsandrhythms.

Chapter1

WhatIsMusicTheory,Anyway?InThisChapter

Checkingoutabitofmusichistory

Gettingtoknowthebasicsofmusictheory

Findingouthowtheorycanaffectyourplaying

Oneofthemostimportantthingstorememberaboutmusictheoryisthatmusiccamefirst.Musicexistedforthousandsofyearsbeforetheorycamealongtoexplainwhatpeopleweretryingtoaccomplishwhenpoundingontheirdrums.Sodon’teverthinkthatyoucan’tbeagoodmusicianjustbecauseyou’venevertakenatheoryclass.Infact,ifyouareagoodmusician,youlikelyalreadyknowalotoftheory.Yousimplymaynotknowtheterminologyortechnicalities.

Theconceptsandrulesthatmakeupmusictheoryaremuchlikethegrammaticalrulesthatgovernwrittenlanguage(whichalsocamealongafterpeoplehadsuccessfullydiscoveredhowtotalktooneanother).Justasbeingabletotranscribelanguagemadeitpossibleforpeoplefarawayto“hear”conversationsandstoriesthewaytheauthorintended,beingabletotranscribemusicallowsmusicianstoreadandplaycompositionsexactlyasthecomposerintended.Learningtoreadmusicisalotlikelearninganewlanguage,tothepointwhereafluentpersoncan“hear”amusical“conversation”whenreadingapieceofsheetmusic.

Plentyofpeopleintheworldcan’treadorwrite,buttheycanstillcommunicatetheirthoughtsandfeelingsverballyjustfine.Inthesameway,plentyofintuitive,self-taughtmusicianshaveneverlearnedtoreadorwritemusicandfindthewholeideaoflearningmusictheorytediousandunnecessary.However,justliketheeducationalleapsthatcancomewithlearningtoreadandwrite,musictheorycanhelpmusiciansmasternewtechniques,performunfamiliarstylesofmusic,anddeveloptheconfidencetheyneedtotrynewthings.

UnearthingMusicTheory’sBeginningsFromwhathistorianscantell,bythetimetheancientworldwasbeginningtoestablishitself—approximately7000B.C.—musicalinstrumentshadalreadyachievedacomplexityindesignthatwouldbecarriedallthewayintothepresent.Forexample,someoftheboneflutesfoundfromthistimeperiodarestillplayable,andshortperformanceshavebeenrecordedonthemformodernlistenerstohear.

Similarly,pictographsandfuneraryornamentshaveshownthatby3500B.C.,Egyptianswereusingharpsaswellasdouble-reedclarinets,lyres,andtheirownversionoftheflute.By1500B.C.,theHittitesofnorthernSyriahadmodifiedthetraditionalEgyptianlute/harpdesignandinventedthefirsttwo-stringedguitar,withalong,frettedneck,tuningpegsatthetopoftheneck,andahollowsoundboardtoamplifythesoundofthestringsbeingplucked.

Alotofunansweredquestionsremainaboutancientmusic,suchaswhysomanydifferentculturescameupwithsomanyofthesametonalqualitiesintheirmusiccompletelyindependentofoneanother.Manytheoristshaveconcludedthatcertainpatternsofnotesjustsoundrighttolisteners,andcertainotherpatternsdon’t.Musictheory,then,verysimply,couldbedefinedasasearchforhowandwhymusicsoundsrightorwrong.Inotherwords,thepurposeofmusictheoryistoexplainwhysomethingsoundedthewayitdidandhowthatsoundcanbemadeagain.

ManypeopleconsiderancientGreecetobetheactualbirthplaceofmusictheory,becausetheancientGreeksstartedentireschoolsofphilosophyandsciencebuiltarounddissectingeveryaspectofmusicthatwasknownthen.EvenPythagoras(thetriangleguy)gotintotheactbycreatingthe12-pitchoctavescalesimilartotheonethatmusiciansandcomposersstillusetoday(seeChapter7 ).HedidthisviathefirstCircleofFifths(seeChapter8),adevicestillreligiouslyusedbymusiciansfromallwalksoflife.

AnotherfamousGreekscientistandphilosopher,Aristotle,isresponsibleformanybooksaboutmusictheory.HebeganarudimentaryformofmusicnotationthatremainedinuseinGreeceandsubsequentculturesfornearlyathousandyearsafterhisdeath.

Infact,somuchmusictheorygroundworkwaslaidinancientGreecethatsubstantialchangesdidn’tseemnecessaryuntiltheEuropeanRenaissancenearly2,000yearslater.NeighborsandconquerorsofGreecewereallmorethanhappytoincorporateGreekmath,science,philosophy,art,literature,andmusicintotheirowncultures.

PuttingtheSpotlightonMusicTheoryFundamentals

Whileitwouldbenicetobeoneofthosepeoplewhocansitatanyinstrumentandplaybeautifulmusicwithoutanytrainingwhatsoever,mostfolksneedsomesortofstructuredinstruction,whetherfromateacherorfromreadingabook.Inthefollowingsections,wegooverthebasicinformationyouneedtostartlearninghowtoreadmusic,playscales,understandkeysignatures,buildchords,andcomposewithforms.

Understandingthefoundation:Notes,rests,andbeatsLearninghowtoreadmusicisessentialtoamusician,especiallyonewhowantstosharehismusicwithothermusiciansordiscoverwhatothermusiciansareplaying.Bystudyingthebasicelements,suchastimevaluesofeachtypeofwrittennote(seeChapter2),musicalrests(seeChapter3),timesignatures(seeChapter4),andrhythm(seeChapter5),youputyourselfonthepathtomasteringmusic.Alltheseelementscometogethertoestablishafoundationthatallowsyoutoread,play,andstudymusic.

ManipulatingandcombiningnotesReadingmusicalnotesonboththetrebleandbassclefstavesaswellasfindingnotesonthepianoandguitar—thetwomostcommoninstrumentsonwhichpeopleteachthemselvestoplay—arecrucialtomakingandstudyingmusic.Chapter6givesyouthefullscoop.

Whenyoucanreadnotesonthestaves,youcandetermineamusicalpiece’skeysignature,whichisagroupofsymbolsthattellsyouwhatkeythatsongiswrittenin.YoucanusetheCircleofFifthstohelptrainyourselftoreadkeysignaturesonsightbycountingthesharpsorflatsinatimesignature.YoucanreadmoreaboutkeysignaturesandtheCircleofFifthsinChapter8.

Afteryou’vebecomefamiliarwithkeysignatures,you’rereadytomoveontointervals,chords,andchordprogressions,whichcreatethecomplexityofmusicalsound—frompleasingandsoothingtotenseandinneedofresolution.AswediscussinChapter9,youbuildscalesandchordsusingsimpleorcompoundintervals:melodicandharmonic.Chapters10and11showyoueverythingyouneedtoknowaboutbuildingchordsandchordprogression,aswellashowtobuildanduseextendedchords.

LinkingthekeyboardtomusicnotationPriortotheRenaissanceperiod,fewtrulyinnovativechangesoccurredinmusictechnology.Stringedinstruments,woodwinds,horns,andpercussioninstrumentshadbeenaroundforthousandsofyears,andalthoughtheyhadexperiencedmanyimprovementsindesignandplayingtechnique,theywereessentiallythesameinstrumentsusedbythepeopleofancientcultures.Itwasn’tuntilthe1300sthatabrandnewmusicalinterfaceappeared:thekeyboard.

Withtheinventionofthekeyboardcamethebeginningofmodernmusicalnotation—writtenmusic.Thekeyboard-notationlinkwasfosteredbecauseoftheeaseofcomposingforfullorchestrasonthekeyboard.Also,mostnewlycommissionedworkwascreatedforkeyboardinstrumentsbecauseofthepublic’sperceptionofthekeyboardasasuperiorinstrument.

Fifteenth-centuryFrenchcomposersbeganaddingasmanylinesastheyneededtotheirmusicalstaves(seeChapter6tofindoutaboutthemusicalstaff).Theyalsowrotemusicwithmultiplestavestobeplayedsimultaneouslybydifferentinstruments.Becausethekeyboardhassomanynotesavailable,separatestavesforleft-andright-handedplayingbegantobeused.Thesestavesarethebassclefandthetrebleclef.

AsnotedinChapter10,keyboardsalsohadtheadvantageofbeingincrediblyeasytobuildchordson.Bythe17thcentury,thefive-linedstaffwasconsideredstandardformostmusicalinstrumentation—probablybecauseitwaseasierandcheapertoprintjustonekindofsheetmusicformusicianstocomposeon.Thesystemhasn’tchangedmuchoverthepastfourcenturies,anditprobablywon’tchangeagainuntilanew,more-appealinginstrumentinterfaceentersthescene.

StudyingmusicalformandcompositionsMostpopularandclassicalmusiciscomposedusingspecificforms.Aformisastructuralblueprintusedtocreateacertaintypeofmusic.Thebuildingblocksofformincludemusicalphrasesandperiods(whichwecoverinChapter14),andrhythm,melody,andharmonyenterthepicturetocreatethegenre,orstyle,ofapieceofmusic.

Whensittingdowntowritemusic,youhavetochoosewhatformyou’regoingtofollow;forexample,classicalorpopular.Youcanchoosefrommanydifferentclassicalandpopularforms,includingsonatas,concertos,16-barblues,andverse-chorusform(Chapters15and16provideplentyofinformationontheformsyoumayencounter).Youcancreatevariedsoundinwhateverformyouchoosebyplayingwithtempo,dynamics,andinstrumenttonecolor(seeChapters12and13formore).

SeeingHowTheoryCanHelpYourMusicIfyoudidn’tknowbetter,youmaythinkthatmusicwassomethingthatcouldstartonanynote,gowhereveritwanted,andstopwhenevertheperformerfeltlikegettingupforaglassoficedtea.Althoughit’struethatmanyfolkshavebeentomusicalperformancesthatactuallydofollowthisstyleof“composition,”forthemostparttheseperformancesareconfusingandannoyinglyself-indulgentandfeelalittlepointless.

Theonlypeoplewhocanpulloffaspontaneousjamwellarethosewhoknowmusicthoroughlyenoughtostackchordsandnotesnexttooneanothersotheymakesensetolisteners.And,becausemusicisinherentlyaformofcommunication,connectingwithyourlistenersisthegoal.

Gettingtoknowmoreaboutmusictheoryisalsoincrediblyinspiring.Nothingcandescribethefeelingyougetwhenthelightbulbgoesoffinyourheadandyousuddenlyrealizeyoucanputa12-barbluesprogressiontogetherandbuildareallygoodsongoutofit.Orwhenyoucanlookatapieceofclassicalmusicandfindyourselflookingforwardtoplayingthroughitforthefirsttime.Orthefirsttimeyousitdowntojamwithyourfriendsandfindyouhavetheconfidencetotakethelead.

Asamusician,theinescapablefactisthis:Whatyougetoutofmusiciswhatyouputintoit.Ifyouwanttobeabletoplayclassicalmusic,youmustknowhowtosight-readandknowhowtokeepasteadybeat.Ifyouplantobecomearockguitarist,knowingwhatnotesyouneedtoplayinagivenkeyisespeciallyimportant.Knowinghowtoplaymusictakesalotofpersonaldiscipline,butintheend,it’sworthallthehardwork.Plus,ofcourse,playingmusicisfun,andknowinghowtoplaymusicwellisincrediblyfun.Everybodylovesarockstar/jazzman/Mozart.

Chapter2

DeterminingWhatNotesAreWorthInThisChapter

Understandingrhythm,beat,andtempo

Reviewingnotesandnotevalues

Counting(andclapping)outdifferentnotes

Gettingtoknowtiesanddottednotes

Combiningnotevaluesandcountingthemout

Justabouteveryonehastakensomesortofmusiclessons,eitherformalpaidlessonsfromalocalpianoteacherorattheveryleastthestate-mandatedrudimentarymusicclassesofferedinpublicschool.Eitherway,we’resureyou’vebeenaskedatsomepointtoknockoutabeat,ifonlybyclappingyourhands.

Maybethemusiclessonseemedprettypointlessatthetimeorservedonlyasagreatexcusetobopyourgrade-schoolneighboronthehead.However,countingoutabeatisexactlywhereyouhavetostartwithmusic.Withoutadiscerniblebeat,youhavenothingtodanceornodyourheadto.Althoughalltheotherpartsofmusic(pitch,melody,harmony,andsoon)areprettydarnedimportant,withoutthebeat,youdon’treallyhaveasong.

Everythingaroundyouhasarhythmtoit,includingyou.Inmusic,therhythmisthepatternofregularorirregularpulses.Themostbasicthingyou’restrivingtofindinsongsistherhythm.Luckily,writtenmusicmakesiteasytointerpretothercomposers’worksandproducethekindofrhythmtheyhadinmindfortheirsongs.

Inthischapter,weprovideyouwithasolidintroductiontothebasicsofcountingnotesanddiscoveringasong’srhythm,beat,andtempo.

Note:Youmaynoticeinthischapterthatwe’vegiventwodifferentnamesforthenotesmentioned—forexample,quarter(crotchet)note.Thefirstname(quarter)isthecommonU.S.nameforthenote,andthesecondname(crotchet)isthecommonU.K.nameforthesamenote.TheU.K.namesarealsousedinmedievalmusicandinsomeclassicalcircles.AfterChapter3,weuseonlytheU.S.commonnamesforthenotes,becausetheU.S.usageismoreuniversallystandard.

MeetingtheBeatAbeatisapulsationthatdividestimeintoequallengths.Atickingclockisagoodexample.Everyminute,thesecondhandticks60times,andeachoneofthoseticksisabeat.Ifyouspeeduporslowdownthesecondhand,you’rechangingthetempoofthebeat.Notesinmusictellyouwhattoplayduringeachofthoseticks.Inotherwords,thenotestellyouhowlongandhowoftentoplayacertainmusicalpitch—theloworhighsoundaspecificnotemakes—withinthebeat.

Whenyouthinkofthewordnoteasassociatedwithmusic,youmaythinkofasound.However,inmusic,oneofthemainusesfornotesistoexplainexactlyhowlongaspecificpitchshouldbeheldbythevoiceoraninstrument.Thenotevalue,indicatedbythesizeandshapeofthenote,determinesthislength.Togetherwiththeprecedingthreefeatures,thenotevaluedetermineswhatkindofrhythmtheresultingpieceofmusichas.Itdetermineswhetherthesongrunsalongveryquicklyandcheerfully,crawlsalongslowlyandsomberly,orprogressesinsomeotherway.

Whenfiguringouthowtofollowthebeat,rhythmsticks(fat,cylindrical,hardwoodinstruments)comeinrealhandy.Sododrumsticks.Ifyou’vegotapair,grab’em.Ifyoudon’t,clappingorsmackingyourhandagainstbongosoryourdesktopworksjustaswell.

Eventually“hearing”abeatinyourhead(or“feeling”abeatinyourbody)isabsolutelyfundamentalwhileyouplaymusic,whetheryou’rereadingapieceofsheetmusicorjammingwithothermusicians.Theonlywayyoucanmasterthisbasictaskispractice,practice,practice.Followingalongwiththebeatissomethingyouneedtopickupifyouwanttoprogressinmusic.

Perhapstheeasiestwaytopracticeworkingwithasteadybeatistobuyametronome.They’reprettycheap(youmayevenbeabletofindanappforyoursmartphone).Evenacrummymetronomeshouldlastyouforyears.Thebeautyofametronomeisthatyoucansetittoawiderangeoftempos,fromvery,veryslowtohummingbirdfast.Ifyou’reusingametronometopractice—especiallyifyou’rereadingfromapieceofsheetmusic—youcansetthebeattowhateverspeedyou’recomfortablewithandgraduallyspeedituptothecomposer’sintendedspeedwhenyou’vefiguredoutthepacingofthesong.

RecognizingNotesandNoteValuesIfyouthinkofmusicasalanguage,thennotesarelikelettersofthealphabet—they’rethatbasictotheconstructionofapieceofmusic.Studyinghownotevaluesfitagainsteachotherinapieceofsheetmusicisasimportantasknowingmusicalpitchesbecauseifyouchangethenotevalues,youendupwithcompletelydifferentmusic.Infact,whenmusicianstalkaboutperformingapieceofmusic“inthestyleof”Bach,Beethoven,orPhilipGlass,they’retalkingasmuchaboutusingtherhythmstructureandpacecharacteristicsofthatparticularcomposer’smusicasmuchasanyparticularchordprogressionsormelodicchoices.

Inthissection,wetakeacloserlookatnotesandwhatthey’remadeof.Wealsodiscussthebasicsonnotevalues.Formorein-depthinfoonnotes,checkoutChapter6.

ExaminingthenotesandtheircomponentsNotesaremadeofuptothreespecificcomponents:notehead,stem,andflag(seeFigure2-1).

Head:Theheadistheroundpartofanote.Everynotehasone.Stem:Thestemistheverticallineattachedtothenotehead.Eighth(quaver)notes,quarter(crotchet)notes,andhalf(minim)notesallhavestems.Flag:Theflagisthelittlelinethatcomesoffthetoporbottomofthenotestem.Eighth(quaver)notesandshorternoteshaveflags.

©JohnWiley&Sons,Inc.

Figure2-1:Thewhole(semibreve)notehasahead;thequarter(crotchet)notehasaheadandstem;andtheeighth(quaver)notehasahead,stem,andflag.

Stemscanpointeitherupordown,dependingwhereonthestafftheyappear(youfindoutallaboutstavesinChapters4and6).Whetherthestempointsupordownmakesnodifferenceinthevalueofthenote.

Insteadofeachnotegettingaflag,noteswithflagscanalsobeconnectedtoeachotherwithabeam,whichisjustacleaner-lookingincarnationoftheflag.Forexample,Figure2-2showshowtwoeighth(quaver)notescanbewrittenaseachhavingaflag,orasconnectedbyabeam.


Figure2-2:Youcanwriteeighth(quaver)noteswithindividualflags,oryoucanconnectthemwithabeam.

Figure2-3showsfoursixteenth(semiquaver)noteswithflagsgroupedthreeseparateways:individually,intwopairsconnectedbyadoublebeam,andallconnectedbyonedoublebeam.Itdoesn’tmatterwhichwayyouwritethem;theysoundthesamewhenplayed.


Figure2-3:Thesethreegroupsofsixteenth(semiquaver)notes,writteninthreedifferentways,allsoundalikewhenplayed.

Likewise,youcanwriteeightthirty-second(demisemiquaver)notesineitherofthewaysshowninFigure2-4.Noticethatthesenotesgetthreeflags(orthreebeams).Usingbeamsinsteadofindividualflagsonnotesissimplyacaseoftryingtocleanupanotherwisemessy-lookingpieceofmusicalnotation.Beamshelpmusicalperformersbyallowingthemtoseewherethelargerbeatsare.Insteadofseeingsixteendisconnectedsixteenth(semiquaver)notes,it’shelpfulforaperformertoseefourgroupsoffoursixteenths(semiquavers)connectedbyabeam.


Figure2-4:Likeeighth(quaver)notesandsixteenth(semiquaver)notes,youcanwritethirty-second(demisemiquaver)notesseparatelyor“beamed”together.

LookingatnotevaluesAsyoumayrememberfromschoolormusiclessons,eachnotehasitsownnotevalue.Wegointodetailoneachkindofnotelaterinthischapter,butfornow,havealookatFigure2-5,whichshowsmostofthekindsofnotesyou’llencounterinmusicarrangedsotheirvaluesaddupthesameineachrow.Atthetopisthewhole(semibreve)note,belowthathalf(minim)notes,thenquarter(crotchet)notes,eighth(quaver)notes,andfinallysixteenth(semiquaver)notesonthebottom.Eachlevelofthe“treeofnotes”isequaltotheothers.Thevalueofahalf(minim)note,forexample,ishalfofawhole(semibreve)note,andthevalueofaquarter(crotchet)noteisaquarterofawhole(semibreve)note.


Figure2-5:Eachlevelofthistreeofnoteslastsasmanybeatsaseveryotherlevel.

Anotherwaytothinkofnotesistoimagineawhole(semibreve)noteasapie,whichiseasybecauseit’sround.Todivvyupthepieintoquarter(crotchet)notes,cutitinquarters.Cuttingthepieintoeightpiecesgivesyoueighth(quaver)notes,andsoon.

Dependingonthetimesignatureofthepieceofmusic(seeChapter4),thenotevaluethat’sequaltoonebeatchanges.Inthemostcommontimesignature,4/4time,alsocalledcommontime,awhole(semibreve)noteisheldforfourbeats,ahalf(minim)noteisheldfortwo,andaquarter(crotchet)notelastsonebeat.Aneighth(quaver)notelastshalfabeat,andasixteenth(semiquaver)notelastsjustaquarterofabeatin4/4time.

Often,thequarter(crotchet)noteequalsonebeat.Ifyousing,“MA-RYHADALIT-TLELA-MB,”eachsyllableisonebeat(youcanclapalongwithit),andeachbeatgetsonequarter(crotchet)noteifthesongisnotatedin4/4time.WetalkmoreabouttimesignaturesandcountingbeatsaccordinglyinChapter4.

CheckingOutWhole(Semibreve)NotesThewholenote(calledasemibrevenoteintheU.K.)laststhelongestofallthenotes.Figure2-6showswhatitlookslike.


Figure2-6:Awhole(semibreve)noteisahollowoval.

In4/4time,awhole(semibreve)notelastsforanentirefourbeats(seeChapter4formoreontimesignatures).Forfourwholebeats(semibreves),youdon’thavetodoanythingwiththatonenoteexceptplayandholdit.That’sit.

Usually,whenyoucountnotevalues,youclaportaponthenoteandsayaloudtheremainingbeats.Youcountthebeatsofwhole(semibreve)notesliketheonesshowninFigure2-7,likethis:

CLAPtwothreefourCLAPtwothreefourCLAPtwothreefour

“CLAP”meansyouclapyourhands,and“twothreefour”iswhatyousayoutloudasthenoteisheldforfourbeats,orafour-count.


Figure2-7:Whenyouseethreewhole(semibreve)notesinarow,eachonegetsitsown“four-count.”

Evenbetterfortheworn-outmusicianiscomingacrossadoublewhole(breve)note.Youdon’tseethemawholeheckofalot,butwhenyoudo,theylooklikeFigure2-8,andthey’regenerallyusedinslow-movingprocessionalmusicorinmedievalmusic.Whenyouseeadoublewhole(breve)note,youhavetoholdthenoteforanentireeightcounts,likeso:

CLAPtwothreefourfivesixseveneight


Figure2-8:Holdadoublewhole(breve)noteforeightcounts.

Youcanalsoshowanotethatlastsforeightcountsbytyingtogethertwowhole(semibreve)notes.Wediscusstieslaterinthischapter.

HomingInonHalf(Minim)NotesIt’ssimplelogicwhatcomesafterwhole(semibreve)notesinvalue—ahalf(minim)note,ofcourse.Youholdahalf(minim)noteforhalfaslongasyouwouldawhole(semibreve)note.Half(minim)noteslooklikethenotesinFigure2-9.Whenyoucountoutthehalf(minim)notesinFigure2-9,itsoundslikethis:

CLAPtwoCLAPtwoCLAPtwo

Becausethehighest-valuednoteinFigure2-9isahalf(minim)note,youcountuponlytothenumbertwo.


Figure2-9:Holdahalf(minim)noteforhalfaslongasawhole(semibreve)note.

Youcouldhaveawhole(semibreve)notefollowedbytwohalf(minim)notes,asshowninFigure2-10.Inthatcase,youcountoutthethreenotesasfollows:

CLAPtwothreefourCLAPtwoCLAPtwo


Figure2-10:Awhole(semibreve)notefollowedbytwohalf(minim)notes.

ConsideringQuarter(Crotchet)NotesDivideawhole(semibreve)note,whichisworthfourbeats,byfour,andyougetaquarter(crotchet)notewithanotevalueofonebeat.Quarter(crotchet)noteslooklikehalf(minim)notesexceptthatthenoteheadiscompletelyfilledin,asshowninFigure2-11.Fourquarter(crotchet)notesarecountedoutlikethis:

CLAPCLAPCLAPCLAP

Becausethehighest-valuednoteisaquarter(crotchet)note,youcountuponlytoone.Fourquarter(crotchet)notestogetherlastaslongasonewhole(semibreve)note.


Figure2-11:Thesefourquarter(crotchet)notesgetonebeatapiece.

Supposeyoureplaceoneofthequarter(crotchet)noteswithawhole(semibreve)noteandonewithahalf(minim)note,asshowninFigure2-12.Inthatcase,youcountoutthenoteslikethis:

CLAPtwothreefourCLAPCLAPCLAPtwo


Figure2-12:Amixtureofwhole(semibreve),half(minim),andquarter(crotchet)notesisgettingclosertowhatyoufindinmusic.

ExaminingEighth(Quaver)NotesandBeyond

Whensheetmusicincludeseighth(quaver)notesandbeyond,itreallystartstolookalittleintimidating.Usually,justoneortwoclustersofeighth(quaver)notesinapieceofmusicalnotationisn’tenoughtofrightentheaveragebeginningstudent,butwhenthatsamestudentopenstoapagethat’slitteredwitheighth(quaver)notes,sixteenth(semiquaver)notes,orthirty-second(demisemiquaver)notes,shejustknowsshehassomeworkaheadofher.Why?Becauseusuallythesenotesarefast.

Aneighth(quaver)note,showninFigure2-13,hasavalueofhalfaquarter(crotchet)note.Eighteighth(quaver)noteslastaslongasonewhole(semibreve)note,whichmeansaneighth(quaver)notelastshalfabeat(in4/4,orcommon,time).


Figure2-13:Youholdaneighth(quaver)noteforone-eighthaslongasawhole(semibreve)note.

Howcanyouhavehalfabeat?Easy.Tapyourtoeforthebeatandclapyourhandstwiceforeverytoetap.

CLAP-CLAPCLAP-CLAPCLAP-CLAPCLAP-CLAP

Oryoucancountitoutasfollows:

ONE-andTWO-andTHREE-andFOUR-and

Thenumbersrepresentfourbeats,andthe“ands”arethehalfbeats.

Justthinkofeachtickofametronomeasaneighth(quaver)noteinsteadofaquarter(crotchet)note.Thatmeansaquarter(quaver)noteisnowtwoticks,ahalf(minim)noteisfourticks,andawhole(semibreve)notelastseightticks.

Similarly,ifyouhaveapieceofsheetmusicwithsixteenth(semiquaver)notes,eachsixteenth(semiquaver)notecanequalonemetronometick,aneighth(quaver)notetwoticks,aquarter(crotchet)notefourticks,ahalf(minim)noteeightticks,andawhole(semibreve)notecanequalsixteenticks.

Asixteenth(semiquaver)notehasanotevalueofonequarterofaquarter(crotchet)note,whichmeansitlastsone-sixteenthaslongasawhole(semibreve)note.A

sixteenth(semiquaver)notelookslikethenoteinFigure2-14.


Figure2-14:Youholdasixteenth(semiquaver)noteforhalfaslongasaneighth(quaver)note.

Ifyouhaveapieceofsheetmusicwiththirty-second(demisemiquaver)notes,asshowninFigure2-15,rememberthatathirty-second(demisemiquaver)noteequalsonemetronometick,asixteenth(semiquaver)noteequalstwo,aneighth(quaver)noteequalsfour,aquarter(crotchet)noteequalseight,ahalf(minim)noteequalssixteen,andawhole(semibreve)noteequalsthirty-twoticks.You’llbegladtohearthatyouwon’trunintothirty-second(demisemiquaver)notesveryoften.


Figure2-15:Youholdathirty-second(demisemiquaver)noteforhalfaslongasasixteenth(semiquaver)note.

ExtendingNoteswithDotsandTiesSometimesyouwanttoaddtothevalueofanote.Youhavetwomainwaystoextendanote’svalueinwrittenmusic:dotsandties.Weexplaineachinthefollowingsections.

Usingdotstoincreaseanote’svalueOccasionally,youcomeacrossanotefollowedbyasmalldot,calledanaugmentationdot.Thisdotindicatesthatthenote’svalueisincreasedbyonehalfofitsoriginalvalue.Themostcommonuseofthedottednoteiswhenahalf(minim)noteismadetolastthreequarter(crotchet)notebeatsinsteadoftwo,asshowninFigure2-16.Anotherwaytothinkaboutdotsisthattheymakeanoteequaltothreeofthenextshortervalueinsteadoftwo.


Figure2-16:Youholdadottedhalf(dottedminim)noteforanadditionalone-halfaslongasaregularhalf(minim)note.

Lesscommon,butstillapplicablehere,isthedottedwhole(dottedsemibreve)note.Thisdottednotemeansthewhole(semibreve)note’svalueisincreasedfromfourbeatstosixbeats.

Ifyouseetwodotsbehindthenote—calledadouble-dottednote—increasethetimevalueofthenotebyanotherquarteroftheoriginalnote,ontopofthehalfincreaseindicatedbythefirstdot.Ahalf(minim)notewithtwodotsbehinditisworthtwobeatsplusonebeatplusone-halfabeat,orthreeandahalfbeats.Yourarelyseethistypeofnotationinmodernmusic.ComposerRichardWagnerwasveryfondofthetriple-dottednoteinthe1800s.

AddingnotestogetherwithtiesAnotherwaytoincreasethevalueofanoteisbytyingittoanothernote,asFigure2-17shows.Tiesconnectnotesofthesamepitchtogethertocreateonesustainednoteinsteadoftwoseparateones.Whenyouseeatie,simplyaddthenotestogether.Forexample,aquarter(crotchet)notetiedtoanotherquarter(crotchet)noteequalsonenoteheldfortwobeats:

CLAP-two!


Figure2-17:Twoquarter(crotchet)notestiedtogetherequalahalf(minim)note.

Don’tconfusetieswithslurs.Aslurlookskindoflikeatie,exceptthatitconnectstwonotesofdifferentpitches.(YoufindoutmoreaboutslursinChapter12.)

MixingAlltheNoteValuesTogetherYouwon’tencountermanypiecesofmusicthatarecomposedentirelyofonekindofnote,soyouneedtopracticeworkingwithavarietyofnotevalues.

ThefourexercisesshowninFigures2-18through2-21canhelpmakeabeatstickinyourheadandmakeeachkindofnoteautomaticallyregisteritsvalueinyourbrain.Eachexercisecontainsfivegroups(ormeasures)offourbeatseach.Themeasuresarenotatedwithverticallines,calledbarlines,whichareexplainedmoreinChapter4.

Intheseexercises,youclapontheCLAPsandsaythenumbersaloud.WhereyouseeahyphenatedCLAP-CLAP,dotwoclapsperbeat(inotherwords,twoclapsinthespaceofonenormalclap).

Toeaseyourselfintoeachexercise,startoutcountingandthendiveinafteryoucountfour.

Exercise1CLAPCLAPCLAPCLAP|CLAPtwothreeCLAP|CLAPtwothreefour|CLAPtwothreefour|CLAPCLAPCLAPfour


Figure2-18:Exercise1.

Exercise2CLAPtwothreefour|CLAPtwothreefour|CLAPCLAPthreeCLAP|CLAPtwoCLAPfour|CLAPtwothreefour



Exercise3CLAPCLAP-CLAPCLAPfour|CLAPtwothreefour|CLAPtwothreeCLAP|CLAP-CLAPCLAPthreefour|CLAPtwoCLAPfour



Exercise4CLAPtwoCLAPfour|CLAPtwothreeCLAP|CLAPtwothreefour|oneCLAPthreefour|CLAPtwothreefour



Chapter3

GivingItaRestInThisChapter

Countingoutthevaluesofrests

Dottingreststolengthentheirbreaks

Mixingupnotesandrests

Sometimesthemostimportantaspectsofaconversationarethethingsthataren’tsaid.Likewise,manytimesthenotesyoudon’tplaymakeallthedifferenceinapieceofmusic.

Thesesilent“notes”arecalled,quitefittingly,rests.Whenyouseearestinapieceofmusic,youdon’thavetodoanythingbutcontinuecountingoutthebeatsduringit.Restsareespeciallyimportantwhenwritingdownyourmusicforotherpeopletoread—andinreadingothercomposers’music—becauserestsmaketherhythmofthatpieceofmusicevenmoreprecisethanmusicalnotesalonewould.

Restsworkparticularlywellwithmusicformultipleinstruments.Restsmakeiteasyforaperformertocountoutthebeatsandkeeptimewiththerestoftheensemble,eveniftheperformer’sinstrumentdoesn’tcomeintoplayuntillaterintheperformance.Likewise,inpianomusic,reststelltheleftorrighthand—orboth—tostopplayinginapiece.

Don’tletthenamefoolyou.Arestinapieceofmusicisanythingbutnaptime.Ifyoudon’tcontinuetosteadilycountthroughtherests,justasyoudowhenyou’replayingnotes,yourtimingwillbeoff,andeventuallythepiecewillfallapart.

Note:Youmaynoticeinthischapterthatwe’vegiventwodifferentnamesforthenotesorrestsmentioned—forexample,quarter(crotchet)rest.Thefirstname(quarter)isthecommonU.S.namefortherest,andthesecondname(crotchet)isthecommonU.K.nameforthesamerest.TheU.K.namesarealsousedinmedievalmusicandinsomeclassicalcircles.Afterthischapter,weonlyusetheU.S.namesfornotesandrests,becausetheU.S.usageismoregloballyrecognized.

GettingtoKnowtheRestsThinkofrestsasthespacesbetweenwordsinawrittensentence.Ifthosespacesweren’tthere,you’djustbestringingonelongwordtogetherintogobbledygook.

Musicalrestsdon’tgetclaps(ornotesfrominstrumentsorvoices).Youjustcountthemoutinyourhead.Justremembertostopplayingyourinstrumentwhileyou’recounting.

Figure3-1showstherelativevaluesofrests,rangingfromawhole(semibreve)restatthetoptothesixteenth(semiquaver)restsatthebottom.Atthetopisthewhole(semibreve)rest,belowithalf(minim)rests,thenquarter(crotchet)rests,eighth(quaver)rests,andsixteenth(semiquaver)rests.Wediscusseachoftheserestsinthefollowingsections.


Figure3-1:Eachlevelofthistreeofrestslastsasmanybeatsaseveryotherlevel.

Whole(semibreve)restsJustlikeawhole(semibreve)note,awhole(semibreve)restisworthfourbeats(inthemostcommontimesignature,4/4;seeChapter4forallyouneedtoknowabouttimesignatures).LookatFigure3-2foranexampleofawhole(semibreve)rest.


Figure3-2:Awhole(semibreve)restlookslikeanupside-downhat.

Thewhole(semibreve)restlookslikeanupside-downhat.Youcanrememberwhatthisrestlookslikebyimaginingit’sahatthathasbeentakenoffandsetdownonatable,becausethisrestisalongone.

Evenbetterthanadoublewhole(breve)notefortheworn-outmusicianistheveryraredoublewhole(breve)rest,whichyoucanseeinFigure3-3.Whenyoucomeacrossoneofthese,usuallyin4/2music,youdon’thavetoplayanythingforeightbeats.


Figure3-3:You’llrarelyencounterthedoublewhole(breve)rest.

Half(minim)restsIfawhole(semibreve)restisheldforfourbeats,thenahalf(minim)restisheldfortwobeats.Half(minim)restslookliketheoneinFigure3-4.


Figure3-4:Thehalf(minim)restlastshalfaslongasthewhole(semibreve)rest.

Asdowhole(semibreve)rests,half(minim)restsalsolooklikehats.However,thehalf(minim)restisrightsideupbecausethewearerdidn’thavetimetolayitdownonatable.

TakealookatthenotesandrestinFigure3-5.Ifyouweretocountoutthismusicin4/4time,itwouldsoundlikethis:

CLAPtwothreefourCLAPtwoRESTtwo


Figure3-5:Awhole(semibreve)note,half(minim)note,andhalf(minim)rest.

Quarter(crotchet)restsDivideawhole(semibreve)restbyfourorahalf(minim)restbytwo,andyougetaquarter(crotchet)rest.Aquarter(crotchet)rest,showninFigure3-6,lastsone-quarteraslongasawhole(semibreve)rest.


Figure3-6:Aquarter(crotchet)rest,writtenlikeakindofsquiggle,islikeasilentquarter(crotchet)note.

Figure3-7showsawhole(semibreve)noteandahalf(minim)noteseparatedbytwoquarter(crotchet)rests.YouwouldclapoutthemusicinFigure3-7asfollows:

CLAPtwothreefourRESTRESTCLAPtwo


Figure3-7:Twoquarter(crotchet)reststuckedbetweennotes.

Eighth(quaver)restsandbeyondEighth(quaver)rests,sixteenth(semiquaver)rests,andthirty-second(demisemiquaver)restsareeasytorecognizebecausetheyallhavelittlecurlicueflags,alittlebitliketheirnotecounterparts,asweexplaininChapter2.Here’sthelowdownonthedifferentnumbersofflagseachnoteandresthas:

Oneflag:Eighth(quaver)noteandeighth(quaver)rest;seeFigure3-8.Twoflags:Sixteenth(semiquaver)noteandsixteenth(semiquaver)rest;seeFigure3-9.Threeflags:Thirty-second(demisemiquaver)noteandthirty-second(demisemiquaver)rest;seeFigure3-10.


Figure3-8:Aneighth(quaver)resthasastemandonecurlyflag.


Figure3-9:Asixteenth(semiquaver)resthastwocurlyflags.


Figure3-10:Athirty-second(demisemiquaver)restisveryrareandhasthreecurlyflags.

Asyoumayimagine,eighth(quaver)restscanbeastrickytocountoutastheirnoteequivalents.Aneighth(quaver)restlastshalfaslongasaquarter(crotchet)rest,whichusuallymeanslessthanawholebeat.Eighteighth(quaver)restsmakeupawhole(semibreve)rest.

Usingametronometocountoutnotesandrestsmayhelpyoufigureoutapieceofmusic.Youcanassigntheticksofthemetronometobeanyportionofthebeatthatyouwant.Havingaquarter(crotchet)noteequalonebeatmayseemnaturalmuchofthetime,butinsteadoftryingtothinkabouthalfbeats,youcanalsoassignaneighth(quaver)notetoequalonetick.Thenaquarter(crotchet)notewouldequaltwoticks,ahalf(minim)notefour,andawhole(semibreve)noteeightticks.Therelationamongthedifferentnotesandrestsalwaysstaysthesamenomatterhowmanymetronometicksinawhole(semibreve)note.

Asixteenth(semiquaver)restlooksliketheoneinFigure3-9.Ithasanotevalueofone-sixteenthofawhole(semibreve)rest.Inotherwords,sixteensixteenth(semiquaver)restsmakeupawhole(semibreve)rest.

Youprobablywon’teverencounterone,butyoustillneedtobeabletorecognizeathirty-second(demisemiquaver)rest.Athirty-second(demisemiquaver)rest,whichisshowninFigure3-10,hasavalueofonethirty-secondofawhole(semibreve)rest.Sothirty-twothirty-second(demisemiquaver)restsmakeupawhole(semibreve)rest.

ExtendingtheBreakwithDottedRestsUnlikenotes,restsarenevertiedtogethertomakethemlonger.Restsare,however,sometimesdottedwhenthevalueoftherestneedstobeextended.Justlikewithnotes,whenyouseearestfollowedbyanaugmentationdot,therest’svalueisincreasedbyonehalfofitsoriginalvalue.(FliptoChapter2fordetailsondotsandties.)

Figure3-11showsadottedhalf(minim)rest,whichyouholdforahalf(minim)restplusone-halfofahalf(minim)rest.Adottedquarter(crotchet)restisextendedbyanotherhalfofaquarter(crotchet)rest.


Figure3-11:Holdadottedhalf(minim)restforahalf(minim)restplusone-halfofahalf(minim)rest,makingitworththreequarter(crotchet)rests.

PracticingBeatswithNotesandRestsThebestwaytoreallyhearthewayrestsaffectapieceofmusicistomixthemupwithnotes.Toavoidaddingtotheconfusion,weuseonlyquarter(crotchet)notesinthefollowingexercises.

ThefiveexercisesshowninFigures3-12through3-16areexactlywhatyouneedtopracticemakingabeatstickinyourheadandmakingeachkindofnoteandrestautomaticallyregisteritsvalueinyourbrain.Eachexercisecontainsthreegroupsoffourbeatseach.

Intheseexercises,withfourbeatsineverymeasure(4/4time),youclaponthenotesandcounttherestsaloud.Startoutcountingandthendiveinafteryoucountfour.

Exercise1CLAPCLAPCLAPCLAP|Onetwothreefour|CLAPtwothreeCLAP



Exercise2Onetwothreefour|CLAPtwoCLAPfour|CLAPtwothreeCLAP



Exercise3OneCLAPthreeCLAP|Onetwothreefour|CLAPtwothreeCLAP



Exercise4OnetwoCLAPCLAP|Onetwothreefour|CLAPCLAPCLAPfour



Exercise5Onetwothreefour|CLAPtwothreeCLAP|OnetwoCLAPCLAP



Chapter4

IntroducingTimeSignaturesInThisChapter

Discoveringmeasuresandtimesignatures

Knowingthedifferencebetweensimpleandcompoundtimesignatures

Findingoutaboutasymmetricaltimesignatures

Ifyou’reworriedabouthowyou’resupposedtokeeptrackofwhereyouareinalongpieceofmusic,neverfear.Thegeniuseswhocameupwithmusicnotationfiguredoutawaytomakeorderoftheonslaughtofnotesandrests.Youjusthavetobecomefamiliarwithtimesignaturesandthestructureofthemusicalstaff,includingtheconceptofmeasures(orbars).Thischapterexplainseverythingyouneedtoknow.

DecodingTimeSignaturesandMeasuresInprintedmusic,rightaftertheclefandthekeysignature(seeChapter8formoreaboutkeysignatures)atthebeginningofthestaff,youseeapairofnumbers,onewrittenovertheother.

Thepairofnumbersiscalledthetimesignature,which,incidentally,isthemaintopicofthischapter.Thetimesignaturetellsyoutwothings:

Thenumberofbeatsineachmeasure:Thetopnumberinthetimesignaturetellsyouthenumberofbeatstobecountedoffineachmeasure.Ifthetopnumberisthree,eachmeasurecontainsthreebeats.Whichnotegetsonebeat:Thebottomnumberinthetimesignaturetellsyouwhichtypeofnotevalueequalsonebeat—mostoften,eighthnotesandquarternotes.Ifthebottomnumberisfour,aquarternoteisonebeat.Ifit’saneight,aneighthnotecarriesthebeat.

Figure4-1showsthreecommontimesignatures.


Figure4-1:Threetypicaltimesignatures,whichyoureadas“three-fourtime,”“four-fourtime,”and“six-eighttime.”

Writtenmusiccontainsthefollowingtwomaintypesoftimesignatures,whichwecoverlaterinthischapter:

Simple:Withsimpletimesignatures,thebeatofapieceofmusiccanbebrokendownintotwo-partrhythms.Compound:Incompoundtimesignatures,thebeatisbrokendownintothree-partrhythms.

Ameasure(sometimescalledabar)isasegmentofwrittenmusiccontainedwithintwoverticallines.Eachmeasureinapieceofmusichasasmanybeatsasisallowedbythetimesignature.Forinstance,ifyou’reworkingwitha4/4timesignature,eachmeasureinthatpieceofmusiccontainsexactlyfourbeats(asstatedbythetopnumberofthetimesignature)carriedbynotesorrests.Ifthetimesignatureis3/4,eachmeasurehasthreebeatsinit,asshowninFigure4-2.Theoneexceptiontothisruleiswhenthemeasureusespick-upnotes(seeChapter5formoreaboutpick-upnotes).Withthesenotes,youputastrongaccentonthefirstbeatofeachmeasure,the“1”beat.Musicianscallthisthedownbeat.


Figure4-2:Giventhe3/4timesignature,eachmeasurecontainsthreebeats,andthequarternoteequalsonebeat.

Practicingcountingthroughmeasuresisagreatwaytomakesureyou’replayingthepieceofmusicinfrontofyouaccordingtothebeatchosenbythecomposer.AswemakeclearinChapters2and3,continuouslycountingbeatsinyourheadwhileyou’replayingisincrediblyimportanttotheresultingsound.Timingiseverythinginmusic.Youmustbecomesocomfortablewiththeinherentbeatofwhateveryou’replayingthatyoudon’tevenknowyou’recountingbeatsanymore.

KeepingThingsEasywithSimpleTimeSignaturesSimpletimesignaturesaretheeasiesttocount,becauseaone-twopulseinapieceofmusicfeelsthemostnaturaltoalistenerandaperformer.Thefollowingfourrequirementsindicatethatatimesignatureisasimpleone:

Eachbeatisdividedintotwoequalcomponents.Ifasinglebeathasmorethanonenote,thosenotesarealwaysgroupedtogethertoequalonebeat.Thischaracteristicismostobviouswhenit’sappliedtoeighthandsmallernotes.Insimpletime,twoeighthnotesarealwaysconnectedtogetherwithabarcalledabeam,asarefoursixteenthnotes,oreightthirty-secondnotes.(Ifyouhavetwosixteenthnotesandoneeighthnote,thosethreenotes,whichequalonebeat,arealsobeamedtogether.)Figure4-3showstheprogressionofhownotesarebeamedtogetherinsimpletime.Thenotethatgetsonebeathastobeanundottednote.Whenyou’recountingasongoutinyourhead,you’regoingtobecountingonlyundottednotesthataredivisiblebytwo.Usuallythismeansyou’llbecountingquarternotes,butyoualsomaybecountinghalfnotes,wholenotes,or,sometimes,eighthnotes.

In4/4time,forexample,inyourheadyou’llbecounting,“One-two-three-four”overandoveragain.In3/4time,it’llbe“one-two-three”overandoveragain;in2/4time,“one-two.”

Thetopnumberisn’tdivisibleby3exceptwhenitis3.Forexample,3/4and3/8areconsideredsimpletimesignatures,whereas6/4,6/8,and9/16aren’t(becausetheyaredivisibleby3;thesearecompoundtimesignatures).Thenumberofbeatsisthesameineverymeasure.Everymeasure,orbar,ofmusicinasimpletimesignaturehasthesamenumberofbeatsthroughoutthesong.Afteryougetintothegrooveofcountingoutthetime,youdon’thavetoworryaboutdoinganythingbutmakingsurethenotesinthesongfollowthatbeatallthewaythrough.


Figure4-3:Eachlevelofthistreeequalseveryotherlayer,andmultiplenoteswithinabeatarealwaysgroupedtogethertoequalonebeat.

Thefollowingsectionsexplainhowtousemeasurestocountinsimpletimeandprovideyouwithsomecountingpractice.

UsingmeasurestocountinsimpletimeMeasures(orbars)helpperformerskeeptrackofwheretheyareinapieceofmusicandhelpthemplaytheappropriatebeat.Insimpletime,themeasureiswherethetruerhythmofapieceofmusiccanbefelt,evenifyou’rejustreadingapieceofsheetmusicwithoutplayingit.

Insimpletime,aslightlystrongeraccentisplacedonthefirstbeatofeachmeasure.

Herearesomecommonexamplesofsimpletimesignatures(someofwhichwedescribeinthefollowingsections):

4/4:Usedinpopular,classical,rock,jazz,country,bluegrass,hip-hop,andhousemusic3/4:Usedforwaltzesandcountryandwesternballads2/4:Usedinpolkasandmarches3/8:Usedinwaltzes,minuets,andcountryandwesternballads2/2:Usedinmarchesandslow-movingprocessionals

Counting4/4timeWhenyouseealineofmusicthathasa4/4timesignatureliketheoneinFigure4-4,thebeatiscountedofflikethis:

ONEtwothreefourONEtwothreefourONEtwothreefour


Figure4-4:Atimesignatureof4/4satisfiestherequirementsofsimpletime.

Thebottomnumber4inthetimesignatureinFigure4-4tellsyouthatthequarternotegetsthebeat,andthetopnumber4tellsyouthateachmeasurecontainsfourbeats,orfourquarternotes.

Because4/4timeissooftenusedinpopulartypesofmusic,it’sfrequentlyreferredtoascommontime.Infact,insteadofwriting“4/4”forthetimesignature,somecomposersjustwritealarge“C”instead.

Counting3/4timeIfthetimesignatureofalineofmusicis3/4,asinFigure4-5,thebeatiscountedlikethis:

ONEtwothreeONEtwothreeONEtwothree



Counting3/8timeIfthetimesignatureis3/8,thefirstnote—whateveritmaybe—getsthebeat.InFigure4-6,thatfirstnoteisaneighthnote.



YoucountoutthebeatofthemusicshowninFigure4-6likethis:

ONEtwothreeONEtwothreeONEtwothree

Thetimesignatures3/8and3/4havealmostexactlythesamerhythmstructureinthewaythebeatiscountedoff.However,because3/8useseighthnotesinsteadofquarternotes,theeighthnotesgetthebeat.

Counting2/2timeIfthetimesignatureofalineis2/2,alsocalledcuttime,thehalfnotegetsthebeat.Andbecausethetopnumberdeterminesthatthemeasurecontainstwobeats,youknowthateachmeasurehastwohalfnotes,asshowninFigure4-7.


Figure4-7:In2/2time,thehalfnotegetsthebeat,andeachmeasurecontainstwobeats.

YoucountthemusicinFigure4-7likethis:

ONEtwoONEtwo

Timesignatureswitha2asthelowernumberwerewidelyusedinmedievalandpre-medievalmusic.Musicfromthisperiodusedarhythmstructure,calledatactus—latercalledaminim—thatwasbasedontherhythmpatternofahumanheartbeat.

PracticingcountingbeatsinsimpletimeUsingtheinformationfromtheprecedingsections,practicecountingoutthebeats(notthenotes)showninFigures4-8through4-12.Whencountingthesebeatsoutloud,remembertogivethefirstbeataslightstress.Forachallenge,trytappingoutthenoteswhileyoucountthebeatsoutloud.

Exercise1ONEtwothreefour|ONEtwothreefour|ONEtwothreefour



Exercise2ONEtwothree|ONEtwothree|ONEtwothree









Exercise5ONEtwo|ONEtwo|ONEtwo



WorkingwithCompoundTimeSignaturesJustaweebittrickierthansimpletimesignaturesarecompoundtimesignatures.Here’sashortlistofrulesthathelpyouimmediatelytellwhenyou’redealingwithacompoundtimesignature:

Thetopnumberisevenlydivisibleby3,withtheexceptionoftimesignatureswherethetopnumberis3.Anytimesignaturewithatopnumberof6,9,12,15,andsoonaccordingtothemultiplesof3isacompoundtimesignature.However,3/4and3/8aren’tcompoundtimesignaturesbecausethetopnumberis3(they’resimpletimesignatures,whichwediscussearlier).Themostcommoncompoundtimesignaturesare6/8,9/8,and12/8.SeeFigure4-13foranexample.Eachbeatisdividedintothreecomponents.Threeeighthnotesarebeamedtogether,asaresixsixteenthnotes.Figure4-14showsthe“three-based”groupingofbeamednotesusedincompoundtime.


Figure4-13:Atimesignatureof6/8isacompoundtimesignature.


Figure4-14:Compoundtimedividesnotesintogroupsofthree.

Thefollowingsectionsexplainhowtousemeasurestocountincompoundtimeandprovideyouwithsomecountingpractice.

UsingmeasurestocountincompoundtimeOnebigdifferencebetweenmusicinasimpletimesignatureandmusicinacompoundtimesignatureisthattheyfeeldifferent,bothtolistentoandtoplay.

Incompoundtime,anaccentisnotonlyplacedonthefirstbeatofeachmeasure(asinsimpletime),butaslightlysofteraccentisalsoplacedoneachsuccessivebeat.Therefore,therearetwodistinctlyaccentedbeatsineachmeasureofmusicwitha6/8time,threeaccentsinapieceof9/8music,andfouraccentsinapieceofmusicwitha12/8timesignature.

Hereareafewexamplesofcompoundtimesignatures(someofwhichwecoverinthefollowingsections):

6/8:Usedinmariachimusic12/8:Foundin12-barbluesanddoo-wopmusic9/4:Usedinjazzandprogressiverock

Todeterminethenumberofaccentspermeasureunderacompoundtimesignature,dividethetopnumberbythree.Doingsohelpsyoufindthepulseinthemusicyou’replayingand,therefore,wheretoputtheaccents.Inapieceof6/8music,forexample,youwouldputtheaccentatthebeginningofeachmeasure,butyoualsowouldputaslightaccentatthebeginningofthesecondgroupofeighthnotesinameasure.

Counting6/8timeInacompound6/8timesignature,youaccentthefirstandthesecondsetsofthreeeighthnotes.Forexample,thebeataccentsinFigure4-15wouldgolikethis:

ONEtwothreeFOURfivesixONEtwothreeFOURfivesix


Figure4-15:Accentthefirstandsecondsetsofthreeeighthnotesinacompound6/8timesignature.

Counting9/4timeIfthetimesignatureissomethingunusual,like9/4,anexampleofwhichisshowninFigure4-16,youwouldcountoffthebeatlikeso:

ONEtwothreeFOURfivesixSEVENeightnine


Figure4-16:Atimesignatureof9/4isacompoundtimesignature.

PracticingcountingbeatsincompoundtimeUsingtheinformationfromtheprecedingsections,practicecountingoutthebeatsinFigures4-17through4-19.Whencountingthesebeatsoutloud,remembertogivethefirstbeataslightstressandputanadditionalstressatthepulsepointsofthemeasure,whicharegenerallylocatedaftereverythirdbeat.(Note:Theandsinthebeatpatternsaremeanttocapturetheliltofsomeofthenoteswithinthebeat.Weadmitthismethodisn’tscientific,butitshouldgiveyouageneralideaofhowtocountoutbeatsindifferenttimesignatures.)

Exercise1ONEtwothreeFOUR-andfivesix|ONEtwothreeFOURfivesix|ONEtwothreeFOURfivesix



Exercise2ONEtwothreeFOUR-and-five-and-six-and|ONEtwothreeFOURfivesix|ONEtwothreeFOUR-and-five-and-six-and



Exercise3ONEtwothreeFOURfivesixSEVENeightnine|ONEtwothreeFOUR-and-five-and-six-andSEVENeightnine

FeelingthePulseofAsymmetricalTimeSignaturesAsymmetricaltimesignatures(alsosometimescalledcomplexorirregulartimesignatures)generallycontainfiveorsevenbeats,comparedtothetraditionaltwo-,three-,andfour-beatmeasuregroupingsintroducedearlierinthischapter(aspartofsimpleandcompoundtimesignatures).Asymmetricaltimesignaturesarecommonintraditionalmusicfromaroundtheworld,includinginEuropeanfolkmusicandinEastern(particularlyIndian)popularandfolkmusic.

Whenyouplayorhearapieceofmusicwithanasymmetricaltimesignature,younoticethatthepulseofthesongfeelsandsoundsquiteabitdifferentfrommusicwrittenundersimpleorcompoundtimesignatures.Musicwith5/4,5/8,and5/16timesignaturesisusuallydividedintotwopulses—eithertwobeatsplusthreebeats,orviceversa.Thestresspatterndoesn’thavetorepeatitselffrommeasuretomeasure;theonlyconstantisthateachmeasurestillcontainsfivebeats.

Forexample,inFigure4-20,thepulseisdefinedbytheplacementsofthehalfnotesineachgrouping,makingthestressesfallonthethirdbeatinthefirstmeasureandonthefourthbeatinthesecondmeasure,likethis:

ONEtwoTHREEfourfive|ONEtwothreeFOURfive


Figure4-20:Inthisexampleof5/4time,thestressisonbeatsone,three,one,andfour.

InFigure4-21,thebeamingoftheeighthnotesshowswherethestressesaretooccur—onthefirsteighthnoteofeachsetofbeamednotes.Here’swhatitlookslikeifyousayitoutloud:

ONEtwoTHREEfourfive|ONEtwothreeFOURfive


Figure4-21:Inthisexampleof5/8time,thestressisonbeatsone,three,one,andfour.

Musicwith7/4,7/8,and7/16timesignatureslookslikethemusicinFigures4-22and4-23.Again,thestresspatternsdon’thavetostaythesamefromonemeasuretothenext.


Figure4-22:Inthisexampleof7/4time,thestressisonbeatsone,four,one,andfive.


Figure4-23:Inthisexampleof7/8time,thestressisonbeatsone,four,six,one,three,andfive.

Ifthetimesignaturewere7/4,asshowninFigure4-22,youwouldcountoffthebeatlikethis:

ONEtwothreeFOURfivesixseven|ONEtwothreefourFIVEsixseven

Here’showyoucountoffatimesignatureof7/8,asshowninFigure4-23:

ONEtwothreeFOURfiveSIXseven|ONEtwoTHREEfourFIVEsixseven

Asymmetricaltimesignaturesareconsidered“complex”onlyfromaWesternpointofview.Theseirregulartimesignatureshavebeenusedregularlythroughouthistoryandaroundtheworld,includinginancientGreeceandPersia.TheyalsocanstillbeheardinBulgarianfolkmusic.ModernWesterncomposersandensemblesasdiverseasSteveAlbini,Beck,DaveBrubeck,Juneof44,AndrewLloydWebber,FrankZappa,PinkFloyd,Yo-YoMa,BobbyMcFerrin,andStereolabhaveallusedasymmetricaltimesignaturesintheirmusic.Awholegenreofrock,calledmathrock,isbasedonusingcomplextimesignatures,suchas7/8,11/8,13/8,andsoon,inordertobreakawayfromthe4/4timethat’sthestandardinrock.

Chapter5

PlayingwithBeatInThisChapter

Understandingwhymusicsometimesstraysfromthebeat

Makingupthedifferencewithpick-upnotes

Mixingthingsupwithtripletsandduplets

Therulesofnotesandrestsmayseemstrict,buteventhemostcasuallistenercanrecognizethatmusicisn’taforcecontrolledbyroboticpercussionistsandgiganticclickingmetronomes.Iftheworlditselfwereaperfectlyorderedorganism,witheverylivingthingonitmovingalonginperfecttime,allmusicmightsoundsimilar.However,eventhehealthiesthumanheartskipsabeatnowandthen,andsodoesmusic.

Thetrickforcomposersandmusictheoristsalikehasbeentotranslatetheseskippedbeatsintowrittennotation,makingsuchdeviationsfitnaturallyintothescore.Thischapterexplainseverythingyouneedtoknowaboutworkingwithabeat.

CreatingStressPatternsandSyncopationTheunderlyingrhythmicpulseofmusiciscalledthebeat.Insomeways,thebeatiseverything.Itdetermineshowpeopledancetomusicorevenhowtheyfeelwhentheyhearit.Thebeatinfluenceswhetherpeoplefeelexcited,agitated,mellow,orrelaxedbymusic.Whenyou’rewritingapieceofmusicdownonpaper,thewayyougroupyournotestogetherinameasure(themusiccontainedwithintwobarlines)reflectsthekindofbeatthemusicwillhave.Asamusician,youcanfeelthisnaturalpulsewhenyouplaymusicandcountoffthebeats.

Placingstress:KnowingthegeneralrulesGenerally,thefirstbeatofameasurereceivesthestrongeststress.Ifmorethanthreebeatsareinameasure,usuallyasecondarystrongbeatcomeshalfwaythroughthemeasure.Lotsoftheoriesexistaboutwhythebrainseemstodemandthatmusicbebrokenupintounitsoftwoandthreebeats(nottheleastbeingthatthebeatofmusictendstobesimilartothebeatofthehumanheart).Butnoonehascometoaconsensusonwhymusicshouldbebrokenupintounitsoftwoorthreebeats.

Inapieceofmusicwithfourbeatsineachmeasure,suchasapiecein4/4time,thefirstbeatinthemeasurehasastrongaccent,andthethirdbeathasaslightlylessstrongaccent.Thebeatswouldbecountedasfollows:

ONEtwoTHREEfour

Apieceofmusicwrittenin6/8time,whichhassixbeatsineachmeasure,iscountedasfollows:

ONEtwothreeFOURfivesix

SeeChapter4formoreontimesignatures.

Syncopation:Hittingtheoff-beatSyncopationis,verysimply,adeliberatedisruptionofthetwo-orthree-beatstresspattern.Musiciansmostoftencreatesyncopationbystressinganoff-beat,oranotethatisn’tonthebeat.

In4/4time,thegeneralstresspatternisthatthefirstandthethirdbeatsarestrong,andthesecondandfourthareweak.Anotherwaytosaythisisthatdownbeats,oraccentedbeats,suchasthoseatthebeginningorhalfwaythroughameasure,arestrong,andupbeats,orunaccentedbeats,aregenerallyweak.

SoifyouhadapieceofmusicthatlookedlikethemusicinFigure5-1,thequarterrestwherethenaturaldownbeatislocatedisconsideredthepointofsyncopationinthemusic.Thefourthbeatofthemeasureisaccentedinsteadofthethirdbeat,whichisnormallyaccented,creatingadifferent-soundingrhythmthanyouwouldnormallyhave

in4/4timemusic.Themeasurewouldbecountedoffassuch:

ONE-two-three-FOUR


Figure5-1:Ameasurewithsyncopation.

InFigure5-1,thenaturalstressofthemeterhasbeendisrupted.ThecountONE-two-(three)-FOURisweirdtoyourearbecauseyouwanttohearthatnonexistentquarternotethatwouldcarrythedownbeatinthemiddleofthemeasure.

Ifyoudoanythingthatdisruptsthenaturalbeatwitheitheranaccentoranupbeatwithnosubsequentdownbeatbeingplayed,youhavecreatedsyncopation.

Peopleoftenmistakesyncopationasbeingcomprisedofcool,complexrhythmswithlotsofsixteenthnotesandeighthnotes,asoftenheardinjazzmusic,butthatisn’tnecessarilytrue.Forexample,Figure5-2showsabunchofeighthnotesandthenabunchofsixteenthandthirty-secondnotes.


Figure5-2:Thesemeasuresmaylookcomplicated,buttheydon’tshowsyncopation.

JustbecauseFigure5-2showsadenserhythmdoesn’tnecessarilymeanthoserhythmsaresyncopated.Asyoucanseefromtheaccentmarks,thedownbeatisstillonthe“one”and“four”countinbothmeasures,whichisthenormaldownbeatin6/8time.

Evenifapieceofmusiccontainsanentiremeasureofeighthnotes,itdoesn’tnecessarilyhavesyncopation.Everyeighthnotehasasubsequentrhythmicresolution.Inotherwords,thedownbeatsstilloccurinthemeasurewherethey’resupposedtobe,ontheaccentednotesshowninthefigure.Thesameistrueofabunchofsixteenthnotesinarow.Theyaren’tsyncopatedbecause,again,eventhoughyouhavesomeinterestingnotesthataren’tonthedownbeat,everythingendsupalwaysresolvingtothebeat,likethefollowingmeasurein4/4time:

ONEtwoTHREEfour

Here’sanotherexampleofthebeatresolvingin6/8time:

ONEtwothreeFOURfivesix

NowtakealookattherhythminFigure5-3.Insideeachboxisapointofsyncopationinthemeasures,givingyouthefollowingrhythm:

ONEtwothreeFOURoneTWOthreeFOUR


Figure5-3:Thismusicshowstwoplaceswherethenoteplacementcreatessyncopation.

Thenaturalstresseshavebeenshiftedoverinbothmeasures,resultinginapurposefullydisjointed-soundingbeat.

Sodoessyncopationinvolveacarefullyplacedrestoranaccentednote?Theanswerisboth.Ifyourperspectiveofwherethedownbeatoccursismoved,apointofsyncopationresultsbecauseit’sshiftingwherethestrongandtheweakaccentsarebuilt.

TrycountingoutthebeatswhilelisteningtotheRollingStones’“Satisfaction,”andyou’llhearsomegreatexamplesofsyncopation.

GettingaJumponPick-UpNotesUpuntilnow,you’vehadtofollowtherulethatsays4/4meterhasfourbeatstoeverymeasure.Thinkofeverymeasurelikeajugofwaterthatyouhavetofillrighttothetopwithoutspillingover—youcan’tendupshortandyoucan’tspillanyover.That’stherule.

Butlikeeverygoodrule,thisonehasanexception.It’scalledapick-upmeasure,whichisanoddmeasureatthebeginningofapieceofmusic,asshowninFigure5-4.Thismeasurecontainspick-upnotes.


Figure5-4:Thequarternotestandingaloneinthefirstmeasureisapick-upnote.

Thepick-upmeasureshowninFigure5-4hasonlyonebeatwherethreeshouldbe(giventhatthepieceisin3/4time).Fromthatpointon,thesongfollowstherulessetforthbythe3/4timesignatureallthewaytotheveryend,whereyousuddenlycomeacrossameasurethatlooksliketheoneinFigure5-5.


Figure5-5:Thelastmeasureofthesong“pickedup”theremainingtwonotesfromthefirstincompletepick-upmeasure.

Thefinalmeasureisthesecondpartofthepick-upmeasure:Thefinaltwobeatsareconsideredtheremainderpartofthefirstmeasure.Inotherwords,thelastmeasure“fixes”whatlookedwrongwiththatfirstmeasure,andthereforeyouhaveapieceofmusicwrittenaccordingtoalltherulesofmusictheory.

Likealotofcaseswhendealingwithmusictheory,thematterofusingpick-upnotesismostlynotational.InFigure5-5,thelistenerdoesn’tnecessarilyknowthatthelastbarisincompleteunlesssheislisteningreallycarefully.Usually,onlythecomposerhastoworryaboutthewholebusinessofbalancingouttheendwiththepick-upmeasure.

Incontemporarymusic,especiallyrockmusic,youcanstillhavethefirstpick-upmeasure,butyoudon’tnecessarilyhavetoadheretotheperfectruleoffinishingitinthefinalmeasure.Oftenmusiciansstartasongwithapick-upmeasure,buttheirlastmeasureisacompleteone.

ExploringIrregularRhythms:TripletsandDuplets

Anotherwayyoucanaddrhythmicinterestandvarietytomusicisthroughtheuseofirregularrhythms(alsocalledirrationalrhythmorartificialdivision).Anirregularrhythmisanyrhythmthatinvolvesdividingthebeatdifferentlyfromwhat’sallowedbythetimesignature.Themostcommonofthesedivisionsiscalledatriplet,whichisthreenotesjoinedtogetherthatequalthebeatofasinglenote.Thesecondmostcommontypeofirregularrhythmisaduplet,whichistwobracketednoteswithanotevalueofthreeofthesamenotes.

Irregularnotedivisions,suchastripletsandduplets,allowformorecomplexrhythmsthan“regular”notationtimenormallyallows.

Thefollowingsectionsdivedeeperintotripletsandduplets.

AddinginterestwithtripletsSayyouwanttoputaquicklittlesequenceofthreenoteswhereyou’dnormallyplayonequarternote.In4/4time,ifyouwanttoplayanevennumberofnotesinyoursequence,youcanuseacoupleofeighthnotes,orfoursixteenthnotes,oreightthirty-secondnotes.Butwhatifyouwanttoplayanoddnumberofnotes,andyouabsolutelywantthatoddnumberofnotestoequalonebeat?

Theansweristoplayatriplet,whichiswhatyougetwhenyouhaveanotethat’susuallydivisiblebytwoequalpartsdividedintothreeequalparts.YoucanseewhataquarternotedividedintotripletslookslikeinFigure5-6.


Figure5-6:Whenaquarternotein4/4timeisdividedintothreeequalnotes,theresultisatriplet.

Agoodwaytocountoutthebeatswhileplayingtripletsistosaythenumberofthebeatfollowedbythewordtriplet(withtwosyllables),makingsuretodividethetripletplayedintothreeequalparts.

Forexample,themeasuresinFigure5-7wouldbecountedofflikethis:

ONEtwoTHREE-trip-letfourONE-trip-lettwoTHREE-trip-letfour


Figure5-7:Apieceofmusicusingbothquarternotesandtriplets.

Youcanshowthetripletnotationintwoways:withthenumber3writtenoverthegroupofthreenotesorwithabracketaswellasthenumber.Readtripletnotationasmeaning“threenotesinthetimeoftwo.”

WorkingwithdupletsDupletsworkliketriplets,exceptinreverse.Composersusedupletswhentheywanttoputtwonotesinaspacewheretheyshouldputthree.

Anexamplewouldbedividingadottedquarternoteintotwoeighthnotesinsteadofthreeeighthnotesasyouwouldinameasureofmusicunderacompoundtimesignature(seeChapter4formoreoncompoundtimesignatures).Agoodwaytocountdupletsistocountthesecondnoteineachpairasandinsteadofassigningitanumbervalueasyouwouldanyotherbeatincompoundmeter.

YoucountthemeasuresshowninFigure5-8likethis:

ONEtwothreeFOUR-andONE-andFOURfivesix


Figure5-8:Eachdupletgetsthesametimevalueasthedottednoteitreplaces.

PartII

PuttingNotesTogether

Visitwww.dummies.com/extras/musictheoryforaninterestingarticle.


Inthispart…Discoverthegrandstaff,trebleandbassclefs,andnotenames.Gettoknowmusicalintervals,scales,andchords.UnderstandtheCircleofFifthsandtherelationshipbetweenkeysandchords.Identifyandcreatechordsandchordprogressions.

Chapter6

MusicNotes(AndWheretoFindThem)InThisChapter

Gettingtoknowthestaff,clefs,andtheirnotes

Understandinghalfsteps,wholesteps,andaccidentals

Applyingknowledgeofthestavestothepianoandtheguitar

Memorizingnoteswithmnemonics

JohannesGutenberg’sinventionoftheEuropeanprintingpressin1450isconsideredbymanytobetheofficialendoftheDarkAgesforEurope.Eventually,hisinventionwouldmakeitpossibleforordinarypeopletoownbooks,andalongtheway,sheetmusicalsobeganbeingprintedforordinarymusicianstoown.Soon,peoplewithalittlemusicalknow-howcouldteachthemselvesalltheprinciplesofmusictheorypreviouslyunavailabletothoseoutsidetheinstitutionsofreligionorhigherlearning.

Astheproficiencyofthe“common”musicianincreased,theneedformorenewsheetmusicincreasedaswell.Aftercomposerslearnedtheycouldturnadecentprofitbysellingmultiple,machine-printedcopiesoftheirmusic—insteadofonelaboriouslyhand-drawncopyatatime—theybeganfloodingthemarketwithnewcompositions.

Thisevolutioneventuallyledtothestandardizationofsheetmusic.Foryears,composerswerefreetouseasmanyorasfewstafflinesastheywantedtoexpressnotation,butbythe1500s,thefive-linestaffthatmusiciansusetodaywasgraduallybecominguniversallyaccepted,atleastinEurope.

Thischapterdiscussesthemusicalstavesandwheretofindnotesonthemaswellastheconceptofhalfsteps,wholesteps,andaccidentals.Masteringtheseconceptsallowsyoutobothnavigateyourwaythroughapieceofsheetmusicandevenbegintolearnhowtoimprovise.

MeetingtheStaff,Clefs,andNotesNotesandrestsinmusicarewrittenonwhatmusicianscallamusicalstaff(orstaves,ifyou’retalkingabouttwo).Astaffismadeoffiveparallelhorizontallines,containingfourspacesbetweenthem,asshowninFigure6-1.


Figure6-1:Thetwoprimarystaves:thetrebleclefstaff(left)andthebassclefstaff(right).

Notesandrestsarewrittenonthelinesandspacesofthestaff.Theparticularmusicalnotesthataremeantbyeachlineandspacedependonwhichclefiswrittenatthebeginningofthestaff.Youmayrunacrossanyofthefollowingclefs(thoughthefirsttwoarethemostcommon):

TrebleclefBassclefCclefs,includingaltoandtenor

Thinkofeachclefasagraphofpitches,ortones,shownasnotesplottedovertimeonfivelinesandfourspaces.Eachpitchortoneisnamedafteroneofthefirstsevenlettersofthealphabet:A,B,C,D,E,F,G,A,B,C…anditkeepsongoingthatwayindefinitely,repeatingthenotenamesasthepitchesrepeatinoctaves.ThepitchesascendasyougofromAtoG,witheveryeighthnote—whereyoureturntoyourstartingletter—signifyingthebeginningofanewoctave.

Thefollowingsectionsgiveyoumoredetailsontheclefsindividuallyandtogether(calledagrandstaff).WealsotakealookattheCclefandwhenyoumightcrosspathswithit.

ThetrebleclefThetrebleclefisforhigher-pitchednotes.ItcontainsthenotesabovemiddleConthepiano,whichmeansallthenotesyouplaywithyourrighthandonthepiano.Ontheguitar,thetrebleclefisusuallytheonlyclefyoueverread.Mostwoodwindinstruments,highbrassinstruments,andviolinssticksolelytothetrebleclef.Anyinstrumentthatmakesupper-register,orhigh,soundshasitsmusicwritteninthetrebleclef.

ThetrebleclefisalsosometimescalledtheGclef.NotethattheshapeofthetrebleclefitselfresemblesastylizedG.Thelooponthetrebleclefalsocirclesthesecondlineon

thestaff,whichisthenoteG,asshowninFigure6-2.


Figure6-2:ThetrebleclefalwaystellsyouthatGisonthesecondstaffline.

Thenotesarelocatedinthetrebleclefonlinesandspaces,inorderofascendingpitch,asshowninFigure6-3.


Figure6-3:Thenotesofthetrebleclef.

ThebassclefOnthepiano,thebassclefcontainslower-pitchednotes,theonesbelowmiddleC,includingallthenotesyouplaywithyourlefthandonthepiano.Musicisgenerallywritteninthebassclefforlowerwindinstrumentslikethebassoon,thelowerbrassinstrumentslikethetuba,andthelowerstringedinstrumentslikethebassguitar.

AnothernameforthebassclefistheFclef.ThecurlytopoftheclefpartlyencircleswheretheFnoteisonthestaff,andithastwodotsthatsurroundtheFnote,asshowninFigure6-4.(ItalsolooksabitlikeacursiveletterF,ifyouuseyourimagination.)


Figure6-4:ThetwodotsofthebassclefsurroundtheFnoteonthestaff.

Thenotesonthebassclefarearrangedinascendingorder,asshowninFigure6-5.


Figure6-5:Thenotesofthebassclef.

ThegrandstaffandmiddleCPutthetrebleandbassclefstogetherandyougetthegrandstaff,asshowninFigure6-6.


Figure6-6:Thegrandstaffcontainsboththetrebleandbassclefs,connectedbyledgerlinesandmiddleC.

MiddleCislocatedonelinebelowthetrebleclefandonelineabovethebassclef.Butit’snotineitherclef.Insteadit’swrittenonaledgerline.Ledgerlinesarelineswrittenabovethebassclefandbelowthetrebleclefthatarenecessarytoconnectthetwoclefs.Putitalltogether,andthenotesflowsmoothlyfromonecleftotheotherwithnointerruptions.

Cclefs:AltoandtenorOccasionally,youmaycomeacrossananimalknownastheCclef.TheCclefisamoveableclefthatyoucanplaceonanylineofthestaff.ThelinethatrunsthroughthecenteroftheCclef,nomatterwhichlinethatis,isconsideredmiddleC,asyoucanseeinFigure6-7.


Figure6-7:NoticehowmovingthepositionofmiddleCchangesthepositionoftheletternamesonthestaff.

CclefsarepreferredinclassicalnotationforinstrumentalrangesthathoverrightaboveorrightbelowmiddleC.Insteadofhavingtoconstantlyswitchbetweenreadingtrebleandbassclefs,amusicianhasjustonemusicalstafftoread.

Cclefsweremorecommonlyusedbeforesheetmusicwasstandardizedandabletoeasilyaccommodateawiderangeoftones.Today,theonlyCclefscommonlyusedarethefollowing:

Thealtoclef:PutsmiddleConthethirdstaffline;mostcommonlyusedforwritingviolamusic.Thetenorclef:PutsmiddleConthenext-to-the-toplineofthestaff;mostcommonlyusedforwritingcello,trombone,andbassoonmusic.

IdentifyingHalfSteps,WholeSteps,andAccidentals

InWesternmusic,anoctaveisbrokenupinto12tonescalledhalfsteps,orsemitones.Butamusicalscalecontainssevennotes,meaningthatsomeofthedistancebetweennotesinascalespansonesemitoneandsomespansatleasttwosemitones.Inotherwords,somehalfstepsareskippedwhenbuildingscales.(CheckoutChapter7formuchmoreonscales.)

WhenmusicianstalkaboutthenotesA,B,C,D,E,F,andG,theymeanthenaturalnotes—specifically,thenotesthatcorrespondtothewhitekeysonakeyboard.Thewhitekeysofthekeyboardwereassignedthenaturalletternotes,whichturnouttobethenotesoftheCmajorscale,beginningwithC.However,becauseyou’redealingwithamusicalvocabularymadeupof12semitones,thekeyboardalsohasfiveblackkeys,repeatedoverandover,whichrepresentthesemitonesthatareskippedintheCscale.Theblackkeyswereaddedmuchlaterthantheoriginalwhitekeysinordertohelpbuildmoreperfectmusicalscalesonthepiano.

Movingawholesteponthepianoorguitarmeansyoumovetwohalfstepsfromyourstartingposition.Halfstepsandwholestepsareintervals,whichwediscussinChapter9.Knowingthedifferencebetweenwholestepsandhalfstepsisimportantwhenworkingwiththepatternsusedtobuildscalesandchords(coveredinChapters7and10,respectively).

Youalsoemployhalfstepswhenyoucomeacrossanaccidental,anotationusedtoraiseorloweranaturalnotepitch.Sowhenanoteissharped,youaddahalfsteptothenote;whenanoteisflatted,youremoveahalfstepfromthenote.

Needabitmoreinfo?Wegointomoredetailabouthalfsteps,wholesteps,andaccidentalsinthefollowingsections.

WorkingwithhalfstepsInWesternmusicalnotation,thesmallestdifferencebetweentwopitchesisthehalfstep,orsemitone.Usingthepianokeyboardasareference,ifyoupickakey,playit,andthenplaythekeythat’srightnexttoit(ontheleftorright)whetherthatkeyisblackorwhite,you’vemovedonehalfstepinpitch.SeeFigure6-8foranillustrationofthisprinciple.


Figure6-8:HalfstepsareidentifiedheretotheleftandrightoftheEkeyonthepiano.

Strictlyspeaking,musicalpitchisacontinuousspectrum,becauseit’sdeterminedbythefrequencyofvibration(seeChapter13).Therefore,manyothermicrotonalsoundsactuallyexistbetweenconsecutivehalfsteps.Westernmusicalnotationrecognizesonlythedivisionofpitchintohalfsteps.Incontrast,manyEasterninstruments,particularlysitarsandfretlessstringedinstruments,usequartertones.Quartertonesarepitcheslocatedhalfwaybetweeneachhalfstep.

AsyoucanseeinFigure6-8,ifyoustartoutplayinganEonthepiano,ahalfsteptotheleftbringsyoutoEflat/Dsharp.AhalfsteptotherightlandsyouonEsharp/Fnatural.

Halfstepsareeveneasierandmorestraightforwardontheguitar:Eachfretisahalfstep.Youjustmoveonefretuporonefretdownfromyourstartingpointonanyguitarstring,andthatmoveofonefretequalsonehalfstep.Movingdowntheneck(towardtheheadstockoftheguitar)flatsthenote(Figure6-9),whilemovinguptheneck(towardthebody)sharpsit(Figure6-10).


Figure6-9:GoingfromGnaturaltoGflat/Fsharpontheguitar.


Figure6-10:GoingfromGflat/FsharptoGnaturalontheguitar.

Whenamusicianreferstoanotebeingflatted,youknowyouneedtomoveonehalfsteptotheleftofthatnaturalnote;ifit’sbeingsharped,youknowtomoveonehalfsteptotheright.Everyblackkeyonapianohastwonames:Itcanbereferredtoastheflatofthewhitekeyonitsrightorthesharpofthewhitekeyonitsleft.Itdoesn’tmatterwhichwayit’snamed.Forexample,whileEflatandDsharparewrittenasdifferentnotes,theyhavethesamepitch,orsound.Noteswiththesamepitcharereferredtoasenharmonic.

TakingwholestepsFollowingthelogicthatahalfsteponthepianoorguitarisonekeyorfretawayfromthestartingpoint(seetheprecedingsection),itonlymakessensethatawholestepwouldbetwokeysorfretsawayfromthestartingpoint.

Say,forexample,thatyoustartonEonthekeyboard.OnewholesteptotheleftofEwouldbeD,asshowninFigure6-11.


Figure6-11:Movingonewholestep,ortwohalfsteps,totheleftofEonthepianobringsyoutoD.

Meanwhile,onewholesteptotherightofEwouldbeFsharp,asshowninFigure6-12.


Figure6-12:Movingonewholestep,ortwohalfsteps,totherightofEonthepianobringsyoutoFsharp.

Ontheguitar,awholestepisrepresentedbyamoveoftwofretsupordowntheneck.

ThedistancebetweentheconsecutivewhitepianokeysEandF,andBandC,

equalahalfstep,whereasthedistancebetweentheremainingwhitekeys(G-A,A-B,C-D,D-E,F-G)isawholestep.That’sbecausethepianoisdesignedaroundtheCscale.

InventorDr.RobertMoog’sThoughtsonKeyboardAlternatives

“Ithinksoundgenerationisamaturetechnology.Betweenanaloganddigitaltechnology,youcanmakejustaboutanysoundyoucanimaginecheaplyandeasily.Whatwedon’thavecheapandeasilyyetarereallygood,newplayerinterfaces—we’restillworkingwiththesameoldelectronicorganprinciple.Thesamekeyboardsthatwereputintoelectronicorgans60yearsagoarebeingusedtoday,andthereisverylittledifference.Theyfeelthesame,and,infact,theorgankeyboardsthatweredevelopedin1935feelbetterthanmostkeyboardsthataredesignedtoday.Akeyboardisjustthestartingpoint,especiallyifyouthinkofallthewaysthatpeopleliketomoveandpushandtouchwhenthey’replayingmusic.Ithinkthefieldiswideopenfordevelopingreallysophisticated,reallyhuman-orientedcontroldevices.

Buttheproblemforinstrumentdesignersisthatpeopledon’twanttogiveuptheirkeyboards.Millionsofpeopleknowhowtoplaythepiano.It’swhatthereiswhenyou’relearninghowtoplaymusic.Ifsomebodyweretostartoffattheageof30or40or50andlearnanewcontroldevice,they’dhavetopracticeasmuchastheydidwhentheywerelearninghowtoplaythepianowhentheywerekids.It’ssimilartotheDvorakkeyboard,whereyoucantype20or30percentfasterthanonaregularQwertykeyboard.Anybodycandoit,butveryfewpeopledoitbecauseittakesacertainamountoflearningwhenyou’reanadult.Yourmother’snotgoingtoteachyouhowtotypeonaDvorakkeyboard.Mostadultsalreadyhaveplentytodo,andthey’renotgoingtorelearnhowtotype.Sonewalternatecontrollersarelikethat,too.Designingthemisgoingtobehalfthejob—theotherhalfisgoingtobemusiciansdevelopingtechniqueonthosenewinterfaces.It’sgoingtotakedecades.”

ChangingpitchwithaccidentalsAccidentalsarenotationsusedtoraiseorloweranaturalnotepitchonthestaffbyahalfstep.Theyapplytothenotethroughoutameasureuntilyouseeanotheraccidental.Youcanusethesedifferenttypesofaccidentals:

SharpsFlatsDoublesharpsDoubleflatsNaturals

Formorespecificsontheseaccidentalsandwhattodowiththem,keepreading.

RaisingpitchwithsharpsAsharpisshowninFigure6-13.


Figure6-13:Asharplookslikeapound,ornumber,sign.

Asharpisplacedbeforeanoteonthestafftoindicatethatthenoteisahalfstephigher,asshowninFigure6-14.


Figure6-14:Asharp,theblackkeytotherightoftheA,isahalfstepupfromA.

Figure6-15showsasharpedE(theenharmonicofFnatural).EsharpisonehalfstepupinpitchfromE.


Figure6-15:EtoEsharp.

UsingflatstolowerpitchYoucanseewhataflatsymbollookslikeinFigure6-16.


Figure6-16:Aflatlooksabitlikealowercaseb.

Aflatdoesjusttheoppositeofasharp:Itlowersthenotebyahalfstep,asshowninFigure6-17.


Figure6-17:Aflat,theblackkeytotheleftoftheA,isahalfstepdownfromA.

Figure6-18showsaflattedE.EflatisonehalfstepdowninpitchfromE.


Figure6-18:EtoEflat.

DoublingpitchwithdoublesharpsandflatsEveryonceinawhile,you’llrunintoadoublesharporadoubleflat,whichareshowninFigure6-19.


Figure6-19:AdoublesharplookskindoflikeanX,whereasadoubleflatisjusttwoflatsinarow.

ThenotationontheleftinFigure6-19isadoublesharp,andtheoneontherightisadoubleflat.Thedoublesharpraisesthenaturalnotetwohalfsteps—oronewholestep—whereasthedoubleflatlowersthenotetwohalfsteps,oronewholestep.

CancellingsharpsandflatswithnaturalsYoumayhaveheardofsharpsandflats,butwhatisthenatural(picturedinFigure6-20)?


Figure6-20:Anaturalcancelsoutanalreadyestablishedsharporflat.

Whenyouseeanaturalsignnexttoanote,itmeansthatanysharporflatthat’salreadyineffect(eithergiveninthekeysignatureorinthesamemeasure;seeChapter8forinformationonkeysignatures)iscancelledfortherestofthemeasure.Inotherwords,you’resupposedtoplaythe“natural”versionofthenoteinsteadofwhateversharporflatwasineffect,evenifitwasadoublesharpordoubleflat.

FindingtheNotesonthePianoandtheGuitar

Sometimesyoujustcan’trememberwhichnoteiswhichwhenyou’replayingamusicalinstrument,especiallywhenyou’reabeginner.Butdon’tworry.Youcanusethefiguresinthissectionasahandyreferencewhenyoucan’tquiteremember.Wefocusonthenotesonthepianoandtheguitarbecausethoseinstrumentsarethetwomostcommonthatmusicianspickupontheirownwhenfirstlearningtoplaymusic.

LookingfornotesonthepianoFigure6-21showsalittlemorethanthreeoctaves’worthofthepianokeyboard.Thecorrespondingnaturalnotesonthegrandstaffarelabeledonthekeyboard.(Wediscussthegrandstaffinmoredetailearlierinthischapter.)Notealsothehandplacement,indicatedabovethekeyboard(RHforrighthand,andLHforlefthand).


Figure6-21:Thepianokeyboard,matchedupwiththenotesfromthegrandstaff.

PickingoutnotesontheguitarThetroublewithlayingouttheneckofaguitaragainstmusicalnotationisthatnotesrepeatthemselvesallalongtheneck,andhavingsomanyoptionsforplayingnotesindifferentwayscangetconfusing.Sowe’vebrokentheguitarneckintothreenonrepeatingsectionstocorrespondalongthenaturalnotesonthestaff,stoppingatthe12thfret(whichusuallyhastwodotsonit).The12thfretisalsoknownastheoctavemark,meaningit’sthesamenoteasthestringplayedopen,exceptoneoctavehigher.

Figures6-22through6-24showthenotesofthefirstthreefretsoftheguitar,thenthenextfive,andthenthenextfour.


Figure6-22:Thefirststringpositioniscalledopen,meaningnofretisdepressed.Thenotesofthefirstthreefretsoftheguitarneckareshownhere.


Figure6-23:Thenotesofthe4ththrough8thfrets.


Figure6-24:Thenotesofthe9ththrough12thfrets.

UsingMnemonicstoHelpRememberNotesAzillionsillywaysexisttoremembertheorderofthenotesalongthemusicalstaff.Infact,weprobablyhaveenoughtobuildanentirebookaround.Inthissection,weprovidejustafewtogetyougoing.Feelfreetocomeupwithyourownmnemonics(memoryhelpers)tohelpkeepthingsstraight.

Herearesomeeasywaystoremembertheorderofthenotesofthetrebleclefstafflines,startingatthefirstline,onE,andheadingupthroughG,B,D,andFonthetoplineofthestaff:

EveryGoodBoyDeservesFavorEveryGoodBoyDeservesFudgeEveryGoodBoyDoesFineEveryGoodBirdDoesFly

Thenotesinthespacesbetweenthetrebleclefstafflinesareeasytoremember.TheyspellthewordFACE,startingatthefirstspacenote,F,andheadinguptotheEinthetopspaceonthestaff.Everybodyusesthisone,andthere’sreallynoreasontotrytocomeupwithacomplicatedphrasewhenFACEisrightthere,staringyouinthe…well,yougetit.

Herearesomemnemonicsforthenotesonthebassclefstafflines,startingatthebottomnote,G,andheadinguptotheAatthetop:

GoBuyDonutsForAlGoodBoysDoFineAlwaysGreatBigDreamsForAmerica

Forthespacenotesbetweenthebassclefstafflines,justrememberanyoneofthefollowing:

AllCowsEatGrassAllCarsEatGasAlleyCatsEatGarbage

Chapter7

MasteringtheMajorandMinorScalesInThisChapter

Understandingmajorscalepatterns

Gettingahandleonminorscales

Accesstheaudiotracksatwww.dummies.com/go/musictheory

Toputitsimply,ascaleisanygroupofconsecutivenotesthatprovidesthematerialforpartorallofapieceofmusic.Wecouldwriteanentireencyclopediaonthedifferenttypesofscalesusedinmusicfromaroundtheworld,butbecausethisbookisprimarilyconcernedwiththeWesterntraditionofmusic,weconfineourdiscussioninthischaptertothetwomostfrequentlyusedscales:themajorandtheminor.

It’simpossibletooveremphasizejusthowimportantknowingyourscalesistoplayingmusic.Anditisn’tenoughtobeabletoplaythescalesbackandforthandupanddown,either.Inordertosuccessfullyimproviseorcompose,youneedtoknowhowtojumparoundonyourinstrumentandstilllandonalltherightnoteswithinthescale.

Sayyou’rejammingwithagroupofmusicians.Ifyouknowwhatkeytherestofthebandisplayingin,andyouknowallthenotesthatarewithinthatkey(scalesaredeterminedbykeys—youcanreadalotmoreaboutkeysandkeysignaturesinChapter8),it’simpossibletomessupsolongasyousticktothosenotes.Infact,youcannoodlealldayintheproperkeyandsoundlikearegularCarlosSantanaorLouisArmstrong.


FollowingMajor-ScalePatternsEventhougheverymajorscalecontainsadifferentsetofnotes,eachscaleisputtogetherexactlythesameway.Thespecificmajor-scalepatternofintervalsiswhatmakesthemmajorscales.

MajorscalesfollowtheintervalpatternofWWHWWWH,whichmeansWholestepWholestepHalfstepWholestepWholestepWholestepHalfstep.WediscusshalfstepsandwholestepsatlengthinChapter6,buthere’saquickrefresher:

Halfstep:Movingonepianokeytotheleftortheright,oroneguitarfretupordown.Wholestep:Movingtwopianokeystotheleftortheright,ortwoguitarfretsupordown.

Pitchwise,ahalf-stepisexactly ofanoctave,or1semitone.Awholestepisexactly

ofanoctave,or2semitones.

Eachoftheeightnotesinamajorscaleisassignedascaledegreeaccordingtotheorderitappearsinthescale:

1stnote:Tonic2ndnote:Supertonic3rdnote:Mediant4thnote:Subdominant5thnote:Dominant6thnote:Submediant7thnote:Leadingtone(orleadingnote)8thnote:Tonic

The1stand8thnotes,thetonics,determinethenameofthescale.(Scalesthatsharethesamestartingnotesarecalledparallelscales.Forexample,CmajorandCminorareparallelscales,becausetheybothstartonthesamenote:C.)Relativetothetonicnote,therestofthenotesinthescaleareusuallyattachedtothenumbers2through7(because1and8arealreadytakenbythetonic).Eachofthesenumbersrepresentsascaledegree,andtheirpatternofwholestepsandhalfstepsdeterminethekeyofthescale.

The1standthe8thnoteshavethesamenameherebecausethey’retheexactsamenote—atthe8thnote,thescalerepeatsitself.Youwon’thearamusiciantalkaboutthe8thdegreeofascale—instead,she’llrefertothe1stnoteasthetonic.

So,forexample,ifyou’replayingapieceofmusicinthekeyofCmajor,whichsequentiallyhasthenotesC,D,E,F,G,A,B,andCinit,andsomeoneasksyoutoplaythe4thand2ndnotesinthescales,youplayanFandaD.Andyoudothesamethingifthatpersonasksyoutoplaythesubdominantandthesupertonic.

Masteringscalesisallaboutrecognizingpatternsonaninstrument.Ifyoulookatapianokeyboardortheneckofaguitar,canyouseewherethe1,2,3,4,5,6,7,and8ofeachscalego?Ifyou’regivenascaleandaskedtoplaythesequence5-3-2-1-6-4-5-8,doyouknowwhatnotesyouwouldplay?Eventually,youwanttobeabletoansweryestothesequestionsforall12majorscales.Here’show:

Pictureeachscaleinyourheadandwhereit’slocatedonyourinstrument.Knowtheletternameandnumberofeachnoteineachscale.Beabletoplaysequencesofnoteswhengiventhekeyandnumber.

Onlywhenyoucandoallthreethingsforthe12majorscalescanyoustoppracticingyourscales.Inthefollowingsections,weexplainhowtoworkwithmajorscalesonthepianoandtheguitar,andwepointyoutowardaudiotracksofthemajorscales.

Themajorscale,orthediatonicscale,isthemostpopularscaleandtheonethat’stheeasiesttorecognizewhenplayed.Songslike“HappyBirthday”and“MaryHadaLittleLamb”arecomposedinthemajor/diatonicscale.

WorkingwithmajorscalesonpianoandguitarIfsomeoneweretoaskyoutoplaythescaleforCmajoronthepiano,youwouldputittogetherliketheoneinFigure7-1.


Figure7-1:TheCmajorscale,likeallmajorscales,followstheWWHWWWHpattern.

Noticethearrowpointingtothestepsinthefigure—everysinglemajorscaleyouworkwithfollowsthispattern,usingdifferentcombinationsofblackandwhitekeysonthepiano,dependingonthescale.

Toplayeachmajorscaleonthepiano,beginwiththepianokeythatisthenameofthescale.FortheAmajorscale,forexample,youbeginwiththeA.(Ifyouhaven’tmemorizedthenotesofthepianokeyboard,refertoChapter6.)Thenplaythemajorscalepattern:WWHWWWH.Thescaleendsonthesamenoteitbegan,onlyanoctavehigher.

Toseethemajorscaleforeverykey,refertoChapter8,whichillustrateskeysignaturesbyshowingthescaleonthestaffforeachkey.Tohearallthemajorscales,listentotheaudiotrackslistedintheupcomingsection“Listeningtothemajorscales.”

Playingscalesontheguitarisevensimplerthanplayingthemonthepiano.Guitarists

thinkoftheguitarneckasbeingbrokenupintoblocksoffourfrets,and,dependingonwhatkeyyouwanttoplayin,yourhandispositionedoverthatblockoffourfrets.Eachfour-fretblockcontainstwooctaves’worthofeverypitchwithinthatscale.

MajorscalesontheguitarfollowthepatternshowninFigure7-2,playingthenotesinthenumberordertheyappear.Remember:The8thnote(tonic)ofthefirstoctaveservesasthe1stnote(tonic)ofthesecondoctave.


Figure7-2:Thismajorscalepatternworksupanddowntheguitarneck.

Toplayeachscaleontheguitar,beginwiththecorrectfretonthefirststring(thetopstringasyouholdtheguitar,thelowEstring)toplaytheEmajorscale:

Openstring:E1stfret:F

2ndfret:F /G3rdfret:G4thfret:G /A5thfret:A6thfret:A /B7thfret:B8thfret:C9thfret:C /D10thfret:D11thfret:D /E212thfret:E13thfret:F

Toplaymajorscalesontheguitar,youjustmovethatpatternalongthenecktobuildwhatevermajorscaleyou’dlike.Youdeterminethekeybythefirstandlastnotesofthescale,soifsomeoneasksyoutoplayaCmajorscale,yousimplystartthescaleonthe8thfret.Noblackkeysorwhitekeystofoolwithhere—justthesamepatternrepeatedalongtheneck,overandover.(Toseethenotesonthefirst12fretsofaguitar,checkoutChapter6.)

Theactualpitchoftheguitarisoneoctave(12halfsteps)lowerthanthewrittenpitch.Thisdiscrepancyoccurssimplybecausemostsheetmusiciswrittenforpiano,sothenoteswouldfallbelowthestaffiftheywereaccuratelywrittenforguitar.Onthepiano,themiddleoctaveisthemostfrequentlyusedandisthereforecenteredonthegrandstaff.Ifcomposershadtowriteguitarpartsattheiractual-soundingpitch,theywouldhavetousetoomanyledgerlinesandthepartwouldbeconfusing.

Listeningtothemajorscales

ListentoAudioTracks1through15toheareachofthemajorscalesplayedonthepianoandguitar.NotethatFsharpandGflat,DflatandCsharp,andBandCflatareallenharmonicscales,orscalesthatsoundthesameasoneanother,butarenotateddifferently,asinBandCflatmajor.

AudioTrack Scale

1 Amajor

2 Aflatmajor

3 Bmajor

4 Bflatmajor

5 Cmajor

6 Cflatmajor

7 Csharpmajor

8 Dmajor

9 Dflatmajor

10 Emajor

11 Eflatmajor

12 Fmajor

13 Fsharpmajor

14 Gmajor

15 Gflatmajor

DiscoveringAllThatMinorScalePatternsHavetoOffer

Whenyouhearthetermminorscales,youmaybeledtobelievethatthissetofscalesismuchlessimportantthanthegrandcollectionofmajorscalesthatweintroduceearlierinthischapter.Oryoumaythinktheminorscalesareonlyforsad,sappysongs.Butthetruthisthatthearrangementsandtones(ornotesounds)availableintheminorscales—divided,accordingtocomposition,intothenatural,harmonic,andmelodicminorscales—canbemuchmoreflexibleforacomposertousethanthemajorscalesalone.

Eventhougheverytypeofminorscalecontainsadifferentsetofnotes,eachtypeofscaleisputtogetherinaspecificway.Thesespecificpatternsofintervalsarewhatputtheminorscalesintotheirlittleniche.Theminorscaledegreesallhavethesamenamesastheonesinmajor,exceptthe7thdegree,whichiscalledthesubtonic.

Eachoftheeightnotesinaminorscalehasaname:

1stnote:Tonic2ndnote:Supertonic3rdnote:Mediant4thnote:Subdominant5thnote:Dominant6thnote:Submediant7thnote:Subtonic8thnote:Tonic

Intheharmonicandmelodicminorscales,the7thdegreeiscalledtheleadingtone.Inthemelodicminorscale,the6thdegreeiscalledthesubmediant.

Inthefollowingsections,wediscussthenatural,harmonic,andmelodicminorscalesandhowtoplaythemonthepianoandtheguitar.

Playingnaturalminorscalesonpianoandguitar

NaturalminorscalesfollowtheintervalpatternofWHWWHWW,which

translatesintoWholestepHalfstepWholestepWholestepHalfstepWholestepWholestep.Thefirstnote(andlast)inthescaledeterminesthescalename.

Anaturalminorscaleistakenfromthemajorscaleofthesamename,butwiththe3rd,6th,and7thdegreesloweredbyonehalfstep.So,forinstance,ifsomeoneasksyoutoplaythescaleforAnaturalminoronthepiano,youputittogetherasshowninFigure7-3.


Figure7-3:TheAnaturalminorscaleonthepiano.

Thesamepatternalsoappliesforeachnoteupanddowntheguitarneck.NaturalminorscalesontheguitarfollowthepatternshowninFigure7-4.Playthenotesinthenumberordershowninthefigure.Yourfirstnoteisindicatedbythe1shownonthefirstEstring.


Figure7-4:Playingtheminorscaleontheguitar.

Justaswithmajorscales,toplaynaturalminorscalesontheguitar,yousimplymovetheFigure7-4patternalongtheneckoftheguitartobuildwhateverminorscaleyou’dlike.Whatevernoteyoustartwithonthetop(lowE)stringisthetonicandthereforenamesthescale.IfsomeoneasksyoutoplayanAminorscaleontheguitar,forexample,youplaythepatternshowninFigure7-5.


Figure7-5:TheAnaturalminorscaleontheguitar.

HavingfunwithharmonicminorscalesonpianoandguitarTheharmonicminorscaleisavariationofthenaturalminorscale(whichwediscussintheprecedingsection).Itoccurswhenthe7thnoteofthenaturalminorscaleisraisedbyahalfstep.Thestepisnotraisedinthekeysignature;instead,it’sraisedthroughtheuseofaccidentals(sharps,doublesharps,ornaturals).YoucanreadaboutaccidentalsinChapter6.

ToplaythescaleforAharmonicminoronthepiano,youputthescaletogetheras

showninFigure7-6.Noticehowthepianoscalechangeswhenyouaddahalfsteptothe7thscaledegree.


Figure7-6:AnAharmonicminorscaleonthepiano.

Whenyou’rewritingmusicandyouwanttouseaharmonicscale,writeitoutusingthenaturalminorkeyfirst(seeprecedingsection),andthengobackandaddtheaccidentalthatraisesthe7thdegreeupahalfstep.

Playingharmonicminorscalesontheguitarissimple.YoujustpositionthepatternshowninFigure7-7overtheroot(tonic)positionthatyouwanttoplayin.Moveitaroundtoadifferentroottoplaythescaleforthatnote.


Figure7-7:Noticehowtheguitarpatternchangeswhenyouaddahalfsteptothe7thscaledegree.

Asalways,thekeyisdeterminedbythefirstandlastnotesofthescale,soifsomeoneasksyoutoplayanAharmonicminorscaleontheguitar,youplaywhat’sshowninFigure7-8.


Figure7-8:AnAharmonicminorscaleontheguitar.

MakinggreatmusicwithmelodicminorscalesonpianoandguitarThemelodicminorscaleisderivedfromthenaturalminorscale(seetheearliersection“Playingnaturalminorscalesonpianoandguitar”fordetails).Inthemelodicminorscale,the6thand7thnotesofthenaturalminorscaleareeachraisedbyonehalfstepwhengoingupthescale.However,keepinmindthattheyreturntothenaturalminorwhengoingdownthescale.

Thisscaleisatrickyone,sowe’regoingtoreiterate:Whileyou’regoingupinpitchwhenplayingapiece,youraisethe6thand7thdegreesofthenaturalminorscaleahalfstep,butduringpartsofthesamepiecewherethepitchgoesdown,youplaythenotesaccordingtothenaturalminorscale.Scalesinwhichthe6thand7thdegreesareflatinnaturalminorrequirenaturalstoraisethosetwodegrees.

ToplayanAmelodicminorscaleascending(goingup)thepiano,youplaywhat’sshowninFigure7-9.Noticehowthepianoscalechangeswhenyouaddahalfsteptoboththe6thand7thdegrees.


Figure7-9:AnAmelodicminorscalegoingupthepiano.

Whenwritingmusicinthemelodicminorscale,composerswriteoutthesongusingthenaturalminorpattern,andthentheyaddtheaccidentalsthatmodifyanyascending6thand7thnotesafterward.

Thewonderfulthingabouttheguitaristhatyouhavetomemorizeonlyonepatternforeachtypeofscaleandyou’reset.ToplaytheascendingAmelodicminorscaleonguitar,playthepatternasshowninFigure7-10.ToplayanAmelodicminorscaleascendingontheguitar,youplayitasshowninFigure7-11.


Figure7-10:Noticehowthepatternchangeswhenyouaddahalfsteptothe6thand7thdegreesofthescale.


Figure7-11:AnAmelodicminorascendingscaleontheguitar.

And,ofcourse,forthedescendingnotesonboththepianoandguitaryoureverttoAnaturalminor.

Listeningtotheminorscales

ListentoAudioTracks16through60toheareachoftheminorscalesplayedonpianoandguitar.

AudioTrack Scale

16 Anaturalminor

17 Aharmonicminor

18 Amelodicminor

19 Aflatnaturalminor

20 Aflatharmonicminor

21 Aflatmelodicminor

22 Asharpnaturalminor

23 Asharpharmonicminor

24 Asharpmelodicminor

25 Bnaturalminor

26 Bharmonicminor

27 Bmelodicminor

28 Bflatnaturalminor

29 Bflatharmonicminor

30 Bflatmelodicminor

31 Cnaturalminor

32 Charmonicminor

33 Cmelodicminor

34 Csharpnaturalminor

35 Csharpharmonicminor

36 Csharpmelodicminor

37 Dnaturalminor

38 Dharmonicminor

39 Dmelodicminor

40 Dsharpnaturalminor

41 Dsharpharmonicminor

42 Dsharpmelodicminor

43 Enaturalminor

44 Eharmonicminor

45 Emelodicminor

46 Eflatnaturalminor

47 Eflatharmonicminor

48 Eflatmelodicminor

49 Fnaturalminor

50 Fharmonicminor

51 Fmelodicminor

52 Fsharpnaturalminor

53 Fsharpharmonicminor

54 Fsharpmelodicminor

55 Gnaturalminor

56 Gharmonicminor

57 Gmelodicminor

58 Gsharpnaturalminor

59 Gsharpharmonicminor

60 Gsharpmelodicminor

Chapter8

KeySignaturesandtheCircleofFifthsInThisChapter

InvestigatingtheCircleofFifths

Examiningthemajorandminorkeys

Recognizingthemajorandminorkeysignaturesonsight

Atthebeginningofmostpiecesofwrittenmusic,youfindagroupofsharpsorflatslocateddirectlytotherightofthetimesignature.Thisgroupofsymbolsiscalledthekeysignature,andittellsyouinwhatkeythesongiswritten.

Whenyouknowasong’skey,orthescalethatthesetofnotesusedtocomposethesongyou’replayingcomesfrom,youmayfindreadingthemusiceasier.Youcananticipatethenotesonthesheetmusicbasedonyourknowledgeofthescalesandthenotesinthosekeys.Also,inasituationwhereyou’replayingwithothermusicians,ifyouknowthekeyyou’replayinginandcananticipatethechords,youcanguesswherethemelodyofthesongisgoing.It’salmostlikeknowingwhatwordisgoingtocomenext—oratleastwhatlimitedselectionofwordscouldcomenext—tofitintoasentence.

Inthischapter,youreadaboutPythagoras’sCircleofFifthsandhowtouseittoreadkeysignatures.Youalsofindoutallaboutkeysignaturesandhowtorecognizethemonsight.Finally,weroundoutthechapterwithadiscussionaboutmajorandminorkeysignaturesandtheirrelativeminorsandmajors.

UnderstandingtheCircleofFifthsandRecognizingMajorKeySignatures

InthesixthcenturyB.C.,theGreekscholarandphilosopherPythagorasdecidedtotryandmakethingseasierforeveryonebystandardizing,oratleastdissecting,musicaltuning.Hehadalreadydiscoveredtherelationshipbetweenpitchfrequenciesandlengthsofstringandhaddefinedwhatanoctavewas,sohefiguredstandardizingtuningwasthenextlogicalstep.

Hedividedacircleinto12equalsections,likeaclock.TheresultofhisexperimentationeventuallybecameknownastheCircleofFifths,whichisstillusedtoday.Eachofthe12pointsaroundthecirclewasassignedapitchvalue,whichroughlycorrespondstothepresentsystemofanoctavewith12halfsteps.WesternmusictheoristshavesinceupdatedPythagoras’sCircleofFifthstowhatyouseeinFigure8-1.


Figure8-1:TheCircleofFifthsshowstherelationshipbetweenmajorkeysandtheirrelativeminors.

Inmathematicalterms,theunitofmeasureusedinthecircleiscents,with1,200centsequaltooneoctave.Eachhalfstep,then,isbrokenupinto100cents.

ThecreationanduseoftheCircleofFifthsistheveryfoundationofmodernWesternmusictheory,whichiswhywetalkaboutitsomuchinthisbook.Figure8-2showsaslightlydifferentversionoftheCircleofFifthsthanisshowninFigure8-1.Theformerfigurecanbeusedtohelpyoulearntoreadkeysignaturesonsightbycountingthesharpsorflatsinatimesignature;yougetthescooponhowtodosointhefollowingsections.


Figure8-2:TheCircleofFifthstellsyouhowmanysharpsandflatsareinthekeysignaturesandscalesofeachkey.

Eachofthecircle’s12stopsisactuallythefifthpitchinthescaleofthe

precedingstop,whichiswhyit’scalledtheCircleofFifths.Forexample,thefifthpitch,orthedominantnote,oftheCscaleisG.IfyoulookattheCircleofFifthsinFigure8-2,youcanseethatGisthenextlettertotherightofC.Ifyoukeepgoingclockwise,youseethatthedominantnoteoftheGscale,D,isthenextstop,andsoonaroundthecircle.(YoucanfindfullcoverageofscalesinChapter7.)

Alongwithbeingyourbestfriendfordecipheringkeysignaturesonsight,theCircleofFifthsisjustasessentialinwritingmusic,becauseitscleverdesignishelpfulincomposingandharmonizingmelodies,buildingchords,andmovingtodifferentkeyswithinacomposition.

Wecan’temphasizeenoughhowusefulknowingtheCircleofFifthsis.It’susefulasacomposer,asaperformer,andasastudentofmusictheory.Allwecandoissayitoverandoverandover:TheCircleofFifths—memorizeitanduseit.

TheCircleofFifthshelpsyoufigureoutwhichsharpsandflatsoccurinthedifferentkeys.Thenameofthekeybeingplayedistheletterontheoutsideofthecircle.Inthefollowingsections,besuretonoticethattheorderofsharpsandflatsgiveninthemnemonicsareexactlytheorderinwhichtheyarewritteninkeysignatures.

Sharps:FatherCharlesGoesDownandEndsBattleTofigureouthowmanysharpsareineachkey,countclockwisefromCatthetopofthecircle.Cmajorhasanumbervalueof0,soithasnosharps.Ghasavalueof1,soithasonesharp.WhenyouplaytheGmajorscaleonthepiano,youplayonlywhitekeysuntilyoucometotheseventhintervalandlandonthatonesharp:Fsharp,inthiscase.Dhastwosharps,Ahasthree,andsoonaroundthecircle.Thenumbervaluebyeachletterontheright-handsideofthecirclerepresentshowmanysharpsareinthatkey,whichisdeterminedbythatkey’sscale.SeeFigure8-3toseethesharpsgoing“up.”


Figure8-3:Thesharpsarearrangedinthekeysignaturegoing“up.”

Thesharpsalwaysappearinaspecificorderineverykey:F,C,G,D,A,E,B.YoucaneasilyrememberthispatternofsharpsbyusingthemnemonicFatherCharlesGoesDownAndEndsBattle.

Forexample,ifyou’replayingasonginthekeyofBmajor,youknowfromtheCircleofFifthsthatBmajorhasfivesharps.AndyouknowfromtheFatherCharlesmnemonicthatthosesharpsareFsharp,Csharp,Gsharp,Dsharp,andAsharp,becausethesharpsarealwaysinthatorder.Ifyou’replayingthekeyofDmajor,whichhastwosharps,youknowthosesharpsareFsharpandCsharpbecauseFatherCharles….Ifyouhaveabettermnemonicthantheonewesuggest,feelfreetouseit.

Flats:BattleEndsandDownGoesCharles’sFatherForthemajorscalesandkeyswithflats,youmovecounterclockwisearoundtheCircleofFifths,startingatC,whichhasanumbervalueof0.Therefore,thekeyofFmajorhasoneflat,thekeyofBflatmajorhastwoflats,andsoon.Figure8-4showstheflatsgoing“down.”


Figure8-4:Theflatsarearrangedinthekeysignaturegoing“down.”

Likethesharps,theflatsappearinaspecificorderineverykey:B,E,A,D,G,C,F.ThemnemonicwesuggesthereisBattleEndsAndDownGoesCharles’sFather,whichis,asyoulikelynotice,theexactreverseoftheorderofsharpsinthecircle(formore,seetheprecedingsectiononsharps).It’seasytorememberthatthefirstflatisalwaysBflatbecausetheflatsignitselflookskindoflikealowercaseb,whichisactuallywhatitoriginallywas.

So,Gflat,forexample,whichissixstepsawayfromCmajoronthecircle,hassixflatsinitsscale,andtheyareBflat,Eflat,Aflat,Dflat,Gflat,andCflat.ThekeyofBflat,whichistwostepsawayfromCatthetopofthecircle,hasBflatandEflatinitskey.

FindingMinorKeySignaturesandRelativeMinors

TheCircleofFifthsworksthesamewayforminorkeysasitdoesformajorkeys.TheminorkeysarerepresentedbythelowercaselettersinsidetheCircleofFifthsshowninFigure8-1.

Theminorkeysontheinsideofthecirclearetherelativeminorsofthemajorkeysontheoutsideofthecircle.Therelativeminoranditsmajorkeyhavethesamekeysignature.Theonlydifferenceisthattherelativeminor’sscalestartsonadifferenttonic,orfirstnote.Thetonic,orstartingpoint,ofarelativeminorisaminorthird—orthreehalfsteps—lowerthanitsrelativemajorkey.

Forexample,Cmajor’srelativeminorisAminor(refertoFigure8-1,theCircleofFifthswhereCisontheoutsideandAisontheinsideofthecircle).Aminor’stonicnoteisA,whichisthreehalfstepstotheleftofConthepianoorthreefretstowardtheheadoftheneckontheguitar.

EventheFatherCharlesandBattleEndsmnemonicsthatwedescribeearlierinthischapterstaythesamewhenyou’redealingwithminorkeys.Nodifferenceexistsinthekeysignaturebetweenamajorkeyanditsrelativeminor.

Onsheetmusic,therelativeminoristhenoteonefulllineorspacebelowthemajorkeynote.Cisinthethirdspaceonthetrebleclef,andA,itsrelativeminor,isinthesecondspace,belowit.

Onthepianoorguitar,amajorchordanditsrelativeminorgotogetherlikebreadandbutter.Many,manysongsusethischordprogressionbecauseitjustsoundsgood.(YoucanfindmoreaboutchordsandchordprogressionsinChapters10and11.)

VisualizingtheKeySignaturesWhetherthekeysignaturesarenewtoyouoryou’reoldchums,rehearsingneverhurtanyone.Inthefollowingsections,weprovidearundownofthemajorandnaturalminorkeysignaturesandacoupleofoctaves’worthofnotesinthosekeys,arrangedinascale.BecausethischapterfocusesontheCircleofFifths,weorderthekeysignaturesfollowingthecircle,asopposedtoalphabeticalorder.WehopethatgoingoverthesekeysignaturesfurthercementsthemandtheCircleofFifthsintoyourmusicalprowess.

Don’tbethrownbythewordnaturalwhenweuseittodescribeminorkeysignaturesinthissection.AsweexplaininChapter7,morethanonekindofminorexists.

CmajorandAnaturalminorFigure8-5showstheCmajorkeysignature,andFigure8-6showstheAnaturalminorkeysignature,C’srelativenaturalminor.


Figure8-5:TheCmajorkeysignatureandscale.


Figure8-6:TheAnaturalminorkeysignatureandscale.

Asyoucansee,theCmajorandtheAnaturalminorhavethesamekeysignature(thatis,nosharpsandnoflats)andthesamenotesinthescalebecauseAistherelative

naturalminorofC.TheonlydifferenceisthattheCmajorscalestartsonC,whereastheAnaturalminorscalestartsonA.

GmajorandEnaturalminorFigure8-7showstheGmajorkeysignature,andFigure8-8showstheEnaturalminorkeysignature,G’srelativenaturalminor.


Figure8-7:TheGmajorkeysignatureandscale.


Figure8-8:TheEnaturalminorkeysignatureandscale.

You’venowaddedonesharp(F)tothekeysignature.Thenextstop(D)hastwo(FandC,becauseFatherCharles…),andyoukeepaddingonemoresharpuntilyougettothebottomoftheCircleofFifths.

DmajorandBnaturalminorFigure8-9showstheDmajorkeysignature,andFigure8-10showstheBnaturalminorkeysignature,D’srelativenaturalminor.


Figure8-9:TheDmajorkeysignatureandscale.


Figure8-10:TheBnaturalminorkeysignatureandscale.

AmajorandFsharpnaturalminorFigure8-11showstheAmajorkeysignature,andFigure8-12showstheFsharpnaturalminorkeysignature,A’srelativenaturalminor.


Figure8-11:TheAmajorkeysignatureandscale.


Figure8-12:TheFsharpnaturalminorkeysignatureandscale.

EmajorandCsharpnaturalminorFigure8-13showstheEmajorkeysignature,andFigure8-14showstheCsharpnaturalminorkeysignature,E’srelativenaturalminor.


Figure8-13:TheEmajorkeysignatureandscale.


Figure8-14:TheCsharpnaturalminorkeysignatureandscale.

B/CflatmajorandGsharp/AflatnaturalminorFigure8-15showstheBmajorkeysignatureandCflatmajorkeysignature.Figure8-16showstheGsharpnaturalminorkeysignatureandtheAflatnaturalminorkeysignature.


Figure8-15:TheBmajorandCflatmajorkeysignaturesandscales.


Figure8-16:TheGsharpnaturalminorandAflatnaturalminorkeysignaturesandscales.

Confusedbythedoublenaminghere?Takealookatakeyboard,andyouseethatablackkeydoesn’texistforCflat.Instead,youseeawhitekey:B.CflatandBareenharmonicequivalentsofoneanother,meaningthey’rethesamebutwithdifferentnames.AllthenotesinthekeyofBmajorandthekeyofCflatmajorsoundexactlythesame—theyjustusedifferentmusicalnotation.ThesamegoesforGsharpnaturalminorandAflatnaturalminor—samenotes,justdifferentnotation.

Fsharp/GflatmajorandDsharp/EflatnaturalminorIntheprevioussections,youmayhavenoticedthatwitheachstopontheCircleofFifths,onesharpisaddedtothekeysignature.Fromthispointon,thenumberofflatsinthekeysignaturewillbegoingdownbyoneuntilreturningtothe12o’clock(Cmajor/Anaturalminor)position.

Figure8-17showstheFsharpmajorkeysignatureandtheGflatmajorkeysignature.Figure8-18showstheDsharpnaturalminorkeysignatureandtheEflatnaturalminorkeysignature.Moreenharmonicequivalents(seeprecedingsection)!


Figure8-17:TheFsharpmajorandGflatmajorkeysignaturesandscales.


Figure8-18:TheDsharpnaturalminorandEflatnaturalminorkeysignaturesandscales.

Csharpmajor/DflatandAsharp/BflatnaturalminorFigure8-19showstheCsharpmajorkeysignatureandtheDflatmajorkeysignature.Figure8-20showstheAsharpnaturalminorkeysignatureandtheBflatnaturalminorkeysignature.


Figure8-19:TheCsharpmajorandDflatmajorkeysignaturesandscales.


Figure8-20:TheAsharpnaturalminorandBflatnaturalminorkeysignaturesandscales.

Thesearethelastoftheenharmonicequivalentkeysignaturesyouhavetoremember.Wepromise.Also,thesearethelastofthekeyswithsharpsintheirsignatures.Intheremainingsections,you’reworkingwithflatsaloneasyoucontinuegoinguptheleftsideoftheCircleofFifths.

AflatmajorandFnaturalminorFigure8-21showstheAflatmajorkeysignatureandtheFnaturalminorkeysignature,whichisAflat’srelativenaturalminor.


Figure8-21:TheAflatmajorandFnaturalminorkeysignaturesandscales.

EflatmajorandCnaturalminor

Figure8-22showstheEflatmajorkeysignatureandtheCnaturalminorkeysignature,whichisEflat’srelativenaturalminor.


Figure8-22:TheEflatmajorandCnaturalminorkeysignaturesandscales.

BflatmajorandGnaturalminorFigure8-23showstheBflatmajorkeysignatureandtheGnaturalminorkeysignature,whichisBflat’srelativenaturalminor.


Figure8-23:TheBflatmajorandGnaturalminorkeysignaturesandscales.

FmajorandDnaturalminorFigure8-24showstheFmajorkeysignatureandtheDnaturalminorkeysignature,whichisFmajor’srelativenaturalminor.


Figure8-24:TheFmajorandDnaturalminorkeysignaturesandscales.

Chapter9

Intervals:TheDistanceBetweenPitchesInThisChapter

Understandingthedifferentkindsofintervals

Checkingoutintervalsfromunisonstooctaves

Creatingyourownintervals

Seeinghowintervalsrelatetothemajorscale

Diggingdeeperintocompoundintervals


Thedistancebetweentwomusicalpitchesiscalledaninterval.Evenifyou’veneverheardthewordintervalusedinrelationtomusicbefore,ifyou’velistenedtomusic,you’veheardhowintervalsworkwithoneanother.Ifyou’veeverplayedmusic,orevenjustaccidentallysetacoffeecupdownonapianokeyboardhardenoughtomakeacoupleofjanglynotessoundout,you’veworkedwithintervals.Scalesandchordsarebothbuiltfromintervals.Musicgetsitsrichnessfromintervals.Thischapterreviewsthetypesofintervalsmostcommonlyusedinmusicanddiscusseshowintervalsareusedinbuildingscalesandchords.


BreakingDownHarmonicandMelodicIntervals

Thefollowingtwotypesofintervalsexist:

Aharmonicintervaliswhatyougetwhenyouplaytwonotesatthesametime,asshowninFigure9-1.Amelodicintervaliswhatyougetwhenyouplaytwonotesseparatelyintime,oneaftertheother,asshowninFigure9-2.


Figure9-1:Aharmonicintervalistwonotesplayedsimultaneously.


Figure9-2:Amelodicintervalistwonotesplayedoneaftertheother.

Theidentityofaninterval,andthisgoesforbothharmonicandmelodicintervals,isdeterminedbytwothings:

QuantityQuality

Weexplainwhatwemeanbyeachoftheseinthefollowingsections.

Quantity:CountinglinesandspacesThefirststepinnaminganintervalisfindingthedistancebetweenthenotesasthey’rewrittenonthestaff.Thequantity,ornumbersize,ofanintervalisbasedonthenumber

oflinesandspacescontainedbytheintervalonthemusicstaff.Musiciansandcomposersusedifferentnamestoindicatethequantityofintervals:

Unison(orprime)SecondThirdFourthFifthSixthSeventhOctave

Youdetermineaninterval’squantitybysimplyaddingupthelinesandspacesincludedintheinterval.Youmustcounteverylineandeveryspacebetweenthenotesaswellasthelinesorspacesthatthenotesareon.Accidentalsdon’tmatterwhencountingintervalquantity.

TakealookatFigure9-3foranexampleofhoweasyitistodetermineaninterval’squantity.Ifyoustartoneitherthetoporbottomnoteandcountallthelinesandspacescontainedintheintervalinthefigure,includingthelinesorspacesthatcontainbothnotes,youendupwiththenumberfive.Therefore,theintervalinFigure9-3hasthequantity,ornumbersize,offive,orafifth.Becausethenotesarewrittentogethertobeplayedatthesametime,it’saharmonicfifth.


Figure9-3:Thefivelinesandspacesinthisinterval’stotalquantityindicatethisintervalisafifth.

Figure9-4showsamelodicsecond.Notethatthesharpaccidental(the )ontheFdoesabsolutelynothingtothequantityoftheinterval.Intervalquantityisonlyamatterofcountingthelinesandspaces.(YoucanreadaboutaccidentalsinChapter6.)


Figure9-4:ThefactthatthefirstnoteisFsharpdoesn’taffectthequantityoftheinterval.

Figure9-5showsintervalquantitiesfromunison(thetwonotesarethesame)tooctave(thetwonotesareexactlyanoctaveapart)andalltheintervalsinbetween.Sharpsandflatsarethrowninforfun,butremember,theydon’tmatterwhenitcomestointervalquantity.


Figure9-5:Melodicintervalsinorderfromlefttoright:unison,second,third,fourth,fifth,sixth,seventh,andoctave.

Whatifanintervalspansmorethanoneoctave?Inthatcase,it’scalledacompoundinterval.Aswithallintervalquantities,youjustcountthelinesandspacesforacompoundinterval.TheexampleshowninFigure9-6hasthequantityoftenandisthereforecalledatenth.(Wediscusscompoundintervalsinmoredetaillaterinthischapter.)


Figure9-6:Acompoundintervalwithatotalquantityoftenandiscalledatenth.

Quality:ConsideringhalfstepsIntervalqualityisbasedonthenumberofhalfstepsfromonenotetoanother.Unlikeinintervalquantity(seetheprevioussection),accidentals(sharpsandflats),whichraiseorlowerapitchbyahalfstep,domatterinintervalquality.(SeeChapter6fordetailsonhalfstepsandaccidentals.)Intervalqualitygivesanintervalitsdistinctsound.

EachoftheintervalsshowninFigure9-7hasexactlythesamequantity,buttheysound

differentbecauseeachonehasadifferentquality.


Figure9-7:Alltheseintervalsarefifths,butthevariousqualitiesofthefifthsmakethemsounddifferent.

PlayAudioTrack61tohearthedifferencesbetweentheintervalsthathavethesamequantity(fifth)butdifferentqualities.

Thetermsusedtodescribequality,andtheirabbreviations,areasfollows:

Major(M):ContainstwohalfstepsbetweennotesMinor(m):Containsahalfsteplessthanamajorinterval,oronehalfstepbetweennotesPerfect(P):Referstotheharmonicqualityofunisons,octaves,fourths,andfifths(whichwedescribelaterinthischapter)Diminished(dimord):ContainsahalfsteplessthanaminororperfectintervalAugmented(augorA):Containsahalfstepmorethanamajororperfectinterval

Namingintervals

Everyintervalgetsitsfullnamefromthecombinationofboththequantityandthequalityoftheinterval.Forexample,youmayencounteramajorthirdoraperfectfifth.Herearethepossiblecombinationsthatyouusewhendescribingintervals:

Perfect(P)canonlybeusedwithunisons,fourths,fifths,andoctaves.Major(M)andminor(m)canonlybeusedwithseconds,thirds,sixths,andsevenths(whichwediscusslaterinthischapter).Diminished(dim)canbeusedwithanyinterval,withtheexceptionofunisons.Augmented(aug)canbeusedwithanyinterval.

LookingatUnisons,Octaves,Fourths,andFifths

Unisons,octaves,fourths,andfifthssharethesamecharacteristicsinthattheyallusethetermsperfect,augmented,ordiminishedtoidentifytheirquality.(Seetheearliersection“Quality:Consideringhalfsteps”formoreinformation.)

PerfectunisonsAperfectmelodicunisonispossiblytheeasiestmoveyoucanmakeonaninstrument(exceptforarest,ofcourse).Youjustpressakey,pluck,orblowthesamenotetwice.Youcanplayunisonsonmoststringedinstrumentsbecausethesamenoteoccursmorethanonceontheseinstruments,suchasontheguitar(thefifthfretonthelowEstringisthesameastheopenAstring,forexample).

Inmusicwrittenformultipleinstruments,aperfectharmonicunisonoccurswhentwo(ormore)peopleplayexactlythesamenote,intheexactsamemanner,ontwodifferentinstruments.

AugmentedunisonsTomakeaperfectunisonaugmented,youaddonehalfstepbetweenthenotes.Youcanaltereitherofthenotesinthepairtoincreasethedistancebetweenthenotesbyahalfstep.

TheintervalfromBflattoBiscalledanaugmentedunison(oraugmentedprime)—unisonbecausethenotenamesarethesame(bothBs)andaugmentedbecausetheintervalisonehalfstepgreaterthanaperfectunison.

Adiminishedunisondoesn’texist,becausenomatterhowyouchangetheunisonswithaccidentals,you’restilladdinghalfstepstothetotalinterval.

OctavesWhenyouhavetwonoteswithanintervalquantityofeightlinesandspaces,youhaveanoctave.Aperfectoctaveisalotlikeaperfectunison(seetheearliersection“Perfectunisons”)inthatthesamenote(onapiano,itwouldbethesamewhiteorblackkeyonthekeyboard)isbeingplayed.Theonlydifferenceisthatthetwonotesareseparatedby12halfsteps,includingthestartingnote,eitheraboveorbelowthestartingpoint.

TheperfectmelodicoctaveinFigure9-8has12halfstepsbetweenthenotes.


Figure9-8:ThesetwoEnotesareaperfectoctave.

Tomakeaperfectoctaveaugmented,youincreasethedistancebetweenthenotesbyonemorehalfstep.Figure9-9showsanaugmentedoctavefromEtoEsharp.Itwasaugmentedbyraisingthetopnoteahalfstepsothat13halfstepscomebetweenthefirstnoteandthelast.YoucouldalsomakeanaugmentedoctavebyloweringthebottomEnoteahalfsteptoEflat.


Figure9-9:Thesetwonotesmakeanaugmentedoctave.

Tomakethesameoctavediminished,youdecreasethedistancebetweenthenotesbyonehalfstep.Forexample,Figure9-10illustratesloweringthetopnoteahalfstepsothatonly11halfstepscomebetweenthefirstnoteandthelast.Youcouldalsoraisethebottomnotebyahalfsteptomakeanotherdiminishedoctave.


Figure9-10:Thesetwonotesmakeadiminishedoctave.

FourthsFourthsarepairsofnotesseparatedbyfourlinesandspaces.Allfourthsareperfectinquality,containingfivehalfstepsbetweennotes—exceptforthefourthfromFnaturaltoBnatural,whichcontainssixhalfsteps(makingitanaugmentedfourth).ComparethenotepairsinFigure9-11onthekeyboardtoseewhatwemean.


Figure9-11:Fourthsasseenonthestaffwiththespecial(augmented)caseoftheFnaturalandtheBnaturalcircled.

Figure9-12showstheconnectionbetweeneachfourthonakeyboard.Notethatunliketherest,theFnaturalandBnaturalrequiresixhalfsteps.


Figure9-12:Onthekeyboard,everynaturalfourthisaperfectfourth(exceptfortheintervalbetweenFnaturalandBnatural).

Becauseaugmentedfourthsareahalfsteplargerthanperfectfourths,youcancreateaperfectfourthbetweenthenotesFnaturalandBnaturalbyeitherraisingthebottomnotetoFsharporloweringthetopnotetoBflat.

Ifthenaturalfourthisperfect,addingthesameaccidental(eitherasharporaflat)tobothnotesdoesn’tchangetheinterval’squality.Itstaysaperfectfourth.Thesamenumberofhalfsteps(five)occursbetweenDnaturalandGnaturalthatoccursbetweenDsharpandGsharp,orDflatandGflat,asshowninFigures9-13and9-14.Ifonenotechangesbuttheotherdoesn’t,thequalityoftheintervaldoeschange.


Figure9-13:Addingaccidentalstobothnotesinaperfectfourthintervaldoesn’tchangeitfrombeingaperfectfourth.


Figure9-14:YoucanseeonakeyboardthesameprincipleshowninFigure9-13.

FifthsFifthsarepairsofnotesseparatedbyfivelinesandspaces(asshowninFigure9-15).

Fifthsareprettyeasytorecognizeinnotation,becausethey’retwonotesthatareexactlytwolinesortwospacesapart.


Figure9-15:Fifthshaveanintervalquantityoffivelinesandspaces.

Allfifthsareperfectfifths,meaningthattheintervalcontainssevenhalfsteps.However,asyoumayhaveguessed,theintervalbetweenBtoFisadiminishedfifth,whichturnsouttohavethesamesoundasanaugmentedfourth.Onlysixhalfstepsoccurbetweenthosetwonoteswhetheryou’regoingfromFnaturaltoBnaturalorBnaturaltoFnatural.

YoucancreateaperfectfifthbetweenFnaturalandBnaturalbyaddingonemorehalfstep—eitherbyturningtheBnaturaltoaBflatorbyraisingtheFnaturaltoanFsharp.Thistime,becausethenotesareflippedaroundfromtheordertheyappearedintheintervaloffourths,bothchangesincreasethesizeoftheinterval.

Again,justasinaperfectfourth,ifafifthisperfect(everycaseexceptFnaturalandBnatural),addingthesameaccidentalstobothnotesintheintervaldoesn’tchangeitsquality.And,aswithfourths,ifonlyoneofthenotesisalteredwithanaccidental,thequalitydoeschange.

RecognizingSeconds,Thirds,Sixths,andSeventhsSeconds,thirds,sixths,andseventhsallsharethecharacteristicofusingthetermsmajor,minor,augmented,anddiminishedtoidentifytheirquality.(Checkouttheearliersection“Quality:Consideringhalfsteps”formoreinformation.)

Amajorintervalmadesmallerbyonehalfstepbecomesminor,whereasamajorintervalmadelargerbyonehalfstepbecomesaugmented.Aminorintervalmadelargerbyonehalfstepbecomesmajor,andaminorintervalmadesmallerbyonehalfstepbecomesdiminished.

Clearasmud,right?Well,don’tworry.Wetellyoueverythingyouneedtoknowinthefollowingsections.Also,Table9-1summarizestheintervalsfromunisontooctave.Noticeinthetablethattheidentityoftheintervalitselfdependsonthequantityoftheintervalnumber—thatis,howmanylinesandspacesareincludedinthetotalinterval.

Table9-1IntervalsfromUnisontoOctave

HalfStepsbetweenNotes IntervalName

0 Perfectunison/diminishedsecond

1 Augmentedunison/minorsecond

2 Majorsecond/diminishedthird

3 Augmentedsecond/minorthird

4 Majorthird/diminishedfourth

5 Perfectfourth/augmentedthird

6 Augmentedfourth/diminishedfifth

7 Perfectfifth/diminishedsixth

8 Augmentedfifth/minorsixth

9 Majorsixth/diminishedseventh

10 Augmentedsixth/minorseventh

11 Majorseventh/diminishedoctave

12 Augmentedseventh/perfectoctave

13 Augmentedoctave

SecondsWhenyouhavetwonoteswithanintervalquantityoftwolinesandspaces,youhavea

second,asyoucanseeinFigure9-16.Secondsareprettyeasytorecognize—they’rethetwonotesperchedrightnexttoeachother,oneonalineandoneinaspace.


Figure9-16:Thesethreesetsofnotesareallseconds.

Ifonehalfstep(onepianokeyoroneguitarfret)existsbetweenseconds,theintervalisaminorsecond(m2).Iftwohalfsteps(onewholestep,ortwoadjacentpianokeysorguitarfrets)existbetweenseconds,theintervalisamajorsecond(M2).

Forexample,theintervalbetweenEnaturalandFnaturalisaminorsecond,becauseonehalfstepoccursbetweenthosetwonotes(seeFigure9-17).


Figure9-17:TheintervalbetweenEandFisaminorsecond,becauseitonlycontainsonehalfstep.

Meanwhile,theintervalbetweenFandGisamajorsecond,becausetwohalfsteps(onewholestep)existbetweenthosetwonotes,asillustratedinFigure9-18.


Figure9-18:TheintervalbetweenFandGisamajorsecond,becauseitcontainstwohalfsteps.

Amajorsecondismademinorbydecreasingitsquantitybyonehalfstep.Youcandecreaseitsquantityeitherbyloweringthetopnoteahalfsteporraisingthebottomnoteahalfstep.Bothmovesreducethedistancebetweenthenotestoonehalfstep(onepianokeyoroneguitarfret),asFigure9-19shows.


Figure9-19:Turningamajorsecondintoaminorsecond.

Aminorsecondcanbeturnedintoamajorsecondbyincreasingtheintervalsizebyonehalfstep.Youcanincreasetheintervalsizeeitherbyraisingthetopnoteahalfsteporbyloweringthebottomnoteahalfstep.Bothmovesmakethedistancebetweenthenotestwohalfsteps(twopianokeysorthreeguitarfrets).

Theonlyplacethathalfstepsoccurbetweenwhite-keysecondsisfromEnaturaltoFnaturalandBnaturaltoCnatural—thetwospotsonthekeyboardwheretherearenoblackkeysbetweenthetwowhitekeys.

Addingthesameaccidentaltobothnotesofanaturalseconddoesn’tchangeitsquality.AllthesecondsshowninFigure9-20aremajorseconds.


Figure9-20:Majorseconds.

AllthesecondsshowninFigure9-21areminorseconds.


Figure9-21:Minorseconds.

Anaugmentedsecond(A2)isonehalfsteplargerthanamajorsecond.Inotherwords,threehalfstepsexistbetweeneachnote.Youturnamajorsecondintoanaugmentedsecondeitherbyraisingthetopnoteorloweringthebottomnoteonehalfstep,asshowninFigures9-22and9-23.


Figure9-22:Turningamajorsecondintervalintoanaugmentedsecond.


Figure9-23:Turningamajorsecondintervalintoanaugmentedsecondonthepiano:FtoGsharp,andFflattoG.

Adiminishedsecondisonehalfstepsmallerthanaminorsecond—meaningnostepsoccurbetweeneachnote.They’rethesamenote.Adiminishedsecondisanenharmonicequivalentofaperfectunison.Anenharmonicmeansthatyou’replayingthesametwonotes,butthenotationforthepairisdifferent.

ThirdsThirdsoccurwhenyouhaveanintervalthatcontainsthreelinesandspacesasFigure9-24does.


Figure9-24:Thirdsarelocatedonadjacentlinesorspaces.

Ifathirdcontainsfourhalfsteps,it’scalledamajorthird(M3).MajorthirdsoccurfromCtoE,FtoA,andGtoB.Ifathirdcontainsthreehalfsteps,it’scalledaminorthird(m3).MinorthirdsoccurfromDtoF,EtoG,AtoC,andBtoD.Figure9-25showsmajorandminorthirdsonthemusicalstaff.


Figure9-25:Majorandminorthirdsonthestaff.

Amajorthirdcanbeturnedintoaminorthirdifyoudecreaseitsintervalsizebyonehalfstep,makingthetotalthreehalfstepsbetweennotes.Youcandecreaseitsintervalsizeeitherbyloweringthetopnoteahalfsteporraisingthebottomnoteahalfstep(seeFigure9-26).


Figure9-26:Turningamajorthirdintoaminorthird.

Aminorthirdcanbeturnedintoamajorthirdbyaddingonemorehalfsteptotheinterval,eitherby—youguessedit—raisingthetopnoteahalfsteporbyloweringthebottomnoteahalfstep,asshowninFigure9-27.


Figure9-27:Turningaminorthirdintoamajorthird.

Aswithseconds,fourths,andfifths,thesameaccidentaladdedtobothnotesofathird(bothmajorandminor)doesn’tchangeitsquality;addinganaccidentaltojustoneofthenotesofathirddoeschangeitsquality.

Anaugmentedthird(A3)isahalfsteplargerthanamajorthird,withfivehalfstepsbetweennotes.Startingfromamajorthird,raisetheuppernoteahalfsteporlowerthebottomnoteahalfstep.Figure9-28showsaugmentedthirds.Anaugmentedthirdisalsotheenharmonicequivalentofaperfectfourth—they’rethesamenote,butthenotationisdifferent.


Figure9-28:Turningamajorthirdintoanaugmentedthird.

Adiminishedthirdisahalfstepsmallerthanaminorthird.Beginningwithaminorthird,eitherraisethebottomnoteahalfsteporlowertheuppernoteahalfstep,makingforanintervaloftwohalfsteps(seeFigure9-29).


Figure9-29:Turningaminorthirdintoadiminishedthird.

SixthsandseventhsWhenyouhavetwonoteswithanintervalquantityofsixlinesandspaces,asinFigure9-30,youhaveasixth.Thenotesinasixtharealwaysseparatedbyeithertwolinesandaspaceortwospacesandaline.


Figure9-30:Harmonicsixthintervals.

Whenyouhavetwonoteswithanintervalquantityofsevenlinesandspaces,asinFigure9-31,youhaveaseventh.Seventhsalwaysconsistofapairofnotesthatarebothonlinesorspaces.They’reseparatedbyeitherthreelinesorthreespaces.


Figure9-31:Harmonicseventhintervals.

BuildingIntervalsThefirststepinbuildinganyintervalwhencreatingapieceofmusicistocreatethedesiredquantity,ornumbersize,aboveorbelowagivennote.Thenyoudeterminethequality.Wedetaileachofthesestepsinthefollowingsections.

DeterminingquantityDeterminingquantityiseasy,especiallyonpaper.For,say,aunisoninterval,justpickanote.Then,rightnexttothefirstnote,putanotheroneexactlylikeit.

Wanttomakeyourintervalanoctave?Putthesecondnoteexactlysevenlinesandspacesaboveorbelowthefirst,makingforatotalintervalquantityofeightlinesandspaces,asshowninFigure9-32.


Figure9-32:OctavesofthenoteG(spanningthetwoclefs,withmiddleCindicated).

Howaboutafourth?Putthesecondnotethreespacesandlinesaboveorbelowthefirstnote,makingforatotalintervalquantityoffourlinesandspaces.Andafifth?Putthesecondnotefourspacesandlinesaboveorbelowthefirstnote,makingforatotalintervalquantityoffivelinesandspaces.

EstablishingthequalityThesecondsteptobuildinganintervalistodecidewhatthequalityoftheintervalwillbe.Say,forexample,yourstartingnoteisanAflat.AndsupposeyouwantyourintervaltobeaperfectfifthaboveAflat.First,youcountoutthequantityneededforthefifthinterval,meaningyoucountanadditionalfourspacesabovethestartingnote,makingforatotalquantityoffivelinesandspaces,asshowninFigure9-33.


Figure9-33:FiguringoutthequantityneededtobuildaperfectfifthaboveAflat.

Next,youhavetoalterthesecondnoteinordertomakeitaperfectfifth.Becauseallfifthsareperfectsolongasbothnoteshavethesameaccidental(exceptfordarnedBandF),inordertomakethispairaperfectfifth,youhavetoflatthesecondnotesoitmatchesthefirst,asshowninFigure9-34.


Figure9-34:Flattingthesecondnotetomatchthefirstmakesaperfectfifth.

Ifyouwanttomakethesecondnoteanaugmentedfifth(abbreviatedaug5orA5)belowA,youcountdownanadditionalfourlinesandspacesfromAtomakeatotalqualityoffivelinesandspaces,andthenyouwritethenote,whichisD.SeeFigure9-35.


Figure9-35:BuildinganaugmentedfifthbelowAstartswithfindingthequantity.

Nowyoualteryouraddednotetomaketheintervalaugmented.Asyounowknow,afifthisanaugmentedfifthwhenanadditionalhalfstepisaddedtotheinterval(7 + 1 = 8halfsteps),soyouwouldlowerthebottomnotetoaDflat,asshowninFigure9-36.


Figure9-36:Addingtheaccidentalmakestheintervalaugmented.

Tomakethesecondnoteadiminishedfifth(abbreviateddim5orD5)aboveA,youcountupanadditionalfourlinesandspaces,tomakeatotalqualityoffivelinesandspaces,andthenwritethenote,whichisE.

Finally,youalteryouraddednotetomaketheintervaldiminished.Afifthisadiminishedfifthwhenahalfstepisremovedfromtheperfectfifth(7–1 = 6halfsteps),soyouwouldlowerthetopnotetoanEflat,asshowninFigure9-37.(Notethatadiminishedfifthisthesameasanaugmentedfourth—bothintervalsaremadeupofsixhalfsteps.)


Figure9-37:Addingtheaccidentalmakesthefifthdiminished.

ShowingMajorandPerfectIntervalsintheCMajorScale

Ascaleisreallynothingmorethanaspecificsuccessionofintervals,startingfromthefirstnoteofthescale,orthetonicnote.Gettingcomfortablewithintervalsandtheirqualitiesisthefirststeptomasteringscalesandchords.(SeeChapter7formuchmoreonmajorandminorscales.)

Table9-2,usingtheCmajorscaleasanexample,illustratestherelationshipbetweenthefirstnoteandeveryintervalusedinamajorscale.

Table9-2IntervalsintheCMajorScale

Note IntervalfromTonic NoteName

Firstnote(tonic) Perfectunison C

Secondnote Major2nd(M2) D

Thirdnote Major3rd(M3) E

Fourthnote Perfect4th(P4) F

Fifthnote Perfect5th(P5) G

Sixthnote Major6th(M6) A

Seventhnote Major7th(M7) B

Eighthnote Perfectoctave(P8) C

Figure9-38showstheintervalsfromTable9-2onthemusicalscale.Theseintervalsarefoundinthesameorderinanymajorscale.Inthemajorscale,onlymajorandperfectintervalsoccurabovethetonicnote.Knowingthiscanmakeidentifyingthequalitiesofintervalsmucheasier.Ifthetopnoteofanintervalisinthemajorscaleofthebottomnote,itmustbemajor(ifit’sasecond,third,sixth,orseventh)orperfect(ifit’saunison,fourth,fifth,oroctave).


Figure9-38:SimpleintervalsintheCmajorscale.

ListentoAudioTrack62tohearsimpleintervalsintheCmajorscale.

CheckingOutCompoundIntervalsThephrasecompoundintervalcansoundabitcomplicatedandscary—maybebecauseofthewordcompounditself.Yet,thetruthofthematteristhatcreatingcompoundintervalswon’tbecompletelyforeignifyou’refamiliarwithanyotherintervalwediscussinthischapter.

Whatdistinguishesacompoundintervalfromotherintervalsisthatacompoundintervalisnotconfinedtooneoctavethewayasimpleintervalis.Acompoundintervalcanbespreadoutoverseveraloctaves,althoughthenotesofthechordsmostoftenjustcomefromtwoneighboringoctaves.Thefollowingsectionsoutlinejusthowtobuildacompoundintervalandreturnittoasimplestate.

CreatingacompoundintervalJusthowdoyougoaboutbuildingacompoundinterval?Youhavetwooptions:

Counttheintervalbetweennotesbyhalfsteps,aswiththetenthinFigure9-6.Takeyourcompoundinterval,putbothnotesinthesameoctave,figureoutthenumbersizeofthatinterval,andthenaddseventothenumbersizeoftheresultinginterval.

Here’sanexampleofhowtocreateacompoundintervalusingthissecondmethod:TakealookatthesimpleintervalsintheCmajorscaleinFigure9-38.Now,turneachofthosefiguresintoacompoundintervalbyaddinganoctavetothesecondnoteineachexample.Whenweaddanoctavetoamajorsecondinterval(M2),itbecomesamajorninth(M9).Whenweaddanoctavetoamajorthird(M3),itbecomesamajortenth(M10).Aperfectfourth(P4)becomesaperfecteleventh(P11),whileaperfectfifth(P5)becomesaperfecttwelfth(P12).Thequalityoftheintervalremainsthesame—allthat’sbeendoneisanextraoctave’sbeenaddedtothequantity(+7).(SeeFigure9-39.)


Figure9-39:MajorcompoundintervalsintheCmajorscale.

ThefirstnoteinthesimpleintervalsinFigure9-38isexactlythesameasthefirstnoteinthecompoundintervalsinFigure9-39.Thesecondnoteinthe

compoundintervalisthesamenoteasthesecondnoteinthesimpleintervalinFigure9-38,justoneoctavehigher.Thequalityofeachintervalremainsthesame,butthesizenumberhasincreasedbyoneoctave,ortheoriginalnumberplus7.

Ifyouweretoincreasethedistancebetweenthenotesbyyetanotherfulloctave,youwouldsimplyadd7tothesizenumberagaintoreflecttheintervalsize:Major16,Major17,Perfect18,Perfect19,Major20,Major21,andPerfect22.

ReturningacompoundtoitssimplestateFindingthequantityandqualityofacompoundintervalisverysimilartotheprocessyoucanusetobuildacompoundinterval(seetheprecedingsection).Justreducethecompoundintervaltoasimpleintervalbyputtingbothnotesinthesameoctave,eitherbymovingthefirstnoteuporthesecondnotedown.

Here’showitworks:InFigure9-40,youhaveacompoundintervalofunknownquantityandquality.Ifyoudon’tmindcountingoutallthelinesandspaces(10)betweenthetwonotes(CandEsharp)tofindthequantity,thenyoudon’thavetoreducetheintervaltoasimpleinterval.However,mostpeoplefinditeasiertofigureoutthequantityandqualityofanintervalifthenotesareclosertogetheronthestaff.


Figure9-40:Theoriginalcompoundintervalofunknownquantityandquality.

Now,reducethecompoundintervaltoasimpleintervalbysimplybringingthetwonotesclosertogethersothatthey’reinthesameoctave.Youcaneitherbringthefirstnoteupanoctave,asshowninFigure9-41,orthesecondnotedownanoctave,asshowninFigure9-42.


Figure9-41:Reducingthecompoundintervalintoasimpleinterval.


Figure9-42:Anotherwaytoreducethecompoundintervalintoasimpleinterval.

Initsreducedstate,thequantityoftheintervalpicturedinFigure9-42isathird.Whenyoutakeathirdandraisetheuppernoteahalfsteporlowerthebottomnoteahalfstep,theintervalbecomesanaugmentedthird(A3).Addanoctave,andthecompoundinterval’squantityandqualityisanA10,orthesimpleintervalquantityandquality,plus7.Qualityhasnobearingonoctavedisplacement—onlythequantitychanges.

Chapter10

ChordBuildingInThisChapter

Gettingagriponmajor,minor,augmented,anddiminishedtriads

Lookingatallthedifferentkindsofseventhchords

Reviewingthetriadsandsevenths

Invertingandchangingvoicingfortriadsandsevenths

Takingalookatextendedchords


Achordis,quitesimply,threeormorenotesplayedtogetheror,inthecaseofarpeggiatedchords,oneafteranother.Bythissimpledefinition,bangingacoffeecuporyourelbowontopofthreeormorepianokeysatthesametimemakesachord—itprobablydoesn’tsoundparticularlymusical,butit’sstilltechnicallyachord.

Totheuninitiatedandexperiencedperformeralike,chordconstructioncansometimesseemlikemagic.There’ssomethingabsolutelybeautifulandamazingaboutthewaytheindividualnotesinachordworktoenhanceoneanother.Mostpeopledon’tappreciateaproperlyplayedchorduntiltheyheartheway“wrong”notessoundagainsteachother—forexample,yourcoffeecuppushingontothepianokeyboardinapoorlyconstructedchord.

InmostWesternmusic,chordsareconstructedfromconsecutiveintervalsofathird—thatis,eachnoteinachordisathirdapartfromtheonebeforeand/orafterit(seeChapter9ifyouneedarefresheronyourintervals).Figure10-1illustratestwostacksofthirdstoshowyouwhatwemean.


Figure10-1:Twostacksofthirds,oneonthelinesandtheotherinthespaces.

Withchordsbasedonintervalsofathird,allthenotesareeithergoingtobelinenotesorspacenotes,restingoneontopofanotherliketheexamplesinFigure10-1.


CreatingTriadswithThreePitchesTriads,whichconsistofanythreepitchesfromthesamescale,arethemostcommontypeofchordusedinmusic.Herearethedifferenttypesoftriadsyou’lllikelyworkwith:

MajorMinorAugmentedDiminished

Inthefollowingsections,weprovideinformationonthesetriads,butfirstweintroducewhattriadsareandwhatthey’remadeof.

Roots,thirds,andfifthsThetermtriadreferstochordsthatcontainthreedifferentpitchesandarebuiltofthirds.Thebottomnoteofatriadiscalledtheroot;manybeginningmusicstudentsaretaughttothinkofatriadasbeingatree,withtherootofatriadbeingits,well,root.Chordscarrytheletternameoftherootnote,asintherootofaCchord,showninFigure10-2.


Figure10-2:TherootofaCchord(eitherCcouldbetheroot).

PlayTrack63toheartherootofaCchord.

Thesecondnoteofatriadisthethird(seeChapter9formoreinformationaboutintervals).Thethirdofachordisreferredtoassuchbecauseit’sathirdintervalawayfromtherootofthechord.Figure10-3showstherootandmajorthirdofaCchord.


Figure10-3:TherootandmajorthirdofaCmajorchord.

PlayTrack64toheartherootandmajorthirdofaCchord.

Thethirdofachordisespeciallyimportantinconstructingchords,becauseit’sthequalityofthethirdthatdetermineswhetheryou’redealingwithamajororminorchord.(WediscussqualitymoreinChapter9.)

Thelastnoteofatriadisthefifth.Thisnoteisreferredtoasafifthbecauseit’safifthfromtheroot,asshowninFigure10-4.


Figure10-4:TherootandfifthofaCmajorchord.

PlayTrack65toheartherootandfifthofaCmajorchord.

Combinetheroot,third,andfifth,andyouhaveatriad,suchasthoseshowninFigure10-5.


Figure10-5:Cmajortriads.

PlayTrack66tohearaCmajortriad.

Thefollowingsectionswalkyouthroughbuildingavarietyofdifferenttriads:major,minor,augmented,anddiminished.Table10-1hasahandycharttohelpyoukeeptheformulasstraight.

Table10-1BuildingTriads

BuildingTriadsbyCountingHalfSteps

Major= Rootposition + 4halfsteps + 3halfsteps(7halfstepsaboveroot)

Minor= Rootposition + 3halfsteps + 4halfsteps(7halfstepsaboveroot)

Augmented= Rootposition + 4halfsteps + 4halfsteps(8halfstepsaboveroot)

Diminished= Rootposition + 3halfsteps + 3halfsteps(6halfstepsaboveroot)

BuildingTriadswithMajorScaleDegrees

Major= 1,3,5

Minor= 1,f3,5

Augmented= 1,3,s5

Diminished= 1,f3,f5

MajortriadsBecausethey’remadeofintervals,triadsareaffectedbyintervalquality(seeChapter9forarefresheronquantityandquality).Thequantitiesofthenotesthatmakeupthetriadareintervalsofroot,third,andfifth,butit’stheintervalqualityofeachnotethatchangesthevoicingofthetriad.

Amajortriadcontainsaroot,amajorthirdabovetheroot,andaperfectfifthabovetheroot.Youcanbuildmajortriadsintwoways.Wedescribeeachmethodinthefollowingsections.

Half-stepcountingmethodYoucancountoutthehalfstepsbetweennotestobuildamajortriadusingthisformula:

Rootposition + 4halfsteps + 3halfsteps(or7halfstepsaboveroot)

Figure10-6showsCmajoronthepianokeyboard.Thepatternstaysthesamenomattertheroot,butitlookstrickierwhenyoumoveawayfromC.Noticethepatternofhalfstepsbetweentheroot,thethird,andthefifth.


Figure10-6:Cmajoronthekeyboard.

First,majorthird,andfifthmethodThesecondwaytoconstructmajortriadsistosimplytakethefirst,third,andfifthnotesfromamajorscale.

Forexample,ifsomeoneasksyoutowritedownanFmajorchord,youfirstwriteoutthekeysignatureforFmajor,asshowninFigure10-7.(SeeChapter8formoreonkeysignatures.)


Figure10-7:ThekeysignatureforFmajor.

Thenyouwriteyourtriadonthestaff,usingFasyourroot,asseeninFigure10-8.


Figure10-8:AddtheFmajortriad.

IfyouweretobuildanAflatmajorchord,youwouldfirstwritedownthekeysignatureforAflatmajorandthenbuildthetriad,asshowninFigure10-9.


Figure10-9:TheAflatmajortriad.

MinortriadsAminortriadismadeupofaroot,aminorthirdabovetheroot,andaperfectfifthabovetheroot.Aswithmajortriads,youcanbuildminortriadstwodifferentways,aswenoteinthefollowingsections.

Half-stepcountingmethodAswithmajortriads(seeearliersection),youcancountoutthehalfstepsbetween

notestobuildaminorchordusingthisformula:

Rootposition + 3halfsteps + 4halfsteps(7halfstepsaboveroot)

Figure10-10showsCminoronthepianokeyboard,andFigure10-11showsitonthestaff.InFigure10-10,noticethepatternofhalfstepsbetweentheroot,thethird,andthefifth.


Figure10-10:Cminoronthekeyboard.


Figure10-11:Cminoronthestaff.

First,minorthird,andfifthmethodThesecondwaytoconstructminortriadsistojusttakethefirst,theminororflatthird(whichmeansyoulowerthethirddegreeofthemajorthirdonehalfstep),andfifthintervalsfromamajorscale.

Forexample,foranFminorchord,youwritedownthekeysignatureforFmajorandthenbuildthetriad,asinFigure10-12.


Figure10-12:TheFminortriadlowersthethirdonehalfstep.

IfyouweretobuildanAflatminorchord,youwouldwritetheAflatkeysignatureandaddthenotes,flattingthethird,asshowninFigure10-13.


Figure10-13:TheAflatminortriadlowersthethirdonehalfstep.

AugmentedtriadsAugmentedtriadsaremajortriadsthathavehadthefifthraisedahalfstep,creatingaslightlydissonantsound.

Anaugmentedtriadisastackofmajorthirdswithfourhalfstepsbetweeneachinterval.

YoucanbuildaCaugmentedtriad(writtenasCaug)bycountingoutthehalfstepsbetweenintervals,likethis:


CaugmentedisshowninFigures10-14and10-15.


Figure10-14:Caugmentedonthekeyboard.


Figure10-15:Caugmentedonthestaff.

Usingthemethodofstartingwiththemajorkeysignaturefirstandthenbuildingthechord,theformulayouwanttorememberforbuildingaugmentedchordsis

Augmentedtriad = 1 + 3 + sharp5

Sothefirstmajorscaledegreeandthirdmajorscaledegreestaythesameinthechord,butthefifthmajorscaledegreeisraisedahalfstep.

It’simportanttonoteherethatsharp5doesn’tmeanthatthenotewillnecessarilybeasharp.Instead,itmeansthatthefifthnoteoccurringinthescaledegreeisraised,orsharped,ahalfstep.

Therefore,ifsomeoneasksyoutowritedownanaugmentedFtriad,youfirstwritethekeysignatureforFandthenwriteyourtriadonthestaff,usingFasyourrootandraisingthefifthpositiononehalfstep,asshowninFigure10-16.


Figure10-16:TheFaugmentedtriad.

IfyouweretobuildanAflataugmentedtriad,youwouldgothroughthesameprocessandcomeupwithatriadthatlooksliketheoneinFigure10-17.NotethattheperfectfifthofAflatmajorisanEflat.GivenAflat’skeysignature,youhaveto“natural”thefifthtogettothatEnatural.


Figure10-17:TheAflataugmentedtriad.

DiminishedtriadsDiminishedtriadsareminortriadsthathavehadthefifthloweredahalfstep.

Diminishedtriadsarestacksofminorthirdswiththreehalfstepsbetweeneachinterval.

YoucanbuildaCdiminishedtriad(writtenasCdim)bycountingoutthehalfstepsbetweenintervals,likethis:


CdiminishedisshowninFigures10-18and10-19.


Figure10-18:Cdiminishedonthekeyboard.


Figure10-19:Cdiminishedonthestaff.

Usingthemethodofstartingwiththemajorkeysignaturefirstandthenbuildingthechord,theformulayouwanttorememberforbuildingdiminishedchordsis

Diminishedtriad = 1 + flat3 + flat5

Sothefirstmajorscaledegreestaysthesame,butthethirdmajorscaledegreeandthefifthmajorscaledegreearebothloweredonehalfstep.

It’simportanttonoteherethatthetermsflat3andflat5don’tmeanthesenoteswillnecessarilybeflats.Thesenotesareonlythethirdandfifthnotesoccurringinthescaledegreeloweredahalfstep.

Therefore,ifsomeoneasksyoutowritedownanFdiminishedtriad,youfirstwritethekeysignatureforF,andthenyouwriteyourtriadonthestaff,usingFasyourrootandloweringthethirdandfifthintervalsonehalfstep,asshowninFigure10-20.


Figure10-20:TheFdiminishedtriad.

IfyouweretobuildanAflatdiminishedtriad,youwouldgothroughthesameprocessandcomeupwithatriadthatlooksliketheoneinFigure10-21.


Figure10-21:TheAflatdiminishedtriad.

NotethattheperfectfifthofAflatmajorisanEflat—flattingthefifthmakesitadoubleflat.

ExpandingtoSeventhChordsWhenyouaddanotherthirdabovethefifthofatriad,you’vegonebeyondthelandoftriads.Younowhaveaseventhchord.Seventhchordsgottheirnamebecausethelastthirdintervalisaseventhintervalabovetheroot.

Severalkindsofseventhchordsexist.Thesixmostcommonlyusedseventhchordsareasfollows:

MajorseventhsMinorseventhsDominantseventhsMinor7flat5chords(alsosometimescalledhalf-diminished)DiminishedseventhsMinor-majorsevenths

Theeasiestwaytounderstandhowseventhsarebuiltistothinkofeachasatriadwithaseventhtackedontoit.Lookingatseventhsthisway,youcanseethatseventhchordsarereallyjustvariationsonthefourtriadsdiscussedearlierinthischapter.Thenamesofthechordstellyouhowtoputtheseventhtogetherwiththetriad.

Thefollowingsectionswalkyouthroughbuildingavarietyofdifferentsevenths:major,minor,dominant,diminished,andmore.Table10-2gathersallthisinfoonhowtobuildsevenths.

Table10-2BuildingSevenths

BuildingSeventhsbyCountingHalfSteps

Major= Root + 4halfsteps + 3halfsteps + 4halfsteps(11halfstepsaboveroot)

Minor= Root + 3halfsteps + 4halfsteps + 3halfsteps(10halfstepsaboveroot)

Dominant= Root + 4halfsteps + 3halfsteps + 3halfsteps(10halfstepsaboveroot)

Minor7flat5= Root + 3halfsteps + 3halfsteps + 4halfsteps(10halfstepsaboveroot)

Diminished= Root + 3halfsteps + 3halfsteps + 3halfsteps(9halfstepsaboveroot)

Minor-major= Root + 3halfsteps + 4halfsteps + 4halfsteps(11halfstepsaboveroot)

BuildingSeventhswithMajorScaleDegrees

Major= 1,3,5,7

Minor= 1, 3,5, 7

Dominant= 1,3,5, 7

Minor7flat5= 1, 3,f5, 7

Diminished= 1, 3,f5, 7

Minor-major= 1, 3,5,7

MajorseventhsAmajorseventhchordconsistsofamajortriadwithamajorseventhaddedabovetheroot.Figure10-22showshowtofirstbuildamajortriadusingtheCmajorexamplefromearlierinthechapter.


Figure10-22:Cmajortriad.

Nowaddamajorseventhtothetopofthepile,asisdoneinFigure10-23.Theresultis

Cmajorseventh = Cmajortriad + majorseventhinterval


Figure10-23:Cmajorseventh(CM7orCmaj7).

Bnaturalisamajorseventhfromtherootofthetriad.Noticethatit’salsoamajorthird(fourhalfsteps)awayfromthefifthofthetriad.

MinorseventhsAminorseventhchordconsistsofaminortriadwithaminorseventhaddedabovetheroot.UsingtheCminorexamplefromearlierinthechapter,youfirstbuildaminortriadliketheoneinFigure10-24.


Figure10-24:Cminortriad(CmorCmi).

Nowaddaminorseventhtothetopofthepile,asisdoneinFigure10-25.Theresultis

Cminorseventh = Cminortriad + minorseventh


Figure10-25:Cminorseventh(Cm7).

Bflatisaminorseventh(tenhalfsteps)fromtherootofthetriad.It’salsoaminorthird(threehalfsteps)awayfromthefifthofthetriad.

Tobuildaminorseventhusingmajorscaledegrees,youpickthefirst,flattedthird,fifth,andflattedseventhdegreesfromthescale.

DominantseventhsAdominantseventhchord,sometimescalledamajor-minorseventhchord,consistsofamajortriadwithaminorseventhaddedabovetheroot,asshowninFigure10-26.Theformulaforthisseventhis

Cdominantseventh = Cmajortriad + minorseventh


Figure10-26:Cdominantseventh(C7).

Tenhalfstepsfallbetweentherootandtheminorseventh,andthreehalfstepsfallbetweenthefifthofthetriadandtheminorseventh.

Thedominantseventhistheonlyseventhchordthatdoesn’ttrulygiveawaytherelationshipbetweenthetriadandtheseventhinitsname.Youjusthavetorememberit.Anddon’tconfusemajorseventhanddominantseventhchords.ThemajorseventhisalwayswrittenasM7,whereasthedominantseventhiswrittensimplyas7(occasionally,dom7).Forexample,GmajorseventhiswrittenGM7,andthedominantiswrittenG7.

Tobuildadominantseventhusingmajorscaledegrees,youpickthefirst,third,fifth,andflattedseventhdegreesfromthescale.

Minor7flat5chordsAminor7flat5chord(orhalf-diminishedseventh)isadiminishedtriadwithaminorseventhaddedabovetheroot.Itsname,minor7flat5,tellsyoueverythingyouneedtoknowabouthowthischordissupposedtobeputtogether.

Minor7referstotheseventhbeingaminorseventh,ortenhalfsteps,fromtheroot,asshowninFigure10-27.


Figure10-27:TherootandminorseventhofaCminor7flat5chord.

Flat5referstothediminishedtriad,whichsharesaflattedthirdwithaminorchordbutalsohasaflattedfifth,asshowninFigure10-28.


Figure10-28:Cdiminishedtriad.

Putthetwotogether,andyouhavetheCminor7flat5(half-diminished)chord,as

showninFigure10-29.


Figure10-29:Cminor7flat5chord.

Tobuildaminor7flat5(half-diminished)chordusingmajorscaledegrees,youpickthefirst,flattedthird,flattedfifth,andflattedseventhdegreesfromthescale.

DiminishedseventhsThediminishedseventhchordisastackofthreeconsecutiveminorthirds.Thenameisalsoisadeadgiveawayonhowthechordistobebuilt.Justaswiththemajorseventh,whichisamajortriadwithamajorseventh,andtheminorseventh,whichisaminortriadwithaminorseventh,adiminishedseventhisadiminishedtriadwithadiminishedseventhfromtheroottackedontoit.YoucanseeadiminishedseventhinFigure10-30.Theformulaforthediminishedseventhisasfollows:

Cdiminishedseventh = Cdiminishedtriad + diminishedseventh


Figure10-30:Cdiminishedseventh(Cdim7).

Notethattheseventhinadiminishedseventhisdouble-flattedfromthemajorseventh,sothediminishedseventhofCdim7isadouble-flattedB.Justaswithintervals,though,spellingcounts—nomatterwhataccidentalsappear,aCseventhchordhastohavesomeformofC,E,G,andB.

Tobuildadiminishedseventhusingmajorscaledegrees,youpickthefirst,flattedthird,flattedfifth,anddouble-flattedseventhdegreesfromthescale.

Minor-majorsevenths

Thenameminor-majorseventhsisn’tsupposedtobeconfusing.Thefirstpartofthenametellsyouthatthefirstpartofthechord,thetriad,isaminorchord,andthesecondpartofthenametellsyouthatthesecondpartofthechord,theseventh,isamajorseventhabovetheroot.

Therefore,tobuildaminor-majorseventhchord,startwithyourminorchord,asshowninFigure10-31.


Figure10-31:Cminortriad.

Thenaddyourmajorseventh,asinFigure10-32.Theformulaisasfollows:

Cminor-majorseventh = Cminor + majorseventhinterval


Figure10-32:Cminor-majorseventh(Cm/M7).

Tobuildaminor-majorseventhusingmajorscaledegrees,youpickthefirst,flattedthird,fifth,andseventhdegreesfromthescale.

LookingatAlltheTriadsandSeventhsThissectionlaysoutallthetypesoftriadsandseventhswediscussinthischapterinorderofappearanceandforeverykey.Figures10-33through10-47illustratethetriadsandsevenths.YoucanalsocheckoutAudioTracks67through81tohearthetriadsandseventhsinaction.

A

PlayTrack67tohearthetriadsandseventhsofA:Amajor,Aminor,Aaugmented,Adiminished,Amajorseventh,Aminorseventh,Adominantseventh,Aminor7flat5,Adiminishedseventh,andAminor-majorseventh.


Figure10-33:Atriadsandsevenths.

Aflat

PlayTrack68tohearthetriadsandseventhsofAflat:Aflatmajor,Aflatminor,Aflataugmented,Aflatdiminished,Aflatmajorseventh,Aflatminorseventh,Aflatdominantseventh,Aflatminor7flat5,Aflatdiminishedseventh,andAflatminor-majorseventh.


Figure10-34:Aflattriadsandsevenths.

B

PlayTrack69tohearthetriadsandseventhsofB:Bmajor,Bminor,B

augmented,Bdiminished,Bmajorseventh,Bminorseventh,Bdominantseventh,Bminor7flat5,Bdiminishedseventh,andBminor-majorseventh.


Figure10-35:Btriadsandsevenths.

Bflat

PlayTrack70tohearthetriadsandseventhsofBflat:Bflatmajor,Bflatminor,Bflataugmented,Bflatdiminished,Bflatmajorseventh,Bflatminorseventh,Bflatdominantseventh,Bflatminor7flat5,Bflatdiminishedseventh,andBflatminor-majorseventh.


Figure10-36:Bflattriadsandsevenths.

C

PlayTrack71tohearthetriadsandseventhsofC:Cmajor,Cminor,Caugmented,Cdiminished,Cmajorseventh,Cminorseventh,Cdominantseventh,Cminor7flat5,Cdiminishedseventh,andCminor-majorseventh.


Figure10-37:Ctriadsandsevenths.

Cflat

PlayTrack72tohearthetriadsandseventhsofCflat:Cflatmajor,Cflatminor,Cflataugmented,Cflatdiminished,Cflatmajorseventh,Cflatminorseventh,Cflatdominantseventh,Cflatminor7flat5,Cflatdiminishedseventh,andCflatminor-majorseventh.

Note:CflatisanenharmonicequivalentofB.ThechordsheresoundexactlyliketheBchords,butintheinterestofbeingcomplete,weincludeCflataswell.


Figure10-38:Cflattriadsandsevenths.

Csharp

PlayTrack73tohearthetriadsandseventhsofCsharp:Csharpmajor,Csharpminor,Csharpaugmented,Csharpdiminished,Csharpmajorseventh,Csharpminorseventh,Csharpdominantseventh,Csharpminor7flat5,Csharpdiminishedseventh,andCsharpminor-majorseventh.


Figure10-39:Csharptriadsandsevenths.

D

PlayTrack74tohearthetriadsandseventhsofD:Dmajor,Dminor,Daugmented,Ddiminished,Dmajorseventh,Dminorseventh,Ddominantseventh,Dminor7flat5,Ddiminishedseventh,andDminor-majorseventh.


Figure10-40:Dtriadsandsevenths.

Dflat

PlayTrack75tohearthetriadsandseventhsofDflat:Dflatmajor,Dflatminor,Dflataugmented,Dflatdiminished,Dflatmajorseventh,Dflatminorseventh,Dflatdominantseventh,Dflatminor7flat5,Dflatdiminishedseventh,andDflatminor-majorseventh.


Figure10-41:Dflattriadsandsevenths.

E

PlayTrack76tohearthetriadsandseventhsofE:Emajor,Eminor,Eaugmented,Ediminished,Emajorseventh,Eminorseventh,Edominantseventh,Eminor7flat5,Ediminishedseventh,andEminor-majorseventh.


Figure10-42:Etriadsandsevenths.

Eflat

PlayTrack77tohearthetriadsandseventhsofEflat:Eflatmajor,Eflat

minor,Eflataugmented,Eflatdiminished,Eflatmajorseventh,Eflatminorseventh,Eflatdominantseventh,Eflatminor7flat5,Eflatdiminishedseventh,andEflatminor-majorseventh.


Figure10-43:Eflattriadsandsevenths.

F

PlayTrack78tohearthetriadsandseventhsofF:Fmajor,Fminor,Faugmented,Fdiminished,Fmajorseventh,Fminorseventh,Fdominantseventh,Fminor7flat5,Fdiminishedseventh,andFminor-majorseventh.


Figure10-44:Ftriadsandsevenths.

Fsharp

PlayTrack79tohearthetriadsandseventhsofFsharp:Fsharpmajor,Fsharpminor,Fsharpaugmented,Fsharpdiminished,Fsharpmajorseventh,Fsharpminorseventh,Fsharpdominantseventh,Fsharpminor7flat5,Fsharpdiminishedseventh,andFsharpminor-majorseventh.


Figure10-45:Fsharptriadsandsevenths.

G

PlayTrack80tohearthetriadsandseventhsofG:Gmajor,Gminor,Gaugmented,Gdiminished,Gmajorseventh,Gminorseventh,Gdominantseventh,Gminor7flat5,Gdiminishedseventh,andGminor-majorseventh.


Figure10-46:Gtriadsandsevenths.

Gflat

PlayTrack81tohearthetriadsandseventhsofGflat:Gflatmajor,Gflatminor,Gflataugmented,Gflatdiminished,Gflatmajorseventh,Gflatminorseventh,Gflatdominantseventh,Gflatminor7flat5,Gflatdiminishedseventh,andGflatminor-majorseventh.


Figure10-47:Gflattriadsandsevenths.

ManipulatingTriadsthroughVoicingandInversion

Here’sariddle:Whenisatriadnotaperfectlittlestackofthirdsbuiltontopofaroot?Answer:Whenitsvoicingisopen,orwhenit’sinverted.Voicing,orspacingasit’sreferredtoinsomeclassicalcircles,simplyreferstothewayachordisarranged.Wegointomoredetailaboutvoicingandinversioninthefollowingsections.

TakingalookatopenandclosevoicingSometimes,thenotesofatriadarespreadoutovertwoormoreoctaves,withthedifferentpartsrearrangedsothat,forexample,therootmaycarrythehighest-soundingnote,orthethird,orthefifthcancarrythelowest-soundingnote.Thenotesarestillthesame(C,E,G,forexample)—they’rejustlocatedanoctaveorevenoctavesaboveorbelowwhereyouwouldexpecttheminanormaltriad.Whenallthenotesofachordareinthesameoctave,thechordisconsideredtobeinaclosevoicing.

Figure10-48showsaCmajorchordwithclosevoicing.


Figure10-48:Cmajorchordwithclosevoicing.

ThechordinFigure10-49,however,isalsoaCmajorchord,butwithopenvoicing,meaningthatthenotesinthechordaren’talllocatedinthesameoctave.


Figure10-49:Cmajorchordwithopenvoicing.

BothchordsinFigures10-48and10-49havethesamenotescontainedinthetriad,butinthelattercasethethirdhasbeenraisedafulloctavefromitscloseposition.Bothchordsarestillconsideredtobeintherootposition,becausetherootnote,C,isstillthelowestnoteofthetriad.

IdentifyinginvertedchordsIfthelowest-soundingpitchofachordisnottheroot,thechordisconsideredtobeinverted.Herearethepossibleinversionsofatriad:

Firstinversion:Ifthethirdofachordisthelowest-soundingnote,thechordisinfirstinversion.Figure10-50showstheCmajorchordinfirstinversion,withclose(sameoctave)andopen(differentoctaves)voicing.Secondinversion:Whenthefifthofachordisthelowest-soundingnote,thechordisinsecondinversion.Figure10-51showstheCmajorchordinsecondinversion.Thirdinversion:Whentheseventhofachordisthelowest-soundingnote,thatchordisinthirdinversion.Figure10-52showstheCmajor7chordinthirdinversion.


Figure10-50:Cmajorchordinfirstinversion,closeandopenvoicing.


Figure10-51:Cmajorchordinsecondinversion,closeandopenvoicing.


Figure10-52:Cmajor7chordinthirdinversion,closeandopenvoicing.

Sohowdoyouidentifyinvertedchords?Simple:Theyaren’tarrangedinstacksofthirds.Tofindoutwhichchorditis,youhavetorearrangethechordintothirdsagain.Onlyonewayexiststorearrangeachordintothirds,soyoudon’thavetoguessontheorderofthenotes.Youmayneedalittlepatience,though.

Lookat,forinstance,thethreeinvertedchordsshowninFigure10-53.


Figure10-53:Invertedchords.

Ifyoutrymovingthenotesupordownoctaves(inordertorearrangethemsothey’reallinstacksofthirds),theyendupbeinganFsharpmajortriad,aGdiminishedseventh,andaDmajortriad(seeFigure10-54).


Figure10-54:Rearrangingtheinvertedchordsintostacksofthirds.

Fromrearrangingthechords,youcantellthatthefirstexamplewasanFsharpmajorinsecondinversion,becausethefifthwasthelowest-soundingnoteinthechord.ThesecondexamplewasaGdiminishedseventh,alsoinsecondinversion,becausethefifthofthechordwasatthebottomofthestack.ThethirdexamplewasaDmajortriadinfirstinversion,becausethethirdofthechordwasthelowest-soundingnote.

DoublingthefunInadditionthemethodswepreviewinthischapter,youalsocanbuildachordthroughdoubling,whichsimplymeansyouhavemultipleversionsoftheroot,third,fifth,orevenseventhinachord.Forexample,aCmajortriadisstillaCmajortriadwithtwoC’sinit,aslongasithasatleastoneEandG.It’salsostillaCmajortriadifithasmultipleE’sorG’s;however,doublingtherootnoteisthemostcommonuseofdoubling.

ExploringExtendedChordsThemostcommonlyusedchordsinWesternmusicaretriads,whichareconstructedofstackedthirds.Triadsaremadeupofthefirst(root),third,andfifthdegreeofascale.Ifyouaddonemorenote,youhaveaseventh,whichisachordmadeupofthefirst,third,fifth,andseventhscaledegrees.Butitdoesn’tstopthere!Youcancontinuetomakebiggerandbiggerchordsbyaddingevenmorethirdstothestack,untileitheryouliterallyhavenomorekeysleftonthepianotoworkwith(orstringsontheguitar)oryourunoutoffingers.Thesebiggerandmorecomplexchordsbuiltfromstackedthirdsarecalledextendedchords.

Justlikewhenyou’reconstructingtriadsandseventhchords(seethesectionsearlierinthischapter),thequantityofeachchordbuiltonascaleremainsthesame,butthequalityorthechordchangesdependingonwhichnotesinthechordareraisedorloweredahalf-stepfromitsmajorscaledegree.(Formoreonquantityandquality,seeChapter9.)

Onethingtorealizewhenyou’rebuildingextendedchordsisthatyoucanfindmanymorepossiblepermutationsoutthere.Tokeepthingsfromgettingtooridiculous,though,we’rejustgoingtogiveyouafewexamplestoworkwith.

Curiousaboutallthepotentialextendedchords?Thinkofitlikeacombinationlock:Whenyouhavethreenotestoworkwith,asintriads,youhaveonlyfourdifferentwaystoconstructachord:major,minor,augmented,anddiminished.Whenyou’reworkingwithseventhchords,we’veshownyousixwaystoconstructchords:majorseventh,minorseventh,flattedseventh,minorseventh,diminishedseventh,andminor-majorseventh.Whenyouaddone,two,orthreemorenotestothemix,youhaveevenmorepossibilitiesavailabletoyou.

Becausethisbookisn’tjustaboutbuildingchords,welimitourselvesinthefollowingsectionstothemostcommonlyusedpermutationsofextendedchords,concentratingmoreontheninthchords,whichareusedprettyextensivelyinpopandjazzmusic.Wealsohighlightjustacoupleofeleventhandthirteenthchords,sincemostpeoplehavehandssmallerthanFatsWaller’sandhavetroublecoveringallthenotes.

NinthchordsAninthchordisachordthathasonemorethirdaddedtoitthanaseventhchord,andresultsinabigger,fullersoundthanevenatriadorseventhchord.So,forexample,aC9M,consistingofthefirst,third,fifth,seventh,andninthdegreeoftheCmajorscale,isjustourCM7chordfromFigure10-37,withonemorethirdstuckontopofthepile.TheresultistheCM9chord,whichyoucanseeinFigure10-55.


Figure10-55:CM9chord.

Aninthchordisformedbycombiningthefirst(root),third,fifth,flattedseventh,andninthdegreesofamajorscale,andiswrittenbyaddingamajorthirdtoadominantseventhchordForexample,intheCmajorscale,youwriteC9.So,ifweweretoconstructninthchordsforeverymajorscaleintheCircleofFifths,itwouldlooklikethechordsfoundinFigure10-56.(FormoreontheCircleofFifths,gotoChapter8.)


Figure10-56:Ninthchordsforallthemajorscales.

MinorninthchordsMinorninthchordsareformedbycombiningthefirst,flattedthird,fifth,flattedseventh,andninthdegreesofamajorscale,oraMinorSeventhchordwithamajorninthadded.Thesymbolyouuseismin9,mi9,m9,or-9.So,forexample,Cminor9wouldbewrittenaseitherCmin9,Cmi9,Cm9,orC-9,dependingonthetranscriber.Ifweweretoconstructminorninthchordsforeverymajorscale,followingtheCircleofFifths,theresultwouldlooklikeFigure10-57.


Figure10-57:Minorninthchordsforallthemajorscales.

MajorninthchordsMajorninthchordsareformedbycombiningthefirst,third,fifth,majorseventh,andninthdegreesofamajorscale—orbyaddingamajorninthtoaMajorSeventhchord—andiswrittenasMa9,orM9.CheckoutFigure10-58toseewhatitwouldlooklikeifweconstructedmajorninthchordsforeverymajorscale,inorderoftheCircleofFifths.


Figure10-58:Themajorninthchordsofthemajorscales.

NinthaugmentedfifthchordsNinthaugmentedfifthchordsareformedbycombiningthefirst,third,sharpedfifth,flattedseventh,andninthdegreesofamajorscale,andiswrittenas9#5,asinC9#5.Wonderingwhatitwouldlooklikeifweconstructedninthaugmentedfifthchordsforeverymajorscale?Well,wondernomore.Figure10-59showsyoutheninthaugmentedfifthchords,followingtheCircleofFifths.


Figure10-59:Theninthaugmentedfifthchordsinallthemajorscales.

Ninthflattedfifthchord

Youformninthflattedfifthchordsbycombiningthefirst,third,flattedfifth,flattedseventh,andninthdegreesofthemajorscale.Whenyou’rewritinganinthflattedfifthforaparticularscale,youadd9 5.Forexample,thechordCninthflattedfifthiswrittenC9 5orC9-5.Figure10-60showswhatitwouldlooklikeifweweretoconstructninthflattedfifthchordsforeverymajorscale,followingtheCircleofFifths.


Figure10-60:Ninthflattedfifthchordsforeverymajorscale.

SeventhflatninthpianochordsWhenyoucombinethefirst,third,fifth,flattedseventh,andflattedninthdegreesofthemajorscale,ortakeaC7chordandaddadiminishedninthtoit,yougetaseventhflatninthchord.Youwriteaseventhflatninthpianochordas7-9or7 9,asinC7-9orC79.Toseetheseventhflatninthchordsforeverymajorscale,checkoutFigure10-61.


Figure10-61:Seventhflatninthchords.

AugmentedninthchordsYoucanbuildanaugmentedninthchordbycombiningthefirst,third,fifth,flattedseventh,andsharpedninthdegreesofachord’smajorscale,oradominantseventhchordplusamajorninth.Whenwritingitout,youwouldadda9+or7 + 9tothechordname.TheCmajoraugmentedninthchordwouldlooklikeC9+orC7 + 9.Ifweweretoconstructaugmentedninthchordsineverymajorscale,followingtheCircleofFifths,itwouldlooklikeFigure10-62.


Figure10-62:Augmentedninthchords.

EleventhchordsJustasaninthchordiscreatedwhenyoustackfivethirdsontopofoneanother(seeprecedingsections),aneleventhchordisformedwhenyouhaveastackofsixthirds.Many,manypermutationsofeleventhchordsarepossible,butsincethey’rerarelyused,theonlytwowe’regoingtocoverareeleventhchordsandaugmentedeleventhchords.

Youcancreateaneleventhchordwhenyoucombinethefirst,third,fifth,flattedseventh,ninth,andeleventhofthemajorscale.Youindicateaneleventhchordbywriting11afterthescale,suchasC11fortheCmajorscale.CheckoutFigure10-63toseesomeexamplesofeleventhchords.


Figure10-63:Eleventhchordsforallthemajorscales.

Tobuildanaugmentedeleventhchord,youcombinethefirst,third,fifth,flattedseventh,ninth,andsharpedeleventhofthemajorscale.Whenwritingoutanaugmentedeleventhchord,youaddeither11+or7aug11tothechordname,asinC11+orC7aug11fortheCmajorscale.SeeFigure10-64foraugmentedeleventhchordsofallthemajorscales.


Figure10-64:Augmentedeleventhchords.

ThirteenthchordsHerewecoverjustthreeofthemost-commonarrangementsofthethirteenthchord:thethirteenthchord,thethirteenthflatninechord,andthethirteenthflatninthflatfifthchord.Wefocusonthesethreebecausethesearethethreeyouaremostlikelycomeacross,becausetheyareprobablythemostharmoniousofthedozensofpossibilities.

Themorethirdsyoustacktogetherinachord,thebiggerthechanceofendingupwithadissonant-soundingchord.Infact,manymusiciansconsiderthirteenth(andbeyond)chordsasmerelytheoreticalchords,inthattheyknowtheyexist,theyknowhowtobuildthem,butthey’renevergoingtousethemwhenwritingorplayingapieceofmusic.

Athirteenthchordisastackofseventhirds:thefirst,third,fifth,flatseventh,ninth,eleventh,andthirteenthdegreesofthemajorscale,oraC11withonemoremajorthirdontop.Writingitoutforthescalesisprettysimple.Allyoudoisaddthenumber13tothescale.So,C13wouldindicateathirteenthchordintheCmajorscale.Figure10-65containsallthethirteenthchordsofthemajorscales.


Figure10-65:Thirteenthchords.

Athirteenthflatninechordismadeupofthefirst,third,fifth,flattedseventh,flattedninth,eleventh,andthirteenthdegreesofamajorscaleandiswrittenas13 9,asinC139fortheCmajorscale.SeeFigure10-66forallthepossiblethirteenthflatninechords.


Figure10-66:Thirteenthflatninechords.

Athirteenthflatninthflatfifthchordismadeupofthefirst,third,flattedfifth,flatted

seventh,flattedninth,eleventh,andthirteenthdegreesofamajorscale.Youcanwriteitoutas13( 9, 5),asinC13( 9, 5)fortheCmajorscale.Figure10-67showsallthepossiblethirteenthflatninthflatfifthchords.


Figure10-67:Thirteenthflatninthflatfifthchords.

Chapter11

ChordProgressionsInThisChapter

Progressingwithdiatonicandchromaticchordsandminorscalemodes

Gettingahandleonchordprogressionsandtheirnotation

Takingadvantageofseventhchords

Understandingfakebooksandtabs

Havingaquickpeekatmodulation

Usingchordprogressionstoproducecadences


Asyoumayhaveguessed,constructingmusicisaboutasfarfromrandomlythrowingnotestogetheraswritingabookisfromrandomlypullinglettersoutofaScrabblebag.Youcanfindaboutasmanyrulestoputtingasongtogetherasyoucantoputtingasentencetogether,andinthischapterweshowyouafewmore.

WhenyouanalyzethebulkofWesternharmonicmusic,youstarttoseecertainpatternsemergeinthewayschordprogressionsarebuilt.It’spossibleforanyonechordtoprogresstoanyoneoftheotherchordsinakey;however,certainchordprogressionsareusedmorefrequentlythanothers.Why?Becausetheysimplysoundbetter.Theseprogressionsobviouslyarenaturalpatternsthatarepleasingtolistenersandcomposersalike,becausethesamepatternscontinuouslyappearinpopularmusic,classical,rock,jazz,andsoon.

Musictheoristshavetakennoteofthesepatternsandhavecomeupwithasetofrulesconcerningchordprogressions.Theserules,whichwediscussthroughoutthischapter,areimmenselyhelpfulinsongwriting.


ReviewingDiatonicChords,ChromaticChords,andMinorScaleModes

InWesternmusic,thekeysignaturetellsyouwhichnotescanbeusedinthatpiece.Therefore,ifyouhaveasongwritteninCmajor,theonlysevennotesthatcanappear(inanyorder)inthesongareC,D,E,F,G,A,andB(withtheoddsharporflatthrowninasrareexceptionsallowedbyaccidentals).IfyoursongiswritteninAmajor,theonlynotesappearinginthatsongwillbeA,B,Csharp,D,E,Fsharp,andGsharp(again,withpossibleaccidentals).Thechordswillalsobemadeofsomecombinationofthesesevennotesforeachkey.

Chordsbuiltonthesevennotesofamajorkeysignaturearecalleddiatonicchords.Chordsthatarebuiltonnotesoutsidethekeysignaturearecalledchromaticchords.

Minorkeysgetalittletrickierbecauseninenotescanpotentiallyfitunderasingleminorkeysignaturewhenyouconsiderthemelodicandharmonicminorscales(reviewChapter7ifyou’reunclearonthesekindsofminorscales).

Becausethenatural,melodic,andharmonicscalesaretaughtasseparatescales,musiciansoftenhavethemisconceptionthatyoumuststicktoonlyoneofthesetypesofminorscaleswhencomposingmusic.Alas,forthosefolkswholikenice,simplerulestobuildmusicagainst,thisjustisn’tso.

Theeasiestwaytothinkaboutchordsbuiltonminorkeysistorecognizethateachkeysignaturehasjustoneminorscale.Onefacetofminorkeysistheflexiblenatureofthe6thand7thdegreesofthescale.

The6thand7thdegreescanbeinthescaleintwodifferentwaysdependingonwhatsoundsbetterinthecontextofthemusic.Oftenthetwodifferentversionsofthosedegrees,ormodes,willappearinthesamepieceofmusic.Theminorscalethereforehaspotentiallyninenotesinit,asshowninFigure11-1.


Figure11-1:TheAminorscale,includingharmonicandmelodicmodesteps.

Noticehowtheuseofarrowsindicateswherethe6thand7thdegreesareeitherraised(uparrow)orunaltered(downarrow).

IdentifyingandNamingChordProgressions

Triadsstrungtogethertoformasuccessionofchordsarecalledprogressions.ChordprogressionsmakeupprettymuchallofWesternharmonicmusic.(YoucanreadmoreabouttriadsinChapter10.)

Whenbreakingdownapieceofmusicbasedonchordprogressions,romannumeralsrepresentthedifferentscaledegrees.Capitalizedromannumeralsrepresentthechordswithamajorthird,andlowercasedromannumeralsrepresenttheminorchords.Otherspecialcharactersindicatewhetherthechordisdiminished(°)oraugmented(+),asyoucanseeinTable11-1.

Table11-1BasicChordLabels

ChordType RomanNumeralFormat Example

Major Uppercase V

Minor Lowercase ii

Diminished Lowercasewith° vii°

Augmented Uppercasewith+ III+

AssigningchordnamesandnumbersBecausethenameofachordcomesfromitsrootnote,it’sonlynaturalthattherootofeachchordlocatedwithinascalewouldalsocarrythescaledegreewithitsname.Inotherwords,achord’snametellsyouwhatthechordis,basedontherootnote,whereasachord’snumbertellsyouwhatthechorddoes,basedonkey.

Forexample,considertheCmajorscale.EachnoteoftheCmajorscaleisassignedascaledegreenumberandname,likeso:

ScaleDegreeNumberandName Note

1Tonic C

2Supertonic D

3Mediant E

4Subdominant F

5Dominant G

6Submediant A

7Leadingtone B

8/1Tonic C

WhenyoubuildtriadswithintheCmajorscale,eachtriadisassignedthescaledegreeoftherootinitsname,asshowninFigure11-2.


Figure11-2:TonictriadsintheCmajorscale.

LookingatchordprogressionsinmajorkeysThechartforchordprogressionsintheCmajorscalelookslikethis:

ScaleDegreeNumber/Name Note

ITonic C

iiSupertonic D

iiiMediant E

IVSubdominant F

VDominant G

viSubmediant A

vii°Leadingtone B

(I)Tonic C

Becausetheleadingtoneisadiminishedtriad,ithasthe°symbolnexttoitsromannumeral.

Figure11-3takesanotherlookattheCmajorscale,thistimewiththechords’namesaccordingtotherootofeachtriadwrittenunderneaththem(andtheirshorthandnames,suchasCMorDm,writtenabovethem).ThecapitalMinthechord’sshorthandname(suchasinCM)standsformajor,andthelowercasem(suchasinEm)standsforminor.


Figure11-3:TriadscontainedwithinthekeyofCmajor.

AsyoucanseeinFigure11-3,thechordprogressionnaturallyfollowsthepatternofascendingthescalestartingwiththetonicnote,inthiscaseC.Figure11-4showsthetriadscontainedwithinthekeyofEflatmajor.Theeightnotesthatmakeupthekeyof

EflatmajorareusedtoproducetheeightchordsshowninFigure11-4.


Figure11-4:TriadscontainedwithinthekeyofEflatmajor.

NoticethatthepatternofmajorandminorchordsisthesameforCmajorandEflatmajor.Infact,it’sthesameforeverymajorkey.Soifyousayachordisaiichord,othermusicianswillautomaticallyknowthatit’sminor.

Table11-2showscommonchordprogressionsformajorkeys.Anyofthetriadsinthetablewithanaddedseventhchordarealsoacceptableinthattriad’snumberedplaceaswell.(Youcanreadmoreaboutseventhchordsinthelatersection“AddingaSeventhChordtoaTriad.”)

Table11-2CommonMajorKeyChordProgressions

Chord LeadsTo

I Canappearanywhereandleadanywhere

ii I,V,orvii°chords

iii I,IV,orvichords

IV I,ii,V,orvii°chords

V Iorvichords

vi I,ii,iii,IV,orVchords

vii° Ichord

Majorkeysignaturescancontainminorchords.

CheckingoutchordprogressionsinminorkeysWhendealingwithminorkeys,theconstructionoftriadsisunfortunatelyalotmoreinvolvedthanitiswiththemajorkeys.The6thand7thdegreesofthescalearevariable,dependingonwhetherthemusicusesnotesfromthenaturalminor,harmonicminor,ormelodicminor.Sofornearlyallminortriads,morepossibilitiesforbuildingchordsexistinthe6thand7thdegreesthantheydointhemajorscale.Therefore,ifyou’relookingatapieceofmusicwritteninCminor,thepossiblechordswithinthatkeyaretheonesinFigure11-5.


Figure11-5:PossibletriadswithinthekeyofCminor.

AlthoughanyofthechordsfromFigure11-5arepossible,themostcommonchoicesmadebytraditionalcomposersarethoseshowninFigure11-6.


Figure11-6:PossiblescaledegreesusedinCminor.

NoticeinFigure11-6thatthesupertonicandtheleadingtonetriadsarediminished,resultinginacombinationofthenatural,harmonic,andmelodicscalesincomingupwiththissetofchords.Neitherchordusesscaledegree6,sothesetwochordsresultfromthenaturalandharmonicminorscalesonly.

Youmayfindithelpfultorememberthat,withtheraised7thdegree,the5th(V)and7th(vii°)degreesofbothmajorandminorscalesofthesameletternameareidentical.

Table11-3showscommonchordprogressionsforminorchords.AnyofthetriadsinTable11-3withaddedseventhchordsarealsoacceptableinthattriad’snumberedplaceaswell.Theparentheticalchordsaretheless-commonlyused,butstillacceptable,chordsthatwouldworkintheprogression.

Table11-3CommonMinorKeyChordProgressions

Chord LeadsTo

ichords Canappearanywhereandleadanywhere

ii°(ii)chords i,V(v),orvii°(VII)chords

III(III+)chords i,iv(IV),VI(#vi°),orvii°(VI)chords

iv(IV)chords i,V(v),orvii°(VII)chords

V(v)chords IorVI(#vi°)chords

VI(#vi°)chords i,III(III+),iv(IV),V(v),orvii°(VII)chords

vii°(VII)chords ichord

Minorkeysignaturescancontainmajorchords.

AddingaSeventhChordtoaTriadOfcourse,wecan’tforgettheseventhchords(youmaywanttopeekatChapter10forarefresheronthesechords).Whenyouaddtheadditionalseventhabovetheregulartriad,youendupwithacombinationofthetriad’schordsymbolsandtheseventh’ssymbol.

Whendealingwithprogressionsthatuseseventhchords,you’llseesymbolsliketheoneinFigure11-7.Thissymbolindicatesaminor7flat5chord,alsosometimescalledahalf-diminishedseventh.


Figure11-7:Thissymbolmeansthechordisaminor7flat5chord(half-diminishedseventh).

Table11-4showstheromannumeralsthatcomposersusetodescribeseventhchords.

Table11-4SeventhChordLabels

SeventhChordType RomanNumeral Example

Major7th UppercasewithM7 IM7

Majorminor7th Uppercasewitha7 V7

Minor7th Lowercasewitha7 iii7

Minor7flat5 Lowercasewith∅7 ii∅7

Diminished7th Lowercasewith° vii°

Beawarethatthe“M7”bytheIandIVchordsiscommontopopularmusic—classicalmusicianstendtojustusea“7”forthesechords.Figure11-8showstheseventhchordsbasedonCmajor.


Figure11-8:SeventhsinCmajor.

Whentakingintoconsiderationthenatural,harmonic,andmelodicscales,16seventhchordscanoccurinaminorkey.TheseventhchordsshowninFigure11-9arethemostcommonlyused.


Figure11-9:SeventhchordsinCminor.

Table11-5collects,inoneplace,themajor,minor,andseventhchordsymbols.

Table11-5MajorandMinorScaleTriadsandSeventhChords

MajorScaleTriads

MinorScaleTriads

RareChordsBasedonMinorScales

7thChordsBasedonMajorScales

7thChordsBasedonMinorScales

I I IM7 i7

ii ii° ii ii7 ii∅7

iii III III+ iii7 IIIM7

IV Iv IV IVM7 iv7

V V v V7 V7

vi VI vi° vi7 VIM7

vii° vii° VII vii∅7 vii°7

Seeing(AndHearing)ChordProgressionsinAction

Inthissection,weshowyousomemusicalexamplessoyoucanseetherulesofchordprogressioninpractice.(Youcanreadabouttheserulesintheearliersection“IdentifyingandNamingChordProgressions.”)Notethatwhenwetalkaboutchords,we’renotonlytalkingaboutthestackedtriadsandsevenths,butwe’retalkingabouttheindividualnotesthatmakeupthechordsaswell.

Takealookatthetraditionalsong“LondonBridge,”aportionofwhichisshowninFigure11-10.


Figure11-10:Firstsevenmeasuresof“LondonBridge.”

NoticethatthefirsttwomeasuresofthesongusethenotesfoundintheCmajortriad(C,E,andG),makingCmajortheIchord.Inthethirdmeasure,thefirstchordisaG7chord(G,B,D,andF).ThefourthmeasuregoesbacktotheC/Ichord,andreturnstotheG7/Vchordintheseventhmeasure.

JudgingfromthecommonchordprogressioninTable11-2,thenextchordwouldhavetobeaIorvichord.SeeFigure11-11tofindoutwhathappensnext.


Figure11-11:”LondonBridge”returnstotheIchord.

TheexampleshowninFigure11-12isaleadsheetforthetraditionalEnglishfolksong“ScarboroughFair.”(Weexplainleadsheetsinthenextsection.)Lesstraditionalversionsofsomeofthechordsintheminorscaleareusedhere:theIII,IV,andVIIchords.Thepatternofprogressionstillholds,though:TheichordleadstotheVIIchord,theIIItotheIV,andthenanotherIIItotheVIIchord.TheI/ichordcanappearanywhereinapieceofmusic—and,inthisone,itcertainlydoes.


Figure11-12:Leadsheetfor“ScarboroughFair.”

Likeeverythinginmusicandartingeneral,you’rethecreatorofyourwork,andyoucandecidewhetheryouwanttofollowtherulesortrysomethingcompletelydifferent.However,Tables11-2and11-3earlierinthechaptermakeagoodlaunchpadforfamiliarizingyourselfonhowchordsfitagainstoneanother.Justforfun,tryplaying,orjustlisteningto,thefollowingchordprogressionstogetafeelofhoweasyitcanbetobuildagreatsong—oratleastahalfwaydecentpopsong.

PlayTrack82toheartheI-V-I(GM-DM-GM)chordprogressioninGmajor.PlayTrack83toheartheI-ii-V-I-iii-V-vii°-I(CM-Dm-GM-CM-Em-GM-Bdim-CM)chordprogressioninCmajor.PlayTrack84tohearthei-iv-V-VI-iv-vii°-i(Fm-Bflatm-CM-DflatM-Bflatm-Edim-Fm)chordprogressioninFminor.

PlayTrack85tohearthei-III-VI-III-VII-i-v7-i(Am-CM-FM-CM-GM-Am-Em7-Am)chordprogressioninAminor.

ApplyingChordKnowledgetoFakeBooksandTabs

Ifyou’veeverpickedupafakebook(thousandsandthousandsoftheseareavailable),you’veseenleadsheets.Leadsheetsprovidejustenoughinformationforaperformertoplayasongcompetentlybyprovidingtheleadmelodylineandnotingthebasicchordsbeneaththemelodylinesorabovethestafftofillouttheharmony,eitherwithastraightchordorwithimprovisation.Figure11-13showsashortexample.


Figure11-13:Asampleleadsheet.

Fakebooksaregreatforworkingonnotereadingandforimprovisingwithinakey.Often,forguitarfakebooks,theleadsheetsgosofarastodrawthechordsforyouwithtablature,ortabs.Figure11-14showstheguitartabforanEmajorchord.


Figure11-14:GuitartabforanEmajorchord.

Whenreadingguitartabs,youjustputyourfingersontheguitarfretboardwherethelittleblackdotsare,andpresto—you’vegotyourchord.Thelinesinthefigurerepresenttheguitarstrings,withthelowEstringonthefarleft.Guitartabsinleadsheetsalsohavethenameofthechordwrittenrightnexttothetab,makingiteveneasiertoeitherimproviseoranticipatethenotesthatmaylogicallybeinthemelodyline.

ModulatingtoaNewKeySometimesapieceofmusictemporarilymovesintoanewkey.Thismoveiscalledmodulation.Modulationiscommonintraditionalclassicalmusic,andlongsymphonyandconcertomovementsalmostalwaysspendatleastsometimeinadifferentkey,usuallyacloselyrelatedkeysuchastherelativeminororrelativemajoroftheoriginalkey.Thekeysignatureofthesepiecesofmusicremainthesame,ofcourse,butthequalitiesofandRomannumeralsassignedtothechordsarecompletelydifferent,leadingtoacompletelydifferentsetofchordprogressions.

Ifyoufindthatapieceofmusicsuddenlycontainschordprogressionsthatyouwouldn’texpectinthatkey,itmaybethatthepiecehasmodulated.Lotsofaccidentalsinapieceoranewkeysignaturestuckinthemiddleofapiecearecluesthatthemusichasmodulated.

Afavoritewayformodulatingcurrentpopmusicistosimplymovethekeyuponewholestep,forexample,fromFmajortoGmajor(alotofmusictheoristscallthisa“truckdriver”modulation,sinceitfeelslikeshiftingintoahighergear).Aslongasyouremembertokeepyourkeysignaturesstraight,dealingwithmodulationwithinapieceusuallyisn’taproblem.

ReachingaMusicalCadencethroughChordProgressions

Acadenceisanyplaceinapieceofmusicthathasthefeelofanending.Cadencecanrefertoastrong,definitestoppingpoint,likeattheendofasongorevenamovementorsection,butitcanalsorefertoashortpausethatcomesattheendofanindividualmusicalphrase.

Apieceofmusiccancometoanendbysimplystopping,ofcourse,butifthatstoppingpositiondoesn’t“makesense”tothelisteners,they’renotgoingtobehappywithit.Endingasongonthewrongnoteornotesislikeendingaconversationmid-sentence,andmostlistenersreactwithdissatisfactionatasongsimplystoppinginsteadofendingproperly.

Auniversallysatisfyingendingprovidescluesinthemusic,throughchordprogressions,thattellthelistenertheendofthesongisnear.Liketheendingofastory(orasentence,paragraph,chapter,orbook),anendinginmusic“makessense”ifitfollowscertainconstraintsorrules.Aswiththecustomsforstorytelling,theseexpectationscanbedifferentindifferentmusicalgenresortraditions.

Ofcourse,ifyou’rewritingmusic,youdon’thavetofollowanyoftherulesofcadence,includingtherulesdesignedtoprovideacertainlevelofcomfortandsatisfactionforyourlisteners.Butifyoudon’t,bepreparedforangry,torch-wieldingmobstofollowyouhomeafteryourperformances.Don’tsaywedidn’twarnyou.

Thebasicfoundationofmostmusicisaharmonicgoal,whereaphrasestartsataIchordandfollowsaseriesofchordprogressionstoendataIVorVchord,dependingonthegenre(popularmusictendstousetheIV-Imoreoften,andclassicalmusicusestheV-I)andthetypeofcadenceusedinthesong(seeChapter10formoreonthedifferenttypesofchords).Asongcanhavetwochordsorahundredchords,anditcanbea3-secondsongora45-minutesong,but,nomatterwhat,eventuallyitwillreachthatharmonicgoaloftheIVorVchordbeforegoingbacktotheIchord.

Acontinuumoftensionandreleasemovesthroughmusic,withtheIchordbeingthepointofrestorreleaseandeverychordleadinguptothereturntotheIchordbeingpointsoftension.Thetwo-chordprogressionbetweentheIVorVchordandtheIchordisthecadence.

Whenyoureallythinkaboutit,theentirehistoryofWesternmusiccanbesummedupbyI-V-IorI-IV-I.FromBaroque-periodmusictorock’n’roll,thisformulaholdsdarnedtrue.What’sreallyamazingisthatthissimpleformulahasresultedinsomanysongsthatsoundsodifferentfromoneanother.Thisvariationispossiblebecausethe

notesandchordsinakeysignaturecanbearrangedinsomanydifferentways.

HerearethefourtypesofcadencescommonlyusedinWesternharmonicmusic:

AuthenticcadencePlagalcadenceDeceptivecadenceHalf-cadence

Wediscusseachofthesecadencesinthefollowingsections.

AuthenticcadencesAuthenticcadencesarethemostobvious-soundingcadencesandarethereforeconsideredthestrongest.Inanauthenticcadence,theharmonicgoalofthemusicalphrasethatstartswithaI/ichordandendswithacadenceistheVchord;thecadenceoccurswhenyoumovefromthatV/vchordtoaI/ichord.ThephraseinvolvedintheauthenticcadenceessentiallyendsattheV/vchord,andthesongeitherendscompletelythereorstartsanewphrasewiththeI/ichord.

ListentoTrack86foranexampleofanauthenticcadence.

Twotypesofauthenticcadencesareusedinmusic:

Perfectauthenticcadence(PAC)Imperfectauthenticcadence(IAC)

Inthefollowingsections,weprovideinformationoneach.

PerfectauthenticcadenceInaperfectauthenticcadence,orPACasit’softencalledbyacronym-lovingmusictheorists,thetwochordsthatmakeupthecadencearebothintheirrootpositions,meaning(aswediscussinChapter10)thatthenoteonthebottomofthestackistheroot(thenotethechordisnamedafter).

ThestrongestPACoccurswhenthesecondchord,theI/ichord,hastherootofthechordonboththebottomandthetopofthestackofnotes.ThisPACmakesforahigh-impactendtoasong.

NoteinFigure11-15howthetopnoteontheIchordisthesameasthebottomnote,makingtherootofthechordboththehighestandlowest-pitchednoteofthechord.


Figure11-15:Aperfectauthenticcadence(PAC).

ListentoTrack87foranexampleofaperfectauthenticcadence.

ImperfectauthenticcadenceAV-Ichordprogressionmadewithinvertedchords—chordswheretheroot,third,andfiftharen’tinaperfectstack—iscalledanimperfectauthenticcadence(IAC).

ThedifferencebetweenaPAC(seetheprecedingsection)andanIACisillustratedinFigure11-16.NotehowthePACendswiththerootofthechordintherootposition,whereastheIACendswithaninvertedchord.


Figure11-16:DifferencebetweenaPACandanIAC.

ListentoTrack88tohearthedifferencebetweenaperfectauthenticcadenceandanimperfectauthenticcadence.

PlagalcadencesTheharmonicgoalofaplagalcadenceisultimatelythefour(IV/iv)chord,withthe

cadenceoccurringwhenthatchordmovestotheone(I/i)chord.PossibleplagalcadencesincludeIV-I,iv-i,iv-I,andIV-i.

Thisstructureoriginatedwithmedievalchurchmusic,mostlyvocalmusic,andisthereforeoftenreferredtoastheAmencadence.Ifyou’refamiliarwithGregorianchantsorevenmanymodernhymns,you’veheardtheAmencadenceinaction.Thecadenceusuallyhappens,notsurprisingly,atthepointwherethechanterssingthetwo-chord“A-men.”

“AmazingGrace,”whosemusicisshowninFigure11-17,containsagreatexampleofaplagalcadence.


Figure11-17:Aplagalcadencein“AmazingGrace.”

ListentoTrack89tohearanexampleofaplagalcadence.

Plagalcadencesareusuallyusedwithinasongtoendaphrase,insteadofattheveryendofasong,becausethey’renotasdecisive-soundingasperfectcadencesare.

Figure11-18showstwomoreexamplesofplagalcadences.


Figure11-18:Twomoreexamplesofplagalcadences.

ListentoTrack90toheartwomoreexamplesofplagalcadences.

DeceptivecadencesAdeceptivecadence(sometimescalledaninterruptedcadence)reachesanultimatepointoftensiononaV/vchord,justliketheauthenticcadence,butthenitresolvestosomethingotherthanthetonic(I/i)chord.Hencethenamedeceptivecadence.Youthinkyou’reabouttoreturntotheIchord,butthenyoudon’t.

AdeceptivecadenceleadsfromtheV/vchordtoanychordotherthantheI/ichord.Deceptivecadencesareconsideredoneoftheweakestcadencesbecausetheyinvokeafeelingofincompleteness.

Themostcommondeceptivecadence,used99timesoutof100,iswhenyouhaveaV/vchordthatmovesuptoavi/VIchord.Thephraselooksandfeelslikeit’sabouttoendandclosewiththeIchord,butinsteaditmovesuptotheviinstead,asshowninFigure11-19.TheVIorviisthemostcommonsecondchordusedindeceptivecadencesbecauseitsharestwonoteswiththeIchordandthusheightensthe“deception”whenalistenerexpectstohearI.


Figure11-19:Deceptivecadence.

ListentoTrack91tohearanexampleofadeceptivecadence.

Half-cadence

Withahalf-cadence,themusicalphraseendsatthepointoftension,theV/vchorditself.ItbasicallyplaystoaVchordandstops,resultinginamusicalphrasethatfeelsunfinished.Thiscadencereceiveditsnamebecauseitjustdoesn’tfeellikeit’sdoneyet.

Themostcommonformofhalf-cadenceoccurswhentheVchordisprecededbytheIchordinsecondinversion(whenthefifthofachordisthelowest-soundingnote;seeChapter10).Thispatternproducestwochordswiththesamebassnote,asyoucanseeinFigure11-20.Thefirstmeasureofthefigureshowskeyboardspacing,andthesecondmeasureshowsvocalspacing.


Figure11-20:Half-cadencesdon’tsoundquitefinished.

ListentoTrack92tohearanexampleofahalf-cadence.

PartIII

MusicalExpressionthroughTempoDynamics



Inthispart…Readandusedynamicmarkings.Understandtempochanges.Getacquaintedwithinstrumenttoneandacoustics.

Chapter12

CreatingVariedSoundthroughTempoandDynamics

InThisChapterKeepingtimewithtempo

Controllingloudnesswithdynamics


Everybodyknowsthatmakinggoodmusicisaboutmorethanjuststringingacollectionofnotestogether.Musicisjustasmuchaboutcommunicationasitisaboutmakingsounds.Andinordertoreallycommunicatetoyouraudience,youneedtograbtheirattention,inspirethem,andwringsomesortofemotionalresponseoutofthem.

Tempo(speed)anddynamics(volume)aretwotoolsyoucanusetoturnthosecarefullymeterednotesonsheetmusicintotheelegantpromenadeofLiszt’sHungarianRhapsodyNo.2,thesweepingexuberanceofChopin’sétudes,or,inamoremoderncontext,theslowcreepinessofNickCave’s“RedRightHand.”

Tempoanddynamicsarethemarkingsinamusicalsentencethattellyouwhetheryou’resupposedtofeelangryorhappyorsadwhenyouplayapieceofmusic.Thesemarkingshelpaperformertellthecomposer’sstorytotheaudience.Inthischapter,wehelpyougetfamiliarwithbothconceptsandtheiraccompanyingnotation.


TakingtheTempoofMusicTempomeans“time,”andwhenyouhearpeopletalkaboutthetempoofamusicalpiece,they’rereferringtothespeedatwhichthemusicprogresses.Thepointoftempoisn’tnecessarilyhowquicklyorslowlyyoucanplayamusicalpiece,however.Temposetsthebasicmoodofapieceofmusic.Musicthat’splayedvery,veryslowly,orgrave,canimpartafeelingofextremesomberness,whereasmusicplayedvery,veryquickly,orprestissimo,canseemmaniacallyhappyandbright.(WeexplaintheseItalianterms,alongwithothers,laterinthissection.)

Theimportanceoftempocantrulybeappreciatedwhenyouconsiderthattheoriginalpurposeofmuchmusicwastoaccompanypeopledancing.Oftenthemovementofthedancers’feetandbodypositionsworkedtosetthetempoofthemusic,andthemusiciansfollowedthedancers.

Priortothe17thcentury,composershadnorealcontroloverhowtheirtranscribedmusicwouldbeperformedbyothers,especiallybythosewhohadneverheardthepiecesperformedbytheircreator.Itwasonlyinthe1600sthatcomposersstartedusingtempo(anddynamic)markingsinsheetmusic.Thefollowingsectionsexplainhowtempogotitsstartandhowit’susedinmusictoday.

Establishingauniversaltempo:TheminimThefirstpersontowriteaseriousbookabouttempoandtiminginmusicwastheFrenchphilosopherandmathematicianMarinMersenne.Fromanearlyage,Mersennewasobsessedwiththemathematicsandrhythmsthatgoverneddailylife—suchastheheartbeatsofmammals,thehoofbeatsofhorses,andthewingflapsofvariousspeciesofbirds.Thisobsessionledtohisinterestinthefieldofmusictheory,whichwasstillinitsinfancyatthetime.

Withthe1636releaseofhisbook,Harmonieuniverselle,Mersenneintroducedtheconceptofauniversalmusictempo,calledtheminim(namedafterhisreligiousorder),whichwasequaltothebeatofthehumanheart,around70to75beatsperminute(bpm).Furthermore,Mersenneintroducedtheideaofsplittinghisminimintosmallerunitssothatcomposerscouldbeginaddingmoredetailtotheirwrittenmusic.

Mersenne’sminimwasgreetedwithopenarmsbythemusicalcommunity.Sincetheintroductionofwrittenmusicafewhundredyearsbefore,composershadbeentryingtofindsomewaytoaccuratelyreproducethetimingneededforothermusicianstoproperlyperformtheirwrittenworks.Musicianslovedtheconceptbecausehavingacommonbeatunittopracticewithmadeiteasierforindividualmusicianstoplaythegrowingcanonofmusicalstandardswithcompletestrangers.

Keepingsteadytimewithametronome

DespitewhatyoumayhavegatheredfromhorrormoviessuchasDarioArgento’sTwoEvilEyesandanumberofAlfredHitchcock’sfilms,thatpyramid-shapedtickingboxdoeshaveapurposebesidesturninghumanbeingsintomindlesszombies.

Practicingwithametronomeisthebestpossiblewaytolearnhowtokeepasteadypacethroughoutasong,andit’soneoftheeasiestwaystomatchthetempoofthepieceyou’replayingtothetempoconceivedbythepersonwhowrotethepiece.

Themetronomewasfirstinventedin1696bytheFrenchmusicianandinventorÉtienneLoulié.Hisfirstprototypeconsistedofasimpleweightedpendulumandwascalledacronométre.TheproblemwithLoulié’sinvention,though,wasthatinordertoworkwithbeatsasslowas40to60 bpm,thedevicehadtobeatleast6feettall.

Itwasn’tuntilmorethan100yearslaterthattwoGermantinkerers,DietrichNikolausWinkelandJohannNepomukMaelzel,workedindependentlytoproducethespring-loadeddesignthat’sthebasisforanalog(non-electronic)metronomestoday.Maelzelwasthefirsttoslapapatentonthefinishedproduct,andasaresult,hisinitialisattachedtothestandardtemposign,MM = 120.MMisshortforMaelzel’smetronome,andthe120meansthat120 bpm,or120quarternotes,shouldbeplayedinthepiece.

Liketheconceptoftheminim(refertotheprevioussection),bothmusiciansandcomposerswarmlyreceivedthemetronome.Fromthenon,whencomposerswroteapieceofmusic,theycouldgivemusiciansanexactnumberofbeatsperminutetobeplayed.Themetronomicmarkingswerewrittenoverthestaffsothatmusicianswouldknowwhattocalibratetheirmetronomesto.Forexample,quarternote = 96,orMM = 96,meansthat96quarternotesshouldbeplayedperminuteinagivensong.Thesemarkingsarestillusedtodayforsettingmostlyelectronicmetronomes,particularlyforclassicalandavant-gardecompositionsthatrequireprecisetiming.

TranslatingtemponotationAlthoughthemetronomewastheperfectinventionforcontrolfreakslikeBeethoven,mostcomposerswerehappytoinsteadusethegrowingvocabularyoftemponotationtogenerallydescribethepaceofasong.Eventoday,composersstillusethesameItalianwordstodescribetempoandpaceinmusic.ThesewordsareinItaliansimplybecausewhenthesephrasescameintouse(1600–1750),thebulkofEuropeanmusiccamefromItaliancomposers.

Table12-1listssomeofthemoststandardtemponotationsinWesternmusic,usuallyfoundwrittenabovethetimesignatureatthebeginningofapieceofmusic,asshowninFigure12-1.

Table12-1CommonTempoNotation

Notation Description

Grave Theslowestpace;veryformalandvery,veryslow

Largo Funeralmarchslow;veryseriousandsomber

Larghetto Slow,butnotasslowaslargo

Lento Slow

Adagio Leisurely;thinkgraduationandweddingmarches

Andante Walkingpace;closetotheoriginalminim

Andantino Slightlyfasterthanandante;thinkPatsyCline’s“WalkingAfterMidnight,”oranyotherlonelycowboyballadyoucanthinkof

Moderato Rightsmackinthemiddle;notfastorslow,justmoderate

Allegretto Moderatelyfast

Allegro Quick,brisk,merry

Vivace Lively,fast

Presto Veryfast

Prestissimo Maniacallyfast;think“FlightoftheBumblebee”


Figure12-1:Allegromeansthemusicwouldbeplayedatabriskpace.

Justtomakethingsalittlemoreprecise,modifyingadverbssuchasmolto(very),meno(less),poco(alittle),andnontroppo(nottoomuch)aresometimesusedinconjunctionwiththetemponotationtermslistedinTable12-1.Forexample,ifapieceofmusicsaysthatthetempoispocoallegro,itmeansthatthepieceistobeplayed“alittlefast,”whereaspocolargowouldmean“alittleslow.”

Ifyouhaveametronome,trysettingittodifferentspeedstogetafeelofhowdifferentpiecesofmusicmaybeplayedtoeachdifferentsetting.

PlayTrack93tohearexamplesof80(slow),100(moderate),and120(fast)beatsperminute.

Speedingupandslowingdown:Changingthe

tempoSometimesadifferenttempoisattachedtoaspecificmusicalphrasewithinasongtosetitapartfromtherest.Thefollowingareafewtempochangesyou’relikelytoencounterinwrittenmusic:

Accelerando(accel.):Graduallyplayfasterandfaster.Stringendo:Quicklyplayfaster.Doppiomovimento:Playphrasetwiceasfast.Ritardando(rit.,ritard.,rallentando,orrall.):Graduallyplayslowerandslower.Calando:Playslowerandsofter.

Attheendofmusicalphrasesinwhichthetempohasbeenchanged,youmayseeatempo,whichindicatesareturntotheoriginaltempoofthepiece.

DealingwithDynamics:LoudandSoftDynamicmarkingstellyouhowloudlyorsoftlytoplayapieceofmusic.Composersusedynamicstocommunicatehowtheywantapieceofmusicto“feel”toanaudience,whetherit’squiet,loud,oraggressive,forexample.

Themostcommondynamicmarkings,fromsoftesttoloudest,areshowninTable12-2.

Table12-2CommonDynamicNotation

Notation Abbreviation Description

Pianissimo pp Playverysoftly

Piano p Playsoftly

Mezzopiano mp Playmoderatelysoftly

Mezzoforte mf Playmoderatelyloudly

Forte f Playloudly

Fortissimo ff Playveryloudly

Dynamicmarkingscanbeplacedatthebeginningoranywhereelsewithinapieceofmusic.Forexample,inthemusicshowninFigure12-2,pianissimo(pp)meansthatthepieceistobeplayedverysoftlyuntilyoureachthenextdynamicmarking.Fortissimo(ff)meansthattherestoftheselectionistobeplayedveryloudly.


Figure12-2:Thedynamicmarkingsheremeanyouwouldplaythefirstbarverysoftly,pianissimo,andthesecondveryloudly,fortissimo.

ModifyingphrasesSometimeswhenreadingapieceofmusic,youmayfindoneofthemarkingsinTable12-3attachedtoamusicalphraseorasectionofmusicgenerallyfourtoeightmeasureslong.

Table12-3CommonModifyingPhrases

Notation Abbreviation Description

Crescendo cresc. Playgraduallylouder

Diminuendo dim. Playgraduallysofter

InFigure12-3,thelongcresc.,calledahairpin,meanstoplaytheselectiongraduallylouderandlouderuntilyoureachtheendofthecrescendo.


Figure12-3:Thecrescendoheremeansplaygraduallylouderandlouderuntiltheendofthehairpin.

InFigure12-4,thehairpinbeneaththephrasemeanstoplaytheselectiongraduallysofterandsofteruntilyoureachtheendofthediminuendo.


Figure12-4:Thediminuendo,ordecrescendo,heremeansplaygraduallysofterandsofteruntiltheendofthehairpin.

Anothercommonmarkingyou’llprobablycomeacrossinwrittenmusicisaslur,whichyoucanseeinFigure12-5.Justlikewhenyourspeechisslurredandthewordssticktogether,amusicalsluristobeplayedwithallthenotes“slurring”intooneanother.Slurslooklikecurvesthatconnectthenotes.


Figure12-5:Slursovergroupsofnotes.

CheckingoutotherdynamicmarkingsYouprobablywon’tseeanyofthefollowingnotationsinabeginning-to-intermediatepieceofmusic,butformoreadvancedpieces,youmayfindoneortwo(listedalphabetically):

Agitato:Excitedly,agitatedAnimato:WithspiritAppassionato:ImpassionedConforza:Forcefully,withstrengthDolce:SweetlyDolente:Sadly,withgreatsorrowGrandioso:GrandlyLegato:Smoothly,withthenotesflowingfromonetothenextSottovoce:Barelyaudible

Thepiano:Acomposer’suniversaltoolSinceitscreation,thepianohasbeentheuniversaltoolofchoiceforcomposingmusic,becausealmosteverynoteyouwouldeverwanttoworkwithispresentrightthereinfrontofyouonthekeyboard.Mostpianoshaveatleastsevenoctavestoworkwith,andafewconcertpianoshaveeight.

Youwanttocomposemusicforabassoon?Thelowerregistersofthepianoworkquitenicely.Pieceswrittenforstringscanbeeasilyhammeredoutinthemiddleandupperregisters.Andunlikemostotherinstruments,youcanplaychordsandmultiplenotessimultaneouslyonapiano,whichworkswellfortryingtofigureouthowthatmulti-instrumentorchestralpieceyou’rewritingwilleventuallysound.

YoucanblamethefactthatthepianowasinventedbyanItalian,BartolomeoCristofori,forthebulkoftempoanddynamicmarkingsbeingItalianwords.Fromthefirstdayofthepiano’sreleasetotheinitiallyItalianmarket,composerswerefindingnewwaystowritemusiconthisspectacularlyflexibleinstrument.

ExaminingthepianopedaldynamicsAdditionaldynamicmarkingsrelatetotheuseofthethreefootpedalslocatedatthebaseofthepiano(somepianoshaveonlytwopedals).Thestandardmodernpianopedalsetupis,fromlefttoright:

Softpedal(orunacordapedal):Onmostmodernuprightpianos,thesoftpedalmovestherestinghammersinsidethepianoclosertotheircorrespondingstrings.Becausethehammershavelessdistancetotraveltoreachthestring,thespeedatwhichtheyhitthestringsisreduced,andthevolumeoftheresultingnotesisthereforemuchquieterandhaslesssustain.

Mostmoderngrandpianoshavethreestringspernote,sowhenyoupressakey,thehammerstrikesallthreesimultaneously.Thesoftpedaliscalledunacorda(“onestring”)becauseitmovesallthehammerstotherightsothattheyonlystrikeoneofthestrings.Thiseffectivelycutsthevolumeofthesoundbytwo-thirds.

Middlepedal:Ifit’spresent(manymodernpianoshaveonlythetwoouterpedalstoworkwith),themiddlepedalhasavarietyofroles,dependingonthepiano.OnsomeAmericanpianos,thispedalgivesthenotesatinny,honky-tonkpianosoundwhendepressed.Someotherpianoshaveabasssustainpedalastheirmiddlepedal.Itworkslikeasustainpedalbutonlyforthebasshalfofthepianokeyboard.Stillotherpianos—specificallymanyconcertpianos—haveasostenutopedalfortheirmiddlepedal,whichworkstosustainoneormorenotesindefinitely,whileallowingsuccessivenotestobeplayedwithoutsustain.Damperpedal(orsustainingorloudpedal):Thedamperpedaldoesexactlytheoppositeofwhatthenamewouldimply—whenthispedalispressed,thedamperinsidethepianoliftsoffthestringsandallowsthenotesbeingplayedtodieoutnaturally.Thiscreatesaringing,echoeyeffectforsinglenotesandchords(whichcanbeheard,forexample,attheveryendofTheBeatles’s“ADayintheLife”).Thedamperpedalcanalsomakeforareallymuddledsoundiftoomuchofamusicalphraseisplayedwiththepedalhelddown.

Insheetmusicnotation,theentiremusicalphrasetobealteredbyuseofpedalsishorizontallybracketed,withthenameofthepedaltobeusedlistedbesideorbeneathit.Ifnopedalnumberisgiven,thedamperpedalistobeautomaticallyusedfortheselection.

Forexample,inFigure12-6,the“Ped.”signifiesthatthedamperpedal(usuallythefootpedalfarthesttoyourright)istobedepressedduringtheselection.Thebreaksinthebrackets(shownwith^)meanthatintheseplaces,youbrieflyliftyourfootoffthepedal.


Figure12-6:Pedaldynamicsshowyouwhichpedaltouseandhowlongtoholditdown.

LookingatthearticulationmarkingsforotherinstrumentsAlthoughmostarticulationmarkingsareconsidereduniversalinstructions—thatis,applicabletoallinstruments—someareaimedspecificallyatcertainmusicalinstruments.Table12-4listssomeofthesemarkingsandtheirrespectiveinstruments.

Table12-4ArticulationMarkingsforSpecificInstruments

Notation WhatItMeans

Stringedinstruments

Martellato Ashort,hammeredstrokeplayedwithveryshortbowstrokes

Pizzicato Topluckthestringorstringswithyourfingers

Spiccato Withalight,bouncingmotionofthebow

Tremolo Quicklyplayingthesamesequenceofnotesonastringedinstrument

Vibrato Slightchangeofpitchonthesamenote,producingavibrating,tremblingsound

Horns

Chiuso Withthehornbellstoppedup(toproduceaflatter,mutedeffect)

Vocals

Acapella Withoutanymusicalaccompaniment

Choro Thechorusofthesong

Parlandoorparlante Singinginaspeaking,oratorystyle

Tessitura Theaveragerangeusedinapieceofvocalmusic

FromharpsichordtopianoTheconceptofusingdynamicmarkingsinsheetmusiccameaboutaroundthesametimeasthepiano—andforgoodreason.BeforetheinventionofthepianobyBartolomeoCristoforiin1709,mostcomposerswereconfinedtowritingmostoftheirpiecesfortheharpsichord,aninstrumentwithoutthecapabilitytoplaybothsoftandloudsoundseasily.

Here’swhyvaryingthesoundsisdifficult:Thebasicinternaldesignoftheharpsichordfollowsthedesignofastringedinstrument.However,insteadofhavingone’sfingersindirectcontactwiththestring(aswithaguitarorfiddle),harpsichordsarefittedwithapluckingmechanisminsidetheinstrumentitself.Whenacertainkeyispressed,thecorrespondinginternalstringispluckedbythemechanism.Nomatterhowhardorsoftyoupresstheinstrument’skeys,theresultingvolumeisprettymuchthesame.

Althoughthepianolooksalotlikeaharpsichord,it’sreallyverydifferent.Thepianoincorporatesahammer-and-levermechanismthatstrikeseachstringwiththesameforceasthehumanfingeronthepianokeydid;thefactthatahammerhitsastringeverytimeyoupressakeyiswhythepianoisconsideredapercussiveinstrument.Thepianomadebothquietandloudsoundspossibleonthesameinstrument,and,therefore,inthesamemusicalpiece.Thisflexibilityiswhythepianowasoriginallynamedthegravicembalocolpianeforte,or“harpsichordwithsoftandloud.”Thenamewaslatershortenedtopianoforteand,finally,tosimplypiano.

Chapter13

InstrumentToneColorandAcousticsInThisChapter

Mixinguptonecolor

Gettingacquaintedwithacoustics

Haveyoueverwonderedwhymoresongsdon’tuseatubaorabassoonfortheleadinstrument,orwhysomanygreatpartsforinstrumentshavebeentakenbypianosandguitars?Okay,maybeyouhaven’tthoughtthatmuchaboutit,butifyou’reconsideringwritingmusic,youprobablyshould.

Thesimpleexplanationforwhysomeinstrumentsareusedforleadlinesinmusicandothersaren’tisthatthehumanearreactsmorefavorablytohigher-pitchedsoundsthantolower-pitchedones.Noticethatitisthehigher-pitchedrangethatbabiesandsmallchildrenbabblein,thatbirdssingin,andthatprettymuchallthehappylittlethingsmakenoisein.Peoplecan’tgetawayfromenjoyingthesesounds—it’spartofthehumanwiring.

High-pitchednotesalsoconveyagreatersenseofimmediacy.Youcanbowthecellountilyourarmfallsoff,butit’snotgoingtosoundasurgentandlivelyasitwouldifthesamepassagewereplayedatthesamespeedonaviolin.Similarly,whenyou’retryingtogetanideaacrossinconversation,especiallyanimportantidea,yourvoicetonetendstodriftuptowardthehigherregisters,notdownintothelowerones.Thisiswhyleadinstrumentsaresometimescalledtalkinginstruments.

Inthischapter,weexaminewhatconstitutesinstrumenttoneandwhatmakeseachinstrumentsoundjustthewayitdoes.Wealsodiscussbasicacousticsandinstrumentharmonics,andexplainwhysmallensemblesandorchestrasareputtogetherthewaytheyare.

DelvingintoToneColorThetonecolor,orcharacter,ofaninstrumentismadeupofthreebasiccomponents:

AttackTimbre(orharmoniccontent)Decay

Thesethreefactorsarewhatmakeeveryinstrumentsounddifferent.Evenifyou’rehearingtheinstrumentthroughyourcarradiospeakers,youcanimmediatelytell,justbylistening,whatinstrumentisbeingplayed.Wediscusseachofthesefactorsinthefollowingsections.

Attack:CheckingoutthebeginningsoundofanoteTheattackistheveryfirstsoundyounoticewhenyouhearanote,andit’spossiblythemostdistinguishingaspectofanoteplayedbyaninstrument.Theviolin,piano,andguitarallhavetheirowndistinctiveattacks.Here’sabriefrundownofeach:

Violin:Whenyouhearthefirstmicrosecondofaviolinbeingplayed,youinstantlyknowit’saviolinbecauseofthatquick,rawsoundofabowbeingdrawnacrossthefamiliar-soundingstring.It’sbeautiful,immediate,andunmistakable.Youdon’tevenknowyou’rehearingthefirsttinypointofcontact,butit’sthere.Ifyouweretoslowdownarecordingofanyvirtuoso’sviolinsolo,youwouldfindthatgorgeous,familiarraspatthebeginningofeverybowstroke.Piano:Eachtimeyouhitthekeyofapiano,atinyhammerstrikesthreemetalstringssimultaneously,producingabeautiful,ringingattack.It’sevenmoreamazingtoopenupapianoandlistentohoweachnotesoundswhenthefrontpieceorlidisn’tmufflingthesound.Guitar:Theguitar’sdistinctiveattackisasharplittletwangwhenthemetalstringsarefirstplucked.However,thesoundisdefinitelylesspronouncedwhentheguitarhasnylonstrings.Thedifferenttypesofstringsarepartlyresponsibleforthevarietyofguitar-playingstylesbymusicians.Rock,pop,andcountrysongsareusuallyplayedwithmetal-strungguitarsbecausethemetalstringsprovideanice,crisp,aggressive-soundingtwang.Classical,flamenco,andmuchoffolkmusicusenylon-strungguitarsbecausetheattackismuchsofter-sounding,makingformellowermusic.

Thespeedofaninstrument’sattackcanplayjustasbigaroleinthesoundofaninstrument:Thepluckingofastringonaharpsichordisquickandsharp,which

ismuchdifferentfromthelanguorousdrawingofabowacrossthestringsofadoublebass.

Timbre:HearingthebodyofanoteThetimbre(pronouncedtam-ber),orharmoniccontent,ofaninstrumentiswhatdeterminesthemiddlepart,orbody,ofeachplayednote.Whenyouremovetheattackandthedecayofsomeinstruments’soundswithdigitalequipment,youfindalotofsurprisingsimilaritiesbetweeninstruments.(Youcanreadaboutdecayinthenextsection.)

Forexample,thetimbreandpitchrangeofafluteandviolinarealmostidentical,butbecauseoneisblownandoneisbowed,theinitialattackofeachseparatenoteiscompletelydifferentandidentifiestheseinstrumentsbytheirveryfirstsplit-secondsounds.

However,theharmonics—orsoundwaves—betweensomeinstrumentsareradicallydifferent,simplybecauseoftheirconstruction.Forexample,theharmoniccontentbetweenanoteonaguitarandthesamenoteonapianoiscompletelydifferent,becauseonenoteonaguitarisonestringbeingplucked,butonenoteonapianoisactuallythreestringsbeinghitwithahammer.

Anysound,nomatterthesource,iscausedbysomethingvibrating.Withoutvibration,sounddoesn’texist.Thesevibrationscausetheairparticlesnexttothesourcetovibrateaswell,andthoseairparticles,inturn,causetheparticlesnexttothemtovibrate,andsoonandsoon,creatingasoundwave.Justlikeawaveinwater,thefartheroutthesoundwavemoves,theweakeritgets,untilitcompletelydissipates.Iftheoriginalvibrationcreatesastrongenoughwave,though,iteventuallyreachesyourearsandregistersasasound.

Youhearsoundsbecauseairvibratesagainstyoureardrums,causingthemtovibrate.Thesevibrationsarethenanalyzedbyyourbrainandregisteredasmusic,traffic,birdssinging—whatever.Becausesoundwavesarepickedupbyeachuniqueeardrumanddissectedbyeachuniquebrain,chancesarethatnobodyhearsthesamesoundexactlythesameasanybodyelse.

Eachcompletevibrationofasoundwaveiscalledacycle.Thenumberofcyclescompletedinonesecondiscalledthefrequencyofthevibration.Oneofthemostnoticeabledifferencesbetweentwosoundsisthedifferenceinpitch;thefrequencyofasounddeterminesitspitch.Frequencyismeasuredinhertz,withonehertz(Hz)beingonecyclepersecond.Onethousandhertziscalledakilohertzandiswrittenas1 kHz.Ahigh-frequencyvibrationproducesahigh-pitchednote;alow-frequencyvibrationgivesalow-pitchednote.

Thehumanhearingrange(audiblerange)isabout16Hzto16 kHz.Thefrequenciesofnotesthatcanbeplayedonapianorangefrom27.5 Hztojustover4 kHz.

Instrumentsgettheirspecificsoundsbecausetheirsoundscomefrommanydifferenttonesallsoundingtogetheratdifferentfrequencies.Asinglenoteplayedonapiano,forexample,actuallyconsistsofseveraltonesallsoundingtogetheratslightlydifferentfrequencies,ormultiplesofthefrequencybase.Themusicalnoteproducedbyatuningforkiscalledapuretonebecauseitconsistsofonetonesoundingatjustonefrequency.

Reproducing“natural”soundswithsynthesizersWhenthefirstsynthesizersweredeveloped,thedesignerswereattemptingtoreproduce“natural”instrumentsinsteadofjustsyntheticsounds(liketheflat,artificialsoundofa1970ssynthesizer,forexample).Thedevelopersofthesynthesizerdiscoveredthatthebiggestchallengeinmakingitsoundnaturalwasn’tinreproducinganotherinstrument’stimbre—whichiswhattheengineershadprimarilyfocusedonfromtheonset—butinreproducingtheattackanddecayofeachinstrument.Eventually,theyhadtorecordsamplesoftheinstrumentsthemselvesintothesynthesizersinordertomakesoundsdistinguishablefromoneanother.

Decay:ListeningforthefinalsoundofanoteDecayisthefinalpartofaninstrument’splayednote.Herearethetwotypesofinstrumentdecay:

Impulsive:Animpulsivedecaybelongstoinstrumentsthatneedtobeplayedcontinuously,orinpulses,inordertocontinuesounding.Tonesareproducedandimmediatelybegintodecayuntilthenextnoteplayedstartstheprocessagain.Commonexamplesofinstrumentswithanimpulsivedecayarethoseproducedbypluckingorstriking,suchastheguitar,mostpercussioninstruments,andthepiano.Sustained:Asustaineddecayisoneforwhichthevibratingcolumnofaninstrument,suchasthebodyofaflute,clarinet,orothercolumn-shapedinstrument,isexcitedcontinuouslysothatthesoundcontinuesinamoreorlesssteadystateaslongasthenoteisbeingplayed.Instrumentsproducingsustainedtonesarethosethatarebowedorblown,suchasviolinsandotherbowedstringedinstruments,woodwinds,free-reedinstrumentssuchastheaccordion,andbrassinstruments.

BuildingtheBand:AnAcousticsLessonNexttimeyougoouttoseeanorchestraorabigbandplay,orevenwhenyouwatchoneofthoselate-nightshowbandsperformonTV,takealookatwheretheperformersaresittinginrelationtoeachother.Payparticularattentiontowhichinstrumentisthe“lead”instrument.

Asyoustudyanorchestraorband,you’lllikelynoticethesetwothings:

Especiallyinanorchestralsetting,alltheperformersplayingthesameinstrumentsaresittingtogether.Thissetupisn’tbecausetheyallhavetosharethesamepieceofsheetmusic—it’sbecausewhenyousticktwoviolinsorflutesorclarinetstogethertheysoundlouderandfuller.Ifyousticktenofthemtogether,you’vegotawallofsoundcomingatyoufromthatareaoftheorchestra.

Incidentally,thissetupisonereasoninstrumentsaresochallengingtoplay.They’renotparticularlytrickytoplaywellinthemselves,butyouoftenhavetoplaytheminexactsynchronizationwithotherperformers.

Theleadinstrumentsareinfrontofalltheotherinstruments,especiallyinacousticperformances.Thissetupisbeneficialbecauseofvolumeandperception:Thesoundwavesfromtheinstrumentsinthefrontoftheensemblewillbeheardamicrosecondbeforetherestofthebandandwill,therefore,beperceivedasbeinglouderbecauseyouhearthemasplitsecondbeforetheotherinstruments.

Thisprincipleappliestoaregularfour-pieceelectricbandsetting,too.Ifyouwantyoursingertobeheardabovetheguitars,makesuretheamplifiercarryinghisorhervoiceisplacedclosertotheaudiencethantheguitarandbassamp.

Thebestplacetositatanorchestralperformanceisdirectlybehindtheconductorbutfarenoughbacktobeatthesameheightlevelashim.Conductorsbuildeachorchestraforeachperformancearoundwheretheystandsotheycanhearexactlywhat’sbeingplayed.Similarly,thissituationmakesitprettyeasyforaseasonedaudioengineertorecordanorchestralperformance.Putthemicrophonesrightwheretheconductor’sstanding,andyou’llrecordthepieceofmusicexactlyastheconductorintendedforittobeheard.

PartIV

MusicalExpressionthroughForm



Inthispart…Discoverthestructureofdifferentkindsofmusic.Exploredifferentformsandgenresofmusic.

Chapter14

TheBuildingBlocksofMusic:Rhythm,Melody,Harmony,andSongForm

InThisChapterReviewingrhythm,melody,andharmony

Understandingmusicalphrasesandperiods

Pickingoutandlabelingthepartsofasong

Whenwetalkaboutmusicalform,wemeanthestructuralblueprintusedtocreateaspecifictypeofmusic.Forexample,ifyouwanttowriteasonata,youfollowaspecificsongstructure.Althoughstyleelementslikethebasicmelody,theme,andkeysignaturewouldbeentirelyuptoyou,thewaythesonataasawholefitstogether—thebeginning,middle,andending—issetrightfromthebeginningbytheconstraintsofthesonataformitself.

Inmanyways,knowinghowformworksmakescomposingmusicextremelyeasy.Afterall,thepattern’salreadythere—youjusthavetofillintheblanks.Therealchallengeismakingyourparticularsonata,fugue,orconcertostandoutfromeveryotherpieceofmusicwritteninthatform.

Alotofcrossoverexistsbetweenthedefinitionsofformandgenre,buttheyaretwodifferentconcepts.Genreismoreabouthowmusicsounds,regardlessofitsstructure;examplesarejazz,pop,country,andclassical(althoughtherearealsocertainformsuniquetoclassicalmusic).

Theproblemwithidentifyingformsinmodernmusicisthatnewmusicisstillevolving.Studentsofmusicforminthe21stcenturymaysoonbestudyinganti-4/4math-rockpioneerslikeSteveAlbinialongsidethecomposersPhilipGlassandBeethoven.

Inthischapter,weexplainexactlywhatwemeanwhenwereferto“musicalform,”andwediscusssomeofthemorecommonmusicalformsyoucanencounter.

EstablishingRhythm

Wecan’ttalkaboutformandgenrewithouttalkingaboutrhythm,whichisthemostbasicelementofmusic.Youcanwriteapieceofmusicwithoutamelodylineorwithoutharmonicaccompaniment,butyoujustcan’twriteapieceofmusicwithoutrhythm—unless,ofcourse,your“music”isonesingle,sustainednotewithnovariationsinpitch.

Often,therhythmdifferentiatesonegenrefromanother—suchasthedifferencebetweenalternativerockandpunkrock,forexample.PutafastertempotoanySonVoltorWilcosong,andyoucanfiletheresultinthesamesectionoftherecordstoreastheRamonesandtheSexPistols.Changetheinherentrhythmpatternsofasong,evenaSexPistolssong,andyoucanchangeittoanythingfromatangotoawaltz.Rhythmisthatimportanttogenre.

Rhythmmovesthroughmusicasagenerativeforceinseveraldifferentways.Itcreatesthebasicpulseofasong,asdiscussedinPartIofthisbook.Rhythmisthepartofthesongyourtoestapalongtoandyourheadnodsto.Meterhelpsorganizenotesintogroupsusingatimesignatureanddefinestherepetitivepatternofstrongandweakbeatsthatnoticeablymoveasongalong.(Theindividualmeasuresinapieceofmusicdeterminethemeter;seeChapter4formoreaboutmeasures.)Thispulsecreatesafeelingoffamiliarityandexpectationforthelistenersothat,theoretically,youcanthrowapileofunexpected,janglynotesandchordsatthelistenerandstillretainafeelingofconnectionwithyouraudiencebyholdingontothemwiththesame,steadybeat.

Theactualrhythmthatyouhearwhenyoulistentoasongisusuallyreferredtoasthesurfacerhythm.Forexample,oftenwhenpeoplesaytheylikethebeatofapopsong,theymeantheyenjoythesurfacerhythm,whichmaysimplybearhythmicpatternonthedrums.Sometimesthesurfacerhythmmatchestheunderlyingpulseofasong(thebeatasdeterminedbythetimesignaturethatgovernstheentirepieceofmusic),especiallyinpopmusic,wherethedrumsandthebasslinesusuallyfollowthebasicbeat.Butsometimes,becauseofsyncopation(whichemphasizesthe“off”beats),thesurfacerhythmandthepulsedon’tmatchup.

Tempocomesintoplaywhenyoudiscussthespeedoftherhythmofapiece.Isitgoingtomovealongquicklyandlivelyorsomberlyandslowly?Thespeedatwhichapieceofmusicisplayeddeterminestheoverallfeelingofthemusicfortheaudience.Rarelydoyouhaveasuper-happysongplayedslowlyandquietly,nordoyouhearasuper-sadsongplayedat“FlightoftheBumblebee”speeds(seeChapter12formoreabouttempo).

ShapingtheMelodyMostoften,themelodyisthepartofthesongyoucan’tgetoutofyourhead.Themelodyistheleadlineofasong—thepartthattheharmonyisbuiltaround,andthepartthatgivesasmuchglimpseintotheemotionofapieceastherhythmdoes.(Refertothelatersectiononharmonyformoreinformation.)

Muchofmelody’sexpressivepowercomesfromtheupwardordownwardflowofpitch.Thepitchofasonggoesup,anditcanmakethesongsoundlikeit’sgettingeithermoretenseormorelively;thepitchofasonggoesdown,anditcangivethatpartofthesonganincreasedmelancholicordarkfeel.Theshapeofthepitch’stravelsiscalleditscontour.

Herearethefourcommonmelodiccontours:

ArchWaveInvertedarchPivotal

Contoursimplymeansthatthemelodyisshapedacertainway;theshapeofamelodyisespeciallyeasytopickoutwhenyouhavethesheetmusicrightinfrontofyou.Thepossibilitiesforbuildingmelodicphraseswithjustfourbasiccontoursarevirtuallyinfinite.(Bybuildingmelodicphrases,wemeanstartingattheIchord,goinguptotheIVorVchord,andendingattheIchord;seeChapter11formoreinformationaboutchordprogressions.)Formoreinformationaboutcomposingmusic,MusicCompositionForDummiesbyScottJarrettandHollyDay(Wiley)isagoodplacetostart.

Figure14-1showsastretchofmusicthathasanarchcontour.Notehowthemelodylineinthetreblecleffirstgoesupinpitchfromalowpointtoahighpointandhowitthengoesbackdownagain,creatingthearch.Whenmusicgoesupinpitchgraduallylikethis,itresultsinanincreaseintensioninthatsectionofthecomposition.Thelowerthepitchgetsinsuchagradualarch,themoretheleveloftensiondecreases.


Figure14-1:Inthearchcontour,thepitchofnotesgoesupandthendown.

Figure14-2showsmusicwithawavecontour.Notehowthemelodylinegoesup,and

down,andupagain,anddownagain—justlikeaseriesofwaves.


Figure14-2:Inthewavecontour,pitchgoesupanddownandupanddown,likewavesonthesea.

Figure14-3showsmusicwithaninvertedarchcontour.YoumayhavenoticedthatthemusicinFigure14-3looksalotlikethatinFigure14-1.TheonlydifferenceisthatthemelodylineinFigure14-3goesdowninpitchandthenuptotheendofthephrase.Therefore,thephrasestartsoutsoundingrelaxedandcalmbutcontainsanincreaseintensionasthearchrisestowardtheendofthephrase.


Figure14-3:Intheinvertedarchcontour,thepitchstartsouthigh,goesdown,andthenheadsupagain.

Figure14-4showsanexampleofmusicwithapivotalcontour.Apivotalmelodylineessentiallypivotsaroundthecentralnoteofthepiece—inthecaseofthemusicinFigure14-4,theE.Apivotalcontourisalotlikeawavecontour,exceptthatthemovementaboveandbelowthecentralnoteisminimalandcontinuouslyreturnstothatcentralnote.Traditionalfolkmusicusesthismelodicpatternalot.


Figure14-4:Thepivotalcontourrevolvesaroundacertainpitch.

Anymelodylineinapieceofmusicgenerallyfallsintooneoftheprecedingcategoriesofcontour.Tryrandomlypickingupapieceofsheetmusicandtracingoutthemelodypatternyourselftoseewhatwemean.

Therangeofamelodyisdeterminedbytheintervalbetweenthehighestandlowestpitchesofthesong.Theriseandfalloftensionisoftenproportionaltoitsrange.Melodieswithanarrowpitchrangetendtohaveonlyaslightamountofmusicaltensioninthem,whereasmelodieswithawiderangeofpitchesaremorelikelytohaveagreaterleveloftension.Astherangeofpitchesinasongiswidened,thepotentialforgreaterlevelsoftensionincreases.

ComplementingtheMelodywithHarmonyHarmonyisthepartofthesongthatfillsoutthemusicalideasexpressedinthemelody(seetheprecedingsectionformoreonmelody).Often,whenyoubuildaharmonybasedonamelodicline,you’reessentiallyfillinginthemissingnotesofthechordprogressionsusedinthesong.Forexample,takealookatthesimplemelodylineshowninFigure14-5.


Figure14-5:AsimplemelodylineinthekeyofC.

YoucanfillouttheharmonyinFigure14-5bysimplygrabbingthenotesoftheIandVchordsandplacingtheminthebassline,asshowninFigure14-6.


Figure14-6:HarmonyforamelodylineinthekeyofC.

Toputitreallysimply,harmonyisallaboutthebuildingofchords,whicharetonescomingfromthescaleinwhichthemusiciscomposed.(YoucanreadmoreaboutchordsinChapter10.)Harmonyalsostemsfromtheorderofthechordprogressionsthemselves,andalsohowaphraseresolvesitselfthroughtheV-IorIV-Icadence(seeChapter11forcoverageofcadences).

Consonantharmoniesarethosethatsoundstableandpleasingtotheear,suchastheIchordattheendofaphrase.Dissonantharmoniessoundunstableandunpleasanttotheear;theymaysoundwrongorseemtoclashuntilthey’reresolvedintoconsonantharmonies.Tensioncanbecreatedinasongthroughharmonybycreatingdissonance,oftenbyaddingextrathirdintervalsontopofatriadtobuildsevenths,ninths,andsoon.(CheckoutChapter9forcoverageofintervals.)Manyseventhchordsaredissonantharmonies.Composersalsousethetensionbetweenconsonanceanddissonancetoestablishasenseofabeginningandendinginasong.

WorkingwithMusicalPhrasesandPeriodsTwoofthebuildingblocksofmusicalformarephrasesandperiods.Amusicalphraseisthesmallestunitofmusicwithadefinedbeginningandend.MostmusicalphrasesconsistofabeginningIchordprogressingtoaIVoraVchordandendingagainontheIchord.Theoretically,thousandsofchordprogressionsmayexistbetweenthatfirstIchordandtheIVorVchord.However,youmayloseyouraudienceinthattime.

Musicalphrasesarelikesentencesinaparagraph—justasmostreadersdon’twanttowadethroughathousandlinesoftexttofindoutthepointofasentence,mostmusicaudiencesarelisteningforthemusicalideaexpressedinaphraseandgetboredifitsoundslikeyou’rejustmeanderingbetweenchordsandnotcomingtoaresolution.

Sohowlongshouldamusicalphrasebe?It’sreallyuptothecomposer,butgenerally,aphraseisusuallytwotofourmeasureslong.Withinthatspace,aphrasebegins,worksthroughoneormorechordprogressions,andresolvesitselfbacktotheIchord.(CheckoutChapter11forthescooponchordprogressions.)

Whenacomposerreallywantsyoutounderstandthatagroupofmeasuresaretobelinkedtogetherinaphraseandplayedasanimportantunit—kindoflikeatopicsentenceinanessay—heorshelinksthephrasetogetherwithacurvedlinecalledaphraseline,asshowninFigure14-7.NoticehowthephrasebothbeginsandendsontheIchord,ortheGmajorchord.(ThenumbersabovetheRomannumeralsarefingeringmarkingsforthepianist;youdon’tneedtoworryaboutthem.)


Figure14-7:Notethephraselineinthebassclef.

Don’tconfusephraselineswithtiesandslurs.Aphraselinetiesanentiremusicalphrasetogether,whereasslursandtiesonlytietogetherasmallpartofaphrase.(Ifyouwanttoreadaboutties,headtoChapter2.WediscussslursinChapter12.)

Thephraserepresentsthesmallestunitendingwithacadenceinapieceofmusic.Thenextlargerunitusedinmusicalformistheperiod.Musicalperiodsarecreatedwhentwoorthreemusicalphrasesarelinkedtogether.Inthecaseofmusicalperiods,thefirstmusicalphraseisonethatendsinahalf-cadence(endingattheV/vchord),andthesecondphraseendswithanauthenticcadence(endingwiththeV/vchordresolving

totheI/ichord).WecovercadencesinChapter11.

Thehalf-cadencecomesacrosslikeacommainasentence,withtheauthenticcadence,orconsequent,endingthelinkedphraseslikeaperiod.

Figure14-8showsanexampleofamusicalperiod.


Figure14-8:Amusicalperiodismadeoflinkedphrases.

LinkingMusicalPartstoCreateFormsThedivisionofmusicintopartsoccurswhenyoulinktwoormoreperiodsthatsoundliketheybelongtogether.(Seetheprecedingsectionforadiscussionofperiods.)Theysharemajorharmonicfocalpoints,similarmelodylines,andsimilarrhythmstructure.Theymayhaveotherresemblances,too.Partscanbefurtherlinkedtogethertocreatemusicalforms.

Composersconventionallygivealphabeticlabelstothemusicalpartswithinacomposition:A,B,C,andsoforth.Ifapartisrepeatedinasong,itsletteralsoisrepeated.Forexample,ABAisafamiliarlayoutinclassicalmusic,wheretheopeningtheme,orthemainmusicalideathatrunsthroughasong(labeledA),aftervanishingduringpartB,isrepeatedattheendofthesong.

Asthecontrastform,whereyouhavedifferentmusicalsectionsthatcandifferwidelyfromoneanother,ABformscomeinaboundlessarrayofpossibilities.Youmayseerecurringsections,uniqueones,oranycombinationofboth.Forexample,arondo—apopularforminclassicalmusic—alternatesbetweenarecurringsectionandothersthatoccuronetimeeach.Arondo,then,wouldbelabeledABACADA…(andsoon).

Youmayevenencounteranongoingform,whichhasnorecurrencewhatsoever:ABCDE….Thisformcreateswhat’sknownasathrough-composedpieceofmusic.

Inthefollowingsections,wedescribesomeofthemostcommonformsyoumayencounterinmusic.

RachelGrimes,composer,onthelimitsofform“Inschool,there’sthetendencytogetdidacticabouttheory,soyougetintothismind-setthatonlycertainchordprogressionsareallowed,andalltherestaren’t.Popmusicisverydidacticthatway.Therearecertainexpectedstandards,likeyou’renotallowedtogotoaVIchordafterresolvingtoaIVoraV—you’rejustexpectedtogototheI,andtherereallyisn’tmuchdeviationfromthatpattern.Ithinkthebiggestchallengeforstudentsandusersofmusictheoryistoacceptthatcertaingroundworkhasbeenlaidoutforthem,sofaraswhatsounds‘right’inWesternmusic,butthatdeviationsfromthatgroundworkandthosepatternsarestillallowed”.

One-partform(A)Theone-partform,alsoknownasAformorunbrokenform,isthemostprimitivesongstructureandisalsosometimesreferredtoastheairformorballadform.Inaone-partform,asimplemelodyisrepeatedwithslightchangestoaccommodatedifferentwords,asinastrophicsonglike“OldMcDonaldHadaFarm.”Thissongrepeatsthesamemusicallinebutchangesthewordswitheachverse.

Theone-partformismostlyfoundinfolksongs,carols,orothersongsthatareshortandhavealimitedthemeandmovement.Aformscomeonlyinasinglevariety.Theymaybelongorshort,butthey’realwaysdescribedasA(orAA,orevenAAA).

Binaryform(AB)Binaryformconsistsoftwocontrastingsectionsthatfunctionasstatementcounterstatement.ThepatternmaybeasimpleAB,asin“MyCountry,’TisofThee,”orinsimpleminuets,wheretheformisusuallyAABB,withthesecondAandsecondBbeingvariationsofthefirstAandB.

InthebinaryformusedintheBaroqueperiod,thepatterncaninvolveachangeofkey,usuallytothekeyofthefifthoftheoriginalkeyifthepieceisinamajorkey.PartAbeginsinonekeyandendsinthekeyofthefifth,whilepartBbeginsinthenewkeyandendsintheoriginalkey.Eachpartisrepeated,givingthepatternAABB.

MusiciansreflectonknowingwhenasongisdoneSteveReich(composer):“WhenIstartout,IalwayshavearoughideaofhowmuchtimeIhavetoworkwithapieceofmusic,whetherit’sgoingtobealongpieceorashortpieceofmusic.Andthat’softendependentonwhoever’scommissioningthepiece.Exactlyhowlongitis,howmanyminutesitendsupbeing—that’sworkedoutbymusicalintuition,whichistherock-bottomfoundationofcomposingmusicforme,and,Ithink,formostcomposers.Inotherwords,yousketchoutthenumberofmovementsyou’regoingtohave,andthebasicharmoniesyou’regoingtobeusingtogetthroughthemovements,andtherestisworkedoutindetaillargelybyintuition,bylisteningtothemusicitself.”

BarryAdamson(NickCaveandtheBadSeeds):“Iguessthere’sapointwhereallthecriteriaaresatisfied,andalso,sometimesthere’sanimmediatefeelingthatyoudidn’twritethesong,thatit’ssomethingperfectandseparatefromyourself,becausenowyou’rehearingthefinishedthingandyoucan’trememberhowitwasputtogether.”

Momus(a.k.a.NickCurrie):“Iworkveryquickly.Concept,lyricalnotes,chordstructure,bassline,percussion,morearrangement,vocal,mix.It’susuallyalldoneinoneultra-concentratedsessionofperhapseighthours.Aday’swork.It’sfinishedwhenyougetthemixyoulike,simpleasthat.It’simportanttomenottoleavethingsopen.Iliketomakequickdecisions,andbringthingstoaconclusion.ThisisprobablyonereasonI’msoprolific.”

JohnHughesIII(soundtrackcomposer):“Withme?Idon’tknow.Ithinkthat’sthebiggestproblemforme.Iknow,withothermusicians,too,it’sjustsortofnotknowingwhentostop.So,usually,IusuallyfeelmybeststuffisthestuffIdon’tfeellikeIhavetokeepworkingon.Usually,ifthere’ssomethingthatIkeeponaddingstuffto,andchangingitoverandover,it’sprobablyalreadydead,andthecoreofitjustisn’tright.Usually,myfavoritestuff,I’llgetdonereallyquick,andthelongerIdwellonit—Idon’tknowifit’sjustbecauseIgetsickofitorwhat—butyoujustkindofknowwhensomething’sdone.”

MikaVainio(PanSonic):“Whenwefeelthatthesongisbearable.”

Three-partform(ABA)SongsfrequentlytaketheformABA,knownasthree-partformorternary/tertiaryform.Thissimpleformisproducedbyvaryingandrepeatingthemelody.Forexample,“Twinkle,Twinkle,LittleStar”statesatune,variesit,andthenrestatesit(whichmakesitABAform).TheBpartheremaybecalledthebridge,orthelink,betweenthetwoAparts.

Here’showthethree-partsongformworks:

Thefirstpart,A,maybeplayedonceorrepeatedimmediately.Themiddlepart,B,isacontrastingsection,meaningit’sdifferentthanthefirstsection.Thelastpartisthesameorverysimilartothefirstpart,A.

Three-partABAformextendstheideaofstatementanddeparturebybringingbackthefirstsection.Bothcontrastandrepetitionareusedinthisform.PopmusicisfrequentlyavariationonABA,calledAABA,whilebluesisoftenAAB.AABAformisusedinsongslike“OvertheRainbow.”

Archform(ABCBA)Musicwritteninarchformismadeupofthreeparts:A,B,andC.Inarchform,theA,B,andCareplayedsequentially,andthenpartBisplayedasecondtime,directlyfollowingtheC,andthesongendswiththereplayingoftheApart.

ComposerBéleBartókusedthisforminmanyofhispieces,includinghisPianoConcertoNo.2andViolinConcertoNo.2.MorerecentexamplesincludeSteveReich’s“TheDesertMusic”andHella’s“BiblicalViolence.”

Chapter15

RelyingonClassicalFormsInThisChapter

Understandingcounterpointandhowitbegan

Reviewingthemanyclassicalandenduringforms

DuringtheGoldenAgeofclassicalmusic,fromthelate1700stothemid-1800s,composerswerecompetingviciouslywithoneanothertocreatenewandmorevibranttypesofmusic.Withtheadoptionofthepianobyclassicalartists,existingwaysofplayingmusiccouldbefurtherdeveloped,includingcounterpoint,whichusesbothhandstocreatemelodyandharmony.Inthischapter,weexplainthedevelopmentofcounterpointanditsuseinavarietyofclassicalformsandgenres,fromsonatasandrondostofugues,symphonies,andmore.

CounterpointasaClassicalRevelationThemostfamousdevelopmentintheGoldenAgeofclassicalmusicwastheemergenceofcounterpointasapopularmusicaltechnique.Composersoftheperiodbeganwritingmusicforthelefthandthatwasjustascomplicatedasthemusicwrittenfortheright.Theleft-handmusictheycreatedoftenmirroredcloselywhattherighthandhadbeenplaying.

PriortotheClassicalperiod,thebasslineinmostmusicwaslimitedtosimplemelodicaccompaniment.ThislimiteduseofthebasslinewasacarryoverfromthemusicoftheCatholicChurch,wheretheorganprovidedsimplebasslines(figuredbass)toaccompanyvocalists.

Theinventionofcounterpointnotonlyenhancedthemelodyofmusicalarrangements,butitalsoblurredexactlywherethemelodyendedandtheharmonybegan.Almosteveryclassicalcomposer,usingalltheformsdiscussedinthischapter,hasusedcounterpointinhisorherownmusic—eventheright-handedones.Figure15-1showsanexampleofcounterpoint.


Figure15-1:ExampleofcounterpointfromJ.S.Bach’s“AusmeinesHerzensGrunde”(“FromtheDepthsofMyHeart”).

SussingOuttheSonataThesonatawasthemostpopularformusedbyinstrumentalcomposersfromthemid-18thcenturyuntilthebeginningofthe20thcentury.ThisformisconsideredbymanytobethefirsttruebreakfromtheliturgicalmusicthathadmadesuchanimpactonWesternmusicfromtheMedievalperiodonthroughtheBaroqueperiod.

Sonatasarebasedonthesong(ternary)form,ABA,whichmeanstheyhavethreedefinedparts:exposition,development,andrecapitulation.(Formoreonthesongformandothercommonforms,checkoutChapter14.)Thetruegeniusofthesonataisthatnotonlydoesitsstructureallowmanyoftherulesofbasicmusictheorytobebroken,butitalsoencouragessuchdefiance.Withasonata,it’sperfectlyallowabletoswitchtoanewkeyandtimesignatureinthemiddleofthesong.Inthefollowingsections,weexplainthethreepartsofasonata.

StartingwiththeexpositionThefirstpartofasonata,calledtheexposition,presentsthebasicthematicmaterialofthemovement,oreachself-containedpartofapieceofmusic.Thispartisalsooftenbrokenupintotwothematicparts:

Firstpart:Generally,thefirstpartoftheexpositionpresentsthemainthemeofthesong,orthemusical“thread”thattiesthepiecetogether.Thisfirstpartusuallyisthelinethatsticksthemostinyourhead.Secondpart:Thesecondpartoftheexpositionisa“reflection”ofthefirstpart,inthatitsoundsalotlikethefirstpartbutisslightlychanged.

PutonBeethoven’sSonatainCMinor,Opus13togetagoodexampleofthesetwodefinedparts,orlookattheexcerptsshowninFigures15-2and15-3fromthesamesonata.


Figure15-2:Excerptfromtheopeningtheme,firstpart,ofBeethoven’sSonatainCMinor,Opus13.


Figure15-3:ExcerptfromthesecondpartofSonatainCMinor,Opus13,whichisareflectivethemeofthefirst.

Movingontosomethingnew:DevelopmentThesecondpartofthesonataform,calledthedevelopment,oftensoundslikeitbelongstoacompletelydifferentpieceofmusicaltogether.Inthispart,youcanmovethroughdifferentkeysignaturesandexploremusicalideasthatarecompletelydifferentfromtheoriginaltheme.

Oftenthispartofthesonataisthemostexciting.Hereyoucanincludeyourbigchordsandincreasetensionwiththeuseofstrongerrhythmandgreaterintervalcontent(numberofintervalstepsbetweeneachnote).

Figure15-4showsanexcerptfromthedevelopmentofSonatainCMinor,Opus13.


Figure15-4:Excerptfromthesecondpart,ordevelopment,ofBeethoven’sSonatainCMinor,Opus13.

TakingarestwithrecapitulationAftertheexcitementofasonata’sdevelopment,itfeelsnaturaltocometorestwhereyoubegan.Thethirdandfinalpartofasonataistherecapitulation,wherethecompositionreturnstotheoriginalkeyandthemusicalthemeexpressedinthefirstsectionandbringsitalltoaclose.Figure15-5showsanexcerptofthefinalmovementofBeethoven’sSonataNo.8.SonatainCMinor,Opus13.


Figure15-5:ExcerptfromthethirdpartofBeethoven’sSonataNo.8.SonatainCMinor,Opus13.

RoundingUptheRondoRondosexpandonthefreedomofexpressioninherentinthesonataform(seetheearliersection“SussingOuttheSonata”)byallowingevenmoredisparatesectionsofmusictobejoinedtogetherbyacommonmusicalsection.TheformulaforarondoisABACA….Technically,witharondoyoucanindefinitelycontinueaddingbrandnewsections—featuringdifferentkeysortimesignatures—toaparticularpiecesolongasyoukeeplinkingthemtogetherwiththeopening(A)theme.TheAsectionofMozart’sRondoAllaTurcatiesmorethansixdifferentmusicalideastogetherusingthisform.SeeFigure15-6foranexcerpt.


Figure15-6:ExcerptfromtheAsectionofMozart’sRondoAllaTurca.

FiguringOuttheFugueAnothermajormusicalformtocomeoutoftheClassicalperiodwasthefugue,theformfullydevelopedbyBach,althoughithadbeenaroundforacenturyorsoprior.Afugueisahighlyevolvedformofimitativecounterpoint,inwhichtwo(ormore)musicallinesusethesametheme,eitheratthesamepitchortransposed.Fuguesaredefinedbythewaythenotesinthetrebleclefandthenotesinthebassclefswitchoffcarryingthemainthemeanddrivingtherhythmofthepiece,resultinginacall-and-responsefeel.

Note,forexample,inFigure15-7howtheeighthnotesandsixteenthnotesappearfirstinoneclefandthenintheother,makingbothclefsalternatelyresponsibleforcarryingtheharmony(eighthnotes)andmelody(sixteenthnotes)ofthemusic.


Figure15-7:ExcerptfromBach’sFugueinCMajor.

CombiningFormsintoaSymphonyLiterally,asymphonyisaharmoniousmeldingofelements.Inmusic,asymphonyisapieceofmusicthatcombinesseveraldifferentmusicalformsandisusuallyperformedbyanorchestra.

Traditionally,asymphonyconsistsoffourmovements(self-containedsectionsinsideasinglemusicalpiece):

Sonataallegro,orfastsonataSlowmovement(freechoice)Minuet(ashort,statelypieceofdancemusicsetintime)Combinationofsonataandrondo

Theideaofasymphonyisthatitcombinesamultitudeofmusicalformsharmoniously,sotheaforementionedpatternisabsolutelynotsetinstone.

Thesymphonyformleavesthefieldformusicalexperimentationwideopen.Somepiecesthathavecomefromthisformarethemostenduringandrecognizableclassicalmusicpieceseverrecorded.Themostfamousone,ofcourse,isBeethoven’sSymphonyNo.5(Opus67),whoseopeningline,“Bu-bu-bu-BUM,”ispossiblythemostuniversallyknownopeningthemeofanytypeofmusic.Figure15-8showsyouthemusicforthislegendarytheme.


Figure15-8:Bu-bu-bu-BUM….

ObservingOtherClassicalFormsTheclassicalformsinthefollowingsectionsareenduringandimportant.They’remoredeterminedbyhowmanyperformersareinvolvedintheperformancethantheofficialstructureofthemusicperformedortheroleoftheperformersthemselves.

ConcertoAconcertoisacompositionwrittenforasoloinstrumentbackedbyanorchestra.Theconcertooftencreatessuperstarsofclassicalmusic,suchaspianistLangLangandviolinistItzhakPerlman.Thesoloistsoftencarryasmuchweightasthelong-deadcomposersthemselvesdo.

DuetAnybodywho’seversatthroughapianolessonhasprobablyplayedaduet,whichisapieceofmusicwrittenfortwopeople.Aduetgenerallyconsistsoftwopianistsorapianistandavocalist.Whenotherinstrumentationisused,suchasabassandaviolin,orsomeothercombination,thetermduoismostcommonlyapplied.

Pianoduetsaremostoftenusedasteachingdevices,withthestudenthandlingthebasicmelodylineandthemoreadvancedpianisthandlingthetrickieraccompaniment.

EtudeAnetudeisabriefmusicalcompositionbasedonaparticulartechnicalaspectofmusic,suchasbuildingscales,designedtohelpinstructtheperformerthroughmusicalexercise.

FantasiaFantasiasarefreeformandtrytoconveytheimpressionofbeingcompletelyimprovisedanddivinelyinspired,andaremostoftenwrittenforasoloinstrumentorasmallensemble.Themodernequivalentofthefantasiaisfreejazz.

Chapter16

TappingIntoPopularGenresandFormsInThisChapter

Dealingwiththeblues

Toppingthechartswithrockandpop

Kickingbackwithjazz

Discussingformwhentalkingaboutpopularmusicistrickybecausethetermisoftenmisused.Thinkofformasbeingthespecificwayapieceofmusicisconstructed,withgoverningrulestothattypeofmusic’sconstruction(suchastheclassicalformsdiscussedinChapter15).Genre,ontheotherhand,referstoasong’sstyle,suchastheinstrumentationused,overalltoneofthemusic,andsoon.

However,somepopularmoderngenresofmusichavebeenaroundlongenoughthatspecificpatternscanbeseenintheiroverallconstruction.Thesegenresare:

BluesFolk/rock/popPopJazz

Wegointomoredetailaboutthesegenresandformsinthefollowingsections.

FeelingtheBluesThebluesisthefirsttrulyAmericanfolkmusic(asidefromtheuniquemusicthattheNativeAmericanshadbeforetheEuropeaninvasion).ThestructureofthebluesisthecommonancestorofprettymuchallotherconstructionsofAmericanpopularmusicandhasbeeninfluentialaroundtheworld.Aroundtheturnofthe20thcentury,fieldholler,churchmusic,andAfricanpercussionhadallmeldedintowhatisnowknownastheblues.By1910,thewordbluestodescribethismusicwasinwidespreaduse.

Bluesmusicusessong,orternary,forminthreepartsthatfollowsanAABApatternofI,IV,andVchordsinagivenscale.(YoucanreadaboutsongforminChapter14.)TheBsectionisthebridge,acontrastingsectionthatpreparesthelistenerorperformerforthereturnoftheoriginalAsection.(Plentyofpeoplecomplainthatrockmusicusesonlythreechords:theI,IV,andVchords.Well,thatallstartedwiththeblues!)

Thebluesisalmostalwaysplayedin4/4time,withtherhythmbeatouteitherinregularquarternotesorineighthnotesandwithstrongaccentsgivenonboththefirstandthirdbeatsofeachmeasure.

Themostcommontypesofbluessongsarethe12-barblues,the8-barblues,the16-barblues,the24-barblues,andthe32-barblues.The“bar”referstohowmanymeasuresareusedineachstyleofblues(seeChapter4formoreaboutmeasures).Ifyou’reinabluesymood,checkoutthefollowingsectionsformoreonthesecommonbluessongtypes.

12-barbluesThenameisprettyself-explanatory:In12-barblues,youhave12bars,ormeasures,ofmusictoworkwith.Ineachverseofthe12-barblues(youcanhaveasmanyversesasyouwant,butusuallya12-barbluescompositionhasthreeorfour),thethird4-barsegmentworkstoresolvetheprevious4bars.Theresolution,orconclusion,totheIchordattheendoftheversemaysignaltheendofthesong.Or,ifthe12thbarisaVchord,theresolutiontotheIchordsignalsthatyougobacktothebeginningofthesongtorepeattheprogressionforanotherverse.Ifthesongcontinuesontoanewverse,theVchordattheendofthesongiscalledtheturnaround.

Themostcommonlyusedpattern—readfromlefttoright,startingatthetopandworkingdown—forthe12-barblueslookslikethis:

I I I I

IV IV I I

V IV I V/I(turnaround)

Soifyouwereplayinga12-barbluessonginthekeyofC,youwouldplayitlikethis:

C C C C

F F C C

G F C G/C(turnaround)

Ifyoucanhitthosechordsinthatorder,youhavethebarebonesforMuddyWaters’sclassic“YouCan’tLoseWhatYouAin’tNeverHad.”Changethetonic(I)chordtoanA(AAAADDAAEDAE/A),andyouhaveRobertJohnson’s“CrossroadsBlues.”

Ifyou’replayingthe12-barbluesinaminorkey,here’sthecommonpatterntouse:

i iv i i

iv iv i i

ii V i v/i(turnaround)

CountBasie’sfamousandmuch-lovedvariationonthe12-barbluestookelementsofboththemajorandminorkeys,asshownhere:

I IV I v

IV IV I VI

ii V I v/I(turnaround)

8-barblues8-barbluesissimilarto12-barblues—itjusthasshorterversesinitandaslightlydifferentcommonuseofchordprogressions.Here’sthestandardpatternusedfor8-barblues:

I IV I VI

ii V I V/I(turnaround)

16-barbluesAnothervariationonthebasic12-barbluesisthe16-barblues.Wherethe8-barbluesisfourbarsshorterthanthe12-barblues,the16-barblues,asyoucanprobablyguess,isthatmuchlonger.

The16-barbluesusesthesamebasicchordpatternstructureasthe12-barblues,withthe9thand10thmeasuresstatedtwice,likeso:

I I I I

IV IV I I

V IV V IV

V IV I V/I

24-barbluesThe24-barbluesprogressionissimilartoa12-bartraditionalbluesprogressionexceptthateachchordprogressionisdoubledinduration,likeso:

I I I I

I I I I

IV IV IV IV

I I I I

V V IV IV

I I I V/I(turnaround)

32-barbluesballadsandcountryThe32-barbluespatterniswhereyouseethetruerootsofrockandjazzmusic.Thisextendedversionofthe12-barbluespatternhastheAABAstructure,alsocalledsongform,thatwasadoptedbyrockbandsinthe1960s.ThepatternisalsoreferredtoastheSRDCModel:Statement(A1),Restatement(A2),Departure(B),andConclusion(A3).

Atypical32-barblueslayoutcanlooksomethinglikethis:

(A1) I I VI VI

ii V IV V

(A2) I I VI VI

ii V IV I

(B) I I I I

IV IV IV IV

(A3) I I VI VI

ii V IV V/I

Whenitwasfirstcreated,32-barblueswasn’tnearlyaspopularwith“true”bluesperformersasthe12-barstructurewas,partlybecauseitdidn’tworkaswellwiththeshortcall-and-responseformoflyricismthatearmarkedtheblues.Itdidworkwellforthecountrymusicgenre,though,andHankWilliams(Sr.)usedthisconstructioninsongslike“YourCheatingHeart”and“I’mSoLonesome(ICouldCry).”FreddyFenderusedthisstructureinhishits“WastedDaysandWastedNights”and“BeforetheNextTeardropFalls.”

However,whenthisparticularbluesstructurewaspickedupbypeoplelikeIrvingBerlinandGeorgeGershwin;alot—perhapsall—ofthetrueheartofbluesdisappearedfromtheresultingmusic.The32-barbluestransitionedintopopularsongslike“FrostytheSnowman”and“IGotRhythm.”

The32-barbluesalsowassignificantlyalteredbytheinterventionofotherclassicallytrainedcomposers,whomixedtheideasofthesonataandtherondo(seeChapter15)withthetraditionalAmericanblues.Theresultwastheeventualcreationofnon-bluesy-soundingsongsthatusedsuchaspectsofclassicalmusicastheabilitytochangekeysduringthebridgesectionofasong.

HavingFunwithRockandPopMostearlyrockandpopsongsfollowthestructureofeitherthe12-barbluesorthe32-barblues(seethosesectionsearlierinthischapter).ChuckBerry’s“JohnnyB.Goode”isonevariationofthe12-barbluesstructureusedinrock,asistheRollingStones’s“19thNervousBreakdown.”TheBeachBoysweremastersofthe32-barstructure,usingitinsuchsongsas“GoodVibrations”and“SurferGirl.”TheBeatlesalsousedthisstructureinmanyoftheirsongs,including“FromMetoYou”and“HeyJude.”JerryLeeLewis’s“GreatBallsofFire,”TheRighteousBrothers’s“You’veLostThatLovingFeeling,”andLedZeppelin’s“WholeLottaLove”allalsousetheAABA32-bar.

In32-barpopmusic,themusicisbrokenintofour8-barsections.SongslikeFatsWaller’s“Ain’tMisbehavin’”andDukeEllington’s“ItDon’tMeanaThing”followtheAABA32-barstructure,whereasCharlieParkertooktherondoapproach(ABAC)tothe32-barvariationinsongslike“Ornithology”and“DonnaLee.”

CompoundAABAformreallyshouldbecalledAABAB2form(butitisn’t),becauseinthisform,afteryouplaythefirst32bars,youmoveintoasecondbridgesection(B2)thatsendsyourightbacktothebeginningofthesongtorepeattheoriginal32barsofthesong.TheBeatles’s“IWanttoHoldYourHand,”ThePolice’s“EveryBreathYouTake,”Boston’s“MoreThanaFeeling,”andTomPettyandtheHeartbreakers’s“Refugee”allfollowthispattern.

Theverse-chorusstructure(alsocalledABABform)isthemostwidelyusedforminrockandpopmusictoday.Verse-chorusformfollowsthestructureofthelyricsattachedtoit.Youcan,ofcourse,writeaninstrumentalpiecethatfollowsthesamepatternasaverse-chorusrockorpopsong,butthestructureitselfgetsitsnamefromthewaythewordsinasongfittogether.

FenderopensuptheworldofrockTherealbreakbetweenbluesandrockcamewhenthefirstelectricguitarshitthemarketinthelate1940s.LeoFenderbuilthisfirstsolid-bodyelectricguitar,theprecursortotheTelecaster,outofhisgarageinOrangeCounty,California,aroundthesametimethatLesPaulwasworkingonasimilardesigninNewYork.BothdesignswerelooselybasedonAdolphRickenbacher’ssolid-bodyprototypesthathadbeenmakingtheroundsinthemusicindustrysincethe1930s.Theelectricguitarprovidedtheopportunitytousesuchmusicaldevicesassustainanddistortion,whichwerepreviouslyunavailabletoyouraveragebluesmanwithanacousticguitar.

Verse-chorussongsarelaidoutlikethis:

Introduction(I):Theintroductionsetsthemoodandisusuallyinstrumental,althoughsometimesitmayincludeaspokenrecitation,likeinPrince’s“Let’sGoCrazy.”Verse(V):Theversebeginsthestoryofthesong.Chorus(C):Thechorusisthemostmemorablelyricalpointsofthesong—thesong’shook.Verse(V):Anotherversecontinuesthestory.Chorus(C):Thesecondchorusreinforcesthehook.Bridge(B):Thebridge,whichmaybeinstrumentalorlyrical,usuallyoccursonlyonceinthesongandformsacontrastwiththerepetitionofversesandchoruses.Chorus(C):Thefinalchorusrepeatstheoriginalchorustofade,oritjuststopsattheIchord.

Thetypicalrockandpopsongstructure,aswedescribeithere,isIVCVCBC.Andjustasinthe12-barbluesstructure,thechordsofchoicearetheI,IV,andVchords.

Thousands,perhapsevenmillions,ofpopularsongsfollowthisstructure.TheBeatles’s“Ob-La-Di,Ob-La-Da,”TomJones’s“SexBomb,”KennyRogers’s“TheGambler,”LadyGaga’s“PokerFace,”andEminem’s“LoseYourself”areallexamplesofthisstructureusedincontemporarypopmusic.Thereallyamazingthingishowdifferentfromoneanother,eitherbyvirtueoflyricsorthemusicitself,onesongcansoundfromthenext.

MarkMallman,musician,ontherulesDon’tlettheorybringyoudown.Theoryisthetoolthatyouusetogetwhereyouwanttogo.Justremember,you’rethebossofyourmusic.Butatthesametime,theoryisalanguagethatwillenableyoutocommunicatemoredecisivelyandmoreeasilywithothermusicians.Sometimes,I’llfindtheneedtobringinanextrabassist,andI’llgettheseguyswhosetechniqueisgreat,andtheyknowallthesetunes,buttheyhavenotheorytraining.I’llyellout,“Let’sgouptothe5!”duringthecourseofasong,andittakesthemforevertofigureoutwhatwe’redoing,andIcan’tusesomeonelikethat.Everymusicianshouldknowthebasicsofmusictheory,likescales,andhowrhythmworks,thereallysimplestuffthatyoucanlearninaweek.KnowingthisstuffislikehavingallthesecretstomakingitthroughSuperMarioBrothers.There’sthismagicthathappensinabandsettingwheneveryoneknowswheretheotherpersonisgoingwithasong,andyoucan’thavethatmagicwithoutknowingtheory.

ImprovisingwithJazzThetruespiritofjazzhasalwaysbeenimprovisation,whichmakesidentifyingtheactualconstructionofjazzmostdifficult.Thegoalinjazzistocreateanewinterpretationofanestablishedpiece(calledastandard),ortobuildonanestablishedpieceofmusicbychangingthemelody,harmonies,oreventhetimesignature.It’salmostlikethepointofjazzistobreakawayfromform.

Theclosestwaytodefinehowjazzisconstructedistotakethebasicideabehindbluesvocalizations—thecall-and-responsevocals—andreplacethevoiceswiththevariousinstrumentsthatmakeupthejazzsound:brass,bass,percussive(includingpiano),andwindinstruments,alongwiththemorerecentinclusion,theelectricguitar.InDixielandjazz,forexample,musicianstaketurnsplayingtheleadmelodyontheirinstrumentswhiletheothersimprovisecountermelodies,orcontrastingsecondarymelodies,thatfollowalonginthebackground.

Theonepredictableelementofmusicinthejazzgenre—excludingfreejazz,wherenorealdiscerniblerulesexistbutjazzinstrumentationisused—istherhythm.Alljazzmusic,withtheexceptionoffreejazz,usesclear,regularmeterandstronglypulsedrhythmsthatcanbeheardthroughoutthemusic.

ThePartofTens

EnjoyanadditionalPartofTenschapteronlineatwww.dummies.com/extras/musictheory.


Inthispart…Knowtheanswerstofrequentlyaskedquestionsaboutmusictheory.Learnthedifferentwaysamusicalscorecanbepresented.Getthebackstoryofsomeofhistory’smostimportantcontributorstomusictheory.

Chapter17

TenFrequentlyAskedQuestionsaboutMusicTheory

InThisChapterKnowingwhatmusictheorycandoforyou

Reviewingsomeofthetopqueriesaboutmusictheory

Youmayhaveskippedtothischapterjusttoseewhetheryourtop-tenquestionsmatchtheoneslistedhere.Withoutthebenefitofawrite-incampaign,wecan’tpossiblyknowexactlywhat’stickingawayinallthosemusicallymindedheadsoutthere,butwegaveitashot.Withthischapter,weaimtoanswertenquestionswe’remostfrequentlyaskedaboutmusictheory,includingwhyit’simportanttomusicalstudiesandwhatitcanhelpyouaccomplish.

WhyIsMusicTheoryImportant?Musictheoryhelpspeoplebetterunderstandmusic.Themoreyouknowaboutmusictheory,thebetteryourcomprehensionofmusic,andthebetteryouwillplayandcompose(ifthat’syourcupoftea).It’slikelearningtoreadandwrite:Theseskillscanhelpyoucommunicatebetter.Aretheyabsolutelynecessary?No.Aretheytremendouslyhelpful?Yes.

Here’sjustoneexample:Byknowinghowtoreadmusic,youcanknowexactlywhatacomposerwantedyoutohearinthepieceofmusicheorshewrotedown,nomatterhowmanyyearsseparatethetwoofyou.

IfICanAlreadyPlaySomeMusicWithoutKnowingMusicTheory,WhyBotherLearningIt?

Plentyofpeopleintheworldcan’treadorwrite,yettheycanstillcommunicatetheirthoughtsandfeelingsverbally.And,similarly,manyintuitive,self-taughtmusicianshaveneverlearnedtoreadorwritemusic.Manyofthemfindthewholeideaofmusictheorytediousandunnecessary.

However,theissueiseducational.Leapsandboundscomefromlearningtoreadandwrite.Inthesameway,musictheorycanhelpmusicianslearnnewtechniquesandnewstylesthattheywouldneverstumbleuponontheirown.Itgivesthemconfidencetotrynewthings.Inshort,learningmusictheorymakesyouasmartermusician,whetheryou’replaying,studying,orcomposing.

WhyIsSoMuchMusicTheoryCenteredonthePianoKeyboard?

Akeyboardinstrument,suchasthepiano,hasseveraladvantagesoverotherinstruments—sofarascomposinggoes,anyway.Heretheyare:

Everythingyouneedisrightthere.Themainadvantageofakeyboardinstrumentisthatthetuningofthekeyboardissuchthattheascendinganddescendingnotesarelaidoutrightinfrontofyouinano-nonsensestraightline.Plus,earlyonwhenthepianowasfirstcreated,thenotesmatchedthepitchnotationsalreadybeingusedinsheetmusic.Soinordertogoupahalfstep,yousimplyhadtogooveronekeyfromwhereyoustarted.Thissimpleclaritywas,andstillis,extremelyhelpfulinthecompositionprocess.Fromthefirsttryatplaying,anyonecanmakemusicalnoiseonakeyboard.Withakeyboardthere’snopracticingwithabow,nolearninghowtoproperlyblowoverorintoamouthpiece,andnofingertipcallusesthatneedtobebuiltup.Akeyboardhasahugerange.Nolimitexiststohowmanyoctavesyoucanpileonakeyboard.Thethreetofouroctavesofthepiano’spredecessor,theharpsichord,wereadequatetocovertherangeofmusicbeingperformedinthe16thcentury.Astheharpsichordquicklyinspiredinstrumentslikethevirginal,thespinet,theclavichord,andeventuallythepiano,moreoctaveswereaddedtothebasicform,untilitbecametheeight-octave,concert-readymonsterusedtoday.

IsThereaQuickandEasyWaytoLearntoReadMusic?

Doesanythinghelpmakelearningtoreadmusicanyeasier?Ofcourse.Allfirst-yearmusicstudentsaregivenacoupleofcheesymnemonicstohelpthemmemorizethelinesandspacesofthetrebleandbassclefs.

Herearejustafewmnemonicstoconsider(andifcomingupwithyourownphrasesworksbetter,goforit!):

Trebleclef(frombottomtotopofstaff)Notesonthelines:EveryGoodBoyDeservesFudge(EGBDF).Notesonthespaces:FACE.That’sit—everyoneusesthisone.

Bassclef(frombottomtotopofstaff)Notesonthelines:GoBuyDonutsForAlan(GBDFA).Notesonthespaces:AllCowsEatGrass(ACEG).

HowDoIIdentifyaKeyBasedontheKeySignature?

Determiningthekeyofapieceofmusicisarealdoozie,especiallyformusicianswhoaren’tcomfortablefollowingapieceofsheetmusicnotefornotebutwhowanttosoundliketheyknowwhatthey’redoingrightoutofthegate—asopposedtonoodlingarounduntiltheyfigureoutwhattheothermusiciansareplaying.

Ifyouknowwhetherapieceofmusiciswritteninamajororminorkey,you’reonyourwaytodeterminingthekey.Withalittlepractice,youcanusuallyfigureoutwhetherapieceisinmajororminorafterhearingjustoneortwomeasuresofasong.Herearesomequickrules:

Ifthekeysignaturehasnosharpsorflats,thepieceisinCmajor(orAminor).Ifthekeysignaturehasoneflat,thepieceisinFmajor(orDminor).Ifthekeysignaturehasmorethanoneflat,thepieceiswritteninthekeyofthenext-to-lastflatinthekeysignature.Ifthekeysignaturehassharps,takethenoteofthelastsharpandgouponenote(changingthelettername).IfthelastsharpisDsharp,thekeyisE.Ifit’sFsharp,thekeyisG.Therelativeminorofakeyisaminorthirddownfromthemajor.Sowhenyoumovethreeadjacentkeys,blackorwhite,totheleft—orthreefretsuptheguitarneck(towardthetuningpegs)—youlandontherelativeminor.

Formoreonthemajorandminorkeys,fliponovertoChapters7and8.

CanITransposeaPieceofMusicintoAnotherKey?

Totransposeapieceofmusicintoanotherkey,youcansimplymoveeverynoteinthepieceupordownbythesameinterval.Forexample,totransposeasongthatyoualreadyknowinthekeyofGintothekeyofC,youneedtomoveeverythingupaperfectfourthordownaperfectfifth.

Anotherwaytotransposeasongistolearnthescaledegreesoftheoriginalpieceofmusic,andthenplaythosesamescaledegreesinthenewkey.MusicCompositionForDummies,writtenbyScottJarrettandHollyDay(Wiley),goesintotransposingmusicingreaterdepth.

WillLearningMusicTheoryHinderMyAbilitytoImprovise?

Learningmusictheorywillabsolutelynotthwartyourimprovskills!Learningpropergrammardidn’tkeepyoufromusingslangorswearing,didit?Seriously,though,understandingthebasicsofmusictheory,especiallychordprogressionsandscaledegrees,willmakeplayingwithothermusiciansandimprovisingthatmucheasier.

DoINeedtoKnowTheoryifIJustPlayDrums?

Alotofdrummers,especiallyearlyon,taketheirroleofbeingdrummertomeanthattheydetermineandkeepthebeatandthateveryoneelseisfollowingtheirlead.Areallygooddrummer,however,realizesthathe’salsoapartoftheband.Heacknowledgesthatinordertoplaywitheveryoneelse,heneedstoknowhowtimesignaturesandnotevaluesworkandhowtousetempoanddynamicstobestfiteachindividualsongjustasmuchaseveryoneelseintheband.Adrummerwhoplaysloudandfastorsoftandslowallnightforeverysinglesonggetsboring.Theguywhocanmixitupandcanplayloudandsoftandfastandslowaddscontrastandmakesthemusicthatmuchmoreinteresting.

WhereDothe12MusicalNotesComeFrom?

Manytheorieshavebeenbandiedaboutregardingtheoriginofthe12notesusedinmusictoday.Somepeoplethinktheiroriginisinmath.Thenumber12iseasilydivisiblebythenumbers2,3,and4,whichmakesforaneasydivisionofthetonesbetweenanoctave.

OthertheoristssaythatPythagoras,aGreekfromtheislandofSamos,hadaculturalreverenceforthenumber12and,therefore,madehisversionoftheCircleofFifthswith12pointsonit.

Ifcomposershadstrictlyusedthesolfègemodel(seeChapter19formoreonsolfège)andabandonedPythagoras’sCircleofFifths(checkoutChapter8),today’smodelwouldhaveninepointsonitinstead.Thebestanswertothequestionofthenotes’origin,however,isfromSchoenberg,whosaidascalehad12notessimplybecause1plus2equals3.Manynon-Westerncultureshavemoreorfewerpitchesintheirmusicalsystemsofscalesandoctaves.

HowDoesKnowingTheoryHelpMeMemorizeaPieceofMusic?

Ifyouknowscales,chords,andintervals,youcanapplyallthisinformationtowhateverpieceofmusicyou’relearningtoplay.Whenyouunderstandtheformandcompositionaltechniquesusedinapiece,itsimplifieswhatyouneedtomemorizeforperformances,bothsoloandinagroup.Knowinghowamusicalpieceisconstructedmakesiteasiertoanticipatewhatneedstocomenextinapiece.

Anothergoodwaytolearnapieceofmusicistodividethepieceintosmallerparts,andthenplayeachofthosesmallpartsuntilyoucanplaythemfrommemory.AswediscussinChapters15and16,manypiecesofmusicarecomposedofsectionsofmusicusedagainandagainwithonlyslightvariations.

Chapter18

TenKeystoReadingaMusicalScoreInThisChapter

Howtoreadsheetmusic

Anoverviewofdifferenttypesofsheetmusic

Oneofthemainreasonsthatmusictheoryexistsatallissomusicianscanwritetheircompositionsdownforothermusicianstoplay.Evenifthoseothermusicianshaveneverheardtheoriginalpiece,iftheycanreadmusic,theycanplaythepieceexactlyhowtheoriginalcomposerintended.Aslongaspeopleknowhowtoreadmusicalnotation,thatpieceofmusiccanbeplayedandreplayedbymusiciansincountriesaroundtheworldtheoreticallyforever.

Youcanfindmanydifferentwaystorepresentapieceofmusic,dependingonhowmanymusiciansormusicalinstrumentsareinvolved,ifthepiecehasvocals,orevenifacomplicatedpiecehasbeenscaleddownintosomethingabeginningmusiciancanplayfirsttimeout.Wesummarizeafewofthemusicalnotationsyoumightseeinthesectionsbelow.

TheBasicsWhilemanyofthebasicmusictheoryconceptsseemtobealmostuniversal,thewaysheetmusicitselfiswrittenoutgenerallyfollowsthewritingpatternsofthesocietyresponsibleforthecreation.Therefore,dependingonthepartoftheworldthecartographeriswritingmusicfor,scorescanbefoundthataremeanttobereadfromlefttoright,fromrighttoleft,orinverticalcolumns.Thisbook,however,concentratesonlyontheEuropeanstandardofmusicalnotation,whichisalwaysreadfromlefttoright,justlikeapieceofwriting.

LeadSheetsAleadsheetconsistsofthemelodyofapieceofmusic—usuallysomethingpopularandeasilyidentifiable—andmostoftenjustcontainsonemusicalstaff.Itoftenhasthelyricswrittenunderneaththenotes,withthechordnamesorchordchartsforaccompanimentwrittenonthetopofthemusic.Leadsheetsareagreat,quickwaytolearnhowtoplayasongonguitar.Youcandigupatonofpopularmusicleadsheetcollections,calledfakebooks,outthereforpeoplewhojustwanttoknowhowtoplaytheirfavoritesongswithoutmessingaroundwithmemorizingscalesorreadingnotes.

FullScoresAfullscoreisamusicalscorethatcontainsmusicforeveryinstrumentusedintheperformance.Generally,eachinstrumentgetsitsownstaffinafullscore,becausealltheinstrumentsareusuallyperformingaslightlydifferentpiecethaneachother.You’remostlikelytoseeoruseafullscoreforanyperformancethatusesalargeensembleofmusicalperformers,suchasanorchestraoramarchingband.

MiniatureScoresAminiaturescoreissimplyanymusicalscorethathasbeenreducedbyasignificantpercentfromitsoriginalsize.Butdonotbedeceived—thisdoesn’tnecessarilymeanthataminiaturescoreissmall.Someprintedminiaturescoresareaslargeasaregularmusicscore,buthavebeenreducedfromaverylargeoriginalscore.Mostminiaturescoresaremadethatwayforportabilityreasons,especiallytheverylargeones,andareveryoftenmadeforpurelyaestheticreasonsforcollectorsoforiginalmusicalcompositions.

StudyScoresAstudyscoreisaprintedscorewithadditionalacademicmarkingsandanalyticalcommentsaddedtothemusic.You’remostlikelytofindstudyscoresinanthologycollectionsofsheetmusic.

PianoScoresApianoscoreis,ofcourse,apieceofmusicmeanttobeperformedonpiano.Themusic,whichmayormaynothaveoriginallybeencomposedwithmultipleinstrumentsinmind,iscondensedorsimplifiedtobecontainedinthetrebleandbassclefstaves.

ShortScoresAshortscoreisusuallythefirststepformanycomposerstocreatingafullscore.Itcarriesthebasicharmonyandmelodyofapieceofmusic,uponwhichacomposercanbuildonandexpandintoapieceformultipleinstrumentsandvoices.Mostshortscoresaren’teverpublishedorusedbyanyoneotherthantheoriginalcomposer.

VocalScoresAvocalscoreismusicwrittenoutspecificallyforavocalist,almostlikeacombinationofapianoscoreandaleadsheet.Theentiremusicalaccompanimentiscondensedtoapianoscore,withthevocalpartswrittenoutonseparatemusicalstavesandaswordsbeneaththevocalsection.

TablatureTablature,ortab,isdesignedspecificallyforguitarandbass.Insteadofusingnotes,rests,andstaves,though,tablatureusesASCII(AmericanStandardCodeforInformationInterchange)numbers.Thesenumbersrepresentthefretnumbertobeplayedandareplacedonfourorsixlinesrepresentingtheinstrument’sstrings.Thelimitationoftablatureisthatcomposershavenowaytowritespecificnotevalues,sooftenthepacingofthesongisuptothemusicianplayingthesong,whichcanleadtomanywonderfulinterpretationsofthesamepiece.ButtheupsideisthattablatureusesASCIIcharacters,sowritingoutandsharingmusicwithpeopleontheInternetisinsanelyeasy.YoucangetatonmoreinfoaboutreadingtablatureinbothMusicCompositionforDummiesbyScottJarrettandHollyDay(Wiley)andGuitarForDummies,3rdEdition,byMarkPhillipsandJonChappell(Wiley).

FiguredBassNotionFiguredbassisalittle-usedformofnotationinwhichonlythebassnoteofapieceisgiven,withnumbersgivingtheintervalquantity(scalesteps)neededfortheaccompanimentwrittenaboveorbelowthenote.So,forexample,ifyouhaveanFnotewrittenonastaff,withthenumbers6and4writtenbelowthatnote,itwouldmeanthattheaccompanimentshouldplayafourthandasixthabovetheF(oraBandaD).FiguredbassnotationwasusedextensivelyinBaroquemusicandisveryrarelyusedtoday.

Chapter19

TenMusicTheoristsYouShouldKnowAbout

InThisChapterSeeingwhohadthemostimpactonmusictheory

Consideringmusictheory’sevolution

Theevolutionofmusictheoryandnotationisalmostasamazingastheevolutionofhumanwriting.ModernmusicnotationissortoflikeEsperantothatlotsofpeoplecanunderstand.PeopleallovertheWesternworld,andmuchoftheEasternworldaswell,knowhowtocommunicatewitheachothereffectivelythroughsheetmusic,chordtheory,andtheCircleofFifths.Inthischapter,weintroducetenmusictheoristswhohavehelpeddefinehowwelookatmusicorhavechangedourviewofmusicentirely.

Pythagoras(582–507BC)Anyonewho’severtakenageometryclasshasheardofPythagoras.Hewasobsessedwiththeideathateverythingintheworldcouldbebrokendownintoamathematicalformulaandthatnumbersthemselvesweretheultimatereality.Asaresult,Pythagorascameupwithallsortsofequationsforcalculatingthings.He’sparticularlywellknownforhisPythagoreantheorem.

ThebeautifulthingaboutancientGreekcultureisthatthestudyofscience,art,music,andphilosophywereconsideredonegreatbigpursuit.Soitwasn’tthatstrangeforsomeonelikePythagorastoturnhisattentiontomusicandtrytocomeupwithmathematicaltheoriestodefineit.

Becausethelyrewasthemostpopularinstrumentoftheday,it’sonlynaturalthatPythagorasuseditandotherstringedinstrumentstocreatehisworkingmodelforwhatwouldeventuallybecalledthePythagoreanCircle,whichtheneventuallyevolvedintotheCircleofFifths.

Accordingtolegend,Pythagorastookapieceofstringfromalyre,pluckedit,measureditstoneandvibrationrate,andthencutthatstringinhalfandmadeanewsetofmeasurements.Henamedthedifferencebetweentherateofvibrationofthefirstlengthofstringandthesecondanoctave,andthenhewenttoworkbreakingtheoctaveupinto12evenlydividedunits.Everypointaroundthecirclewasassignedapitch

value,andeachpitchvaluewasexactly octavehigherorlowerthanthenotenexttoit.

TheproblemwithPythagoras’sCirclewasthathewasn’tamusician.EventhoughtheCirclewasmathematicallysoundandanamazingconceptualleap,someofthe“tunings”heproposedweren’tparticularlypleasingtotheear.Also,duetovariationsinthesizeofsoundwavesthathe(andeveryoneelsewholived2,500 yearsago)wasn’tprivyto,hisoctavesquicklyfelloutoftunethefartheryouwentfromthestartingpoint.Forexample,ahighC,tunedtohisperfectfifths,wasdefinitelynotintunewithalowC,becauseinhissystemyoumovedjustabitoutofpitchwitheachnewoctaveinbetween.

Forthenext2,000 years,musiciansandtheoristsalikeconcentratedontemperingthisCircle,withits12spotsandshapeleftintact,buttheyretunedsomeofhis“perfect”fifthsusingPythagoreancommastocreateaCirclethatwasmuchmoremusician-andaudience-friendly.Tocheckoutthemodern-dayCircleofFifths,seeChapter8.

Boethius(480–524AD)Ifithadn’tbeenfortheRomanstatesmanandphilosopherAniciusManliusSeverinusBoethius,theGreekcontributiontomusictheorymayhavebeencompletelylost,alongwithmuchofEurope’sownmusicalhistory.BoethiuswasaremarkablemanwhodedicatedhisshortlifetostudyingGreekmathematics,philosophy,history,andmusictheory.HewasthefirstscholarafterPythagorastotrytoconnectthepitchofanotewiththevibrationofsoundwaves.

Notcontenttositathomewritingbooks,Boethius’smostambitiousprojectwasalsooneofhismostenduring.HebeganventuringoutintothewesternEuropeancountrysidewithmusicscribeswhotranscribedthefolkmusicofthedifferentgroupsofpeoplethatmadeupthelandscape.Becauseofthiswork,youcanstillheartodaywhatsortofmusicruralpeoplewereplayingandsingingduringthistimeperiod.

Formalmusictraditionallydidn’thavelyrics;musicwithlyricswasconsideredlowbrowandaestheticallyinbadtaste.Ironically,hisstudyofcommonmusicledtoBoethius’sexplorationofwritingsongswithlyricsthattoldastory—anideathatwouldonedayleadtoahighbrowgenreofmusic:theopera.

Sadly,beforeBoethiuscouldwritehisownfullyformedopera,ortranslatetheentireworksofPlatoandAristotle,orcomeupwithaunifyingtheorytoexplainGreekphilosophy(allthreewerelifetimegoalsofhis),hewasthrowninprisonunderchargesofpracticingmagic,sacrilege,andtreason.

Despitefacingadeathsentence,Boethiuscontinuedtowriteinprison.HislastworkwastheDeconsolationephilosophia(TheConsolationofPhilosophy),anovella-sizedtreatiseabouthowthegreatestjoysinlifecamefromtreatingotherpeopledecentlyandfromlearningasmuchaspossibleabouttheworldwhileliving.Wellintothe12thcentury,Boethius’smanytextswerestandardreadinginreligiousandeducationalinstitutionsalloverEurope.

Gerbertd’Aurillac/PopeSylvesterII(950–1003)

GerbertofAurillac,laterknownasPopeSylvesterII,wasborninAquitaine.HeenteredtheBenedictinemonasteryofSt.GeraldinAurillacwhenhewasachildandreceivedhisearlyeducationthere.Highlyintelligentandavoraciousreader,GerbertroseupamongtheranksofthemonasterysoquicklythatrumorsbeganthathehadreceivedhisgeniusfromtheDevil.

From972to989,GerbertwastheabbotattheroyalAbbeyofSt.RemiinReims,France,andattheItalianmonasteryatBobbio(Italy).AtSt.Remi,hetaughtmathematics,geometry,astronomy,andmusic,incorporatingBoethius’smethodofteachingallfouratonceinasystemcalledthequadrivium.Atthetime,thelawsofmusicwereconsideredtobedivineandobjective,andlearningtherelationshipsamongthemusicalmovementofthecelestialspheres,thefunctionsofthebody,andthesoundsofthevoiceandmusicalinstrumentswasimportant.

GerbertresurrectedaninstrumentfromancientGreececalledamonochordforhisstudents,fromwhichitwaspossibletocalculatemusicalvibrations.HewasthefirstEuropeanafterthefallofRometocomeupwithastandardnotationofnotesintonesandsemitones(halfsteps).Hewroteextensivelyaboutthemeasurementoforganpipesandeventuallydesignedandbuiltthefirsthydraulicallypoweredmusicalorgan(asopposedtothehydraulicallypoweredsirenoftheRomanarenas).Itexceededtheperformanceofanyotherpreviouslyconstructedchurchorgan.

GuidoD’Arezzo(990–1040)GuidoD’ArrezowasaBenedictinemonkwhospentthefirstpartofhisreligioustrainingatthemonasteryofPomposa,Italy.Whilethere,herecognizedthedifficultysingershadinrememberingthepitchestobesunginGregorianchantsanddecidedtodosomethingaboutit.Hereworkedtheneumaticnotation(earlymusicmarkings)usedinGregorianchantanddesignedhisownmusicalstaffforteachingGregorianchantsmuchfaster.Heattractedpositiveattentionfromhissupervisorsbecauseofhiswork.However,healsoattractedanimosityfromtheothermonksinhisownabbeyandsoonleftthemonasticlifeforthetownofArezzo,whichhadnoofficialreligiousorderbutdidhavealotofdecentsingerswhodesperatelyneededtraining.

WhileinArezzo,heimprovedhismusicalstaff.Headdedatimesignatureatthebeginningtomakeiteasierforperformerstokeepupwithoneanother.Healsodevisedsolfège,avocalscalesystemthatusedsixtones,asopposedtothefourtonesusedbytheGreeks—ut(laterchangedtodo),re,mi,fa,so,andla—tobeplacedinspecificspotsonthestaff.Later,whenthediatonicscalewascombinedwiththe“GuidonianScale,”asit’ssometimescalled,thetisoundfinishedtheoctave(latermakingTheSoundofMusicpossible).TheMicrologus,writtenatthecathedralatArezzo,containsGuido’steachingmethodandhisnotesregardingmusicalnotation.

NicolaVicentino(1511–1576)NicolaVicentinowasanItalianmusictheoristoftheRenaissanceperiodwhoseexperimentswithkeyboarddesignandequal-temperamenttuningrivalthoseofmany20thcenturytheorists.Around1530,hemovedfromVenicetoFerrara,ahotbedofexperimentalmusic.HeservedbrieflyasamusictutorfortheDukeofEstetosupporthimselfwhilewritingtreatisesontherelevanceofancientGreekmusictheoryincontemporarymusicandonwhy,inhisopinion,thewholePythagoreansystemshouldbethrownoutthewindow.Hewasbothadoredandreviledbycontemporariesforhisdisdainforthe12-tonesystemandwasinvitedtospeakatinternationalmusicconferencesonhisbeliefs.

Vicentinoamazedthemusicworldevenmorewhen,tofurtherprovetheinadequaciesofthediatonicscale,hedesignedandbuilthisownmicrotonalkeyboardthatmatchedamusicscaleofhisowndevising,calledthearchicembalo.Onthearchicembalo,eachoctavecontained31tones,makingitpossibletoplayacousticallysatisfactoryintervalsineverykey—predatingthewell-temperedmeantonekeyboardinusetodaybynearly200years.Unfortunately,heonlybuiltafewoftheinstruments,andbeforehisworkcouldcatchon,hediedoftheplague.

ChristiaanHuygens(1629–1695)ChristiaanHuygensdidasmuchforscienceandthescientificrevolutionofthe17thcenturyasPythagorasdidformathematics.Huygenswasamathematician,astronomer,physicist,andmusictheorist.Hisdiscoveriesandscientificcontributionsarestaggeringandwellknown.

Inhislateryears,heturnedhisimmensebraintotheproblemofmeantonetemperament—asystemoftuningmusicalinstruments—inthemusicalscaleanddevisedhisown31-tonescale,whichheintroducedinhisbooksLettreTouchantleCycleHarmoniqueandNovuscyclusharmonicus.

Inthesebooks,hedevelopedasimplemethodforcalculatingstringlengthsforanyregulartuningsystem,workedouttheuseoflogarithmsinthecalculationofstringlengthsandintervalsizes,anddemonstratedthecloserelationshipbetweenmeantonetuningand31-toneequaltemperament.

AsmuchaspeopleinthescientificcommunityapplaudedHuygens’sgenius,peopleinthemusicalworldweren’tyetready(andstillaren’t)togiveuptheirPythagorean12-tonescale.Soasidefromafewexperimentalinstrumentsbuiltonhiscalculations,themainprincipleadoptedfromhistheorieswastorebuildandretuneinstrumentssothat12tonescouldfinallybuildatrueoctave.

ArnoldSchoenberg(1874–1951)ArnoldSchoenbergwasanAustrian-borncomposerwhoimmigratedtotheU.S.in1934toescapeNazipersecution.He’sprimarilyknownforhisexplorationsofatonalismand12-tonemusicalsystems(or,serialism),butSchoenbergwasalsoanaccomplishedexpressionistpainterandpoet.

Schoenberg’scompositionsweren’twell-receivedinhishomecountry.Thepresstheredeclaredhim“insane”afterhearingaperformanceof“StringQuartet#2,op.10.”Hispiece“PierreLunaire,”whichfeaturedawomanalternatelysingingandramblingaboutwitchcraftagainstabackdropofseeminglycompetinginstruments,wasdubbed“creepyandmaddening”byhiscriticsinBerlin.Hismusic,alongwithAmericanjazz,waseventuallylabeled“degenerateart”bytheNaziParty.

Throughouthiscareer,Schoenberg’sworkfeaturedmanyfirsts.Hissymphonicpoem,“PelleasandMelisande,”featuredthefirstknownrecordedtromboneglissando.Hisopera,“MosesundAron,”wasthefirstonetodrawonbothhisexperimentswiththe12-toneseriesandonatonality.Hismostmassivecomposition,“Gurrelieder,”combinedorchestra,vocals,andanarrator—over400performerswererequiredfortheoriginalperformanceofthepiece.Eventoday,hisvibrantcompositionsfeeldisturbing,chaotic,beautiful,andamazinglycontemporary.

HarryPartch(1901–1974)Atage29,HarryPartchgatheredup14yearsofmusichehadwritten,basedonwhathecalledthe“tyrannyofthepiano”andthe12-tonescale,andburneditallinabigironstove.Forthenext45years,Partchdevotedhisentirelifetoproducingsoundsfoundonlyinmicrotonalscales—thetonesfoundbetweenthenotesusedonthepianokeys.

Partchdevisedcomplextheoriesofintonationandperformancestoaccompanythem,includinga43-tonescale,withwhichhecreatedmostofhiscompositions.Becausetherewerenoavailableinstrumentsuponwhichtoperformhis43-tonescale,Partchbuiltapproximately30instruments.

SomeofhisremarkableinstrumentsincludetheKitharasI&II,lyre-likeinstrumentsmadeofglassrodsthatproducedglidingtonesonfourofthechords;twoChromelodeons,reedpumporganstunedtothecomplete43-toneoctavewithtotalrangesofmorethanfiveacousticoctaves;theSurrogateKithara,withtwobanksofeightstringsandslidingglassrodsunderthestringsasdampeners;andtwoAdaptedGuitarsthatusedaslidingplasticbarabovethestrings,withonestringtunedtoasix-stringunisonwitha1:1frequencyratioandtheothertunedtoaten-stringchordwhosehigherthreenotesareafewmicrotonalvibrationsapart.

Partch’sorchestrasalsoincorporatedunusualpercussiveinstruments,suchasthesub-bassMarimbaEroica,whichusedtonesthatvibrateatsuchalowfrequencythatthelistenercan“feel”thenotesmorethanhearthem;theMazdaMarimba,madeupoftunedlightbulbsseveredatthesocket;theZymo-Xyl,whichcreatedloud,piercingshrieksbyvibratingsuspendedliquorbottles,autohubcaps,andoarbars;andtheSpoilsofWar,whichconsistedofartilleryshellcasings,Pyrexchemicalsolutionjars,ahighwoodblock,alowmarimbabar,springsteelflexitones(WhangGuns),andagourd.

KarlheinzStockhausen(1928–2007)Stockhausen’sgreatestinfluenceasatheoristcanbestbefeltinthegenresofmusicthatcamedirectlyoutofhisteachings.Duringthe1950s,hehelpeddevelopthegenresofminimalismandserialism.Muchofthe1970s“krautrock”scenewascreatedbyhisformerstudentsattheNationalConservatoryofCologne,Germany.Histeachingsandcompositionsalsogreatlyinfluencedthemusicalrenaissanceof1970sWestBerlin(notablecharactersincludedDavidBowieandBrianEno).

Inthelongrun,Stockhausencanbeseenasthefatherofambientmusic,andtheconceptofvariableform,inwhichtheperformancespaceandtheinstrumentaliststhemselvesareconsideredapartofacompositionandchangingevenoneelementofaperformancechangestheentireperformance.

He’salsoresponsibleforpolyvalentforminmusic,inwhichapieceofmusiccanbereadupside-down,fromleft-to-right,orfromright-to-left.Or,ifmultiplepagesareincorporatedinacompositioninthisform,thepagescanbeplayedinanyordertheperformerwishes.AsformerstudentandcomposerIrminSchmidtsaid,“StockhausentaughtmethatthemusicIplayedwasmine,andthatthecompositionsIwrotewereforthemusicianswhoweretoplayit.”

RobertMoog(1934–2005)Althoughnooneknowsforsurewhobuiltthefirstfrettedguitarorwhotrulydesignedthefirstrealkeyboard,musichistoriansdoknowwhocreatedthefirstpitch-proper,commerciallyavailablesynthesizer:RobertMoog.He’swidelyrecognizedasthefatherofthesynthesizerkeyboard,andhisinstrumentrevolutionizedthesoundofpopandclassicalmusicfromthedaytheinstrumenthitthestreetsin1966.

HespeciallydesignedkeyboardsforeveryonefromWendyCarlostoSunRatotheBeachBoys,andheevenworkedwithgroundbreakingcomposerslikeMaxBrand.Unfortunately,Moogwasn’tthegreatestbusinessman—orperhapshewasjustverygenerouswithhisideas—andsotheonlysynthesizer-relatedpatentheeverfiledwasforsomethingcalledalow-passfilter.

Whenhefirstbeganbuildingsynthesizers,hisgoalwastocreateamusicalinstrumentthatplayedsoundsthatweredifferentfromanyinstrumentthatcamebefore.However,aspeoplebegantousesynthesizerstore-create“real”instrumentsounds,hebecamedisillusionedwiththeinstrumentanddecidedthattheonlywaytogetpeopletoworkwith“new”soundswastobreakawayfromtheantiquatedkeyboardinterfacealtogether.SohisNorthCarolina-basedcompany,BigBriar,beganworkingonLeonTheremin’stheremindesigntocreateaMIDItheremin,whichwasdesignedtoeliminatetheintervalstepsbetweeneachnotebutstillkeepthetonalcolorofeachindividualinstrument’sMIDIpatch.

Outsideofbuildinginstruments,Moogalsowrotehundredsofarticlesspeculatingonthefutureofmusicandmusictechnologyforavarietyofpublications,includingComputerMusicJournal,ElectronicMusician,andPopularMechanics.Hisideaswerewayaheadoftheirtime,andmanyofhispredictions,suchasthosefromhis1976articleinTheMusicJournalistthatpredictedtheadventofMIDIinstrumentsandtouch-sensitivekeyboards,havealreadycometrue.

PartVI

Appendixes



Inthispart…Findtheaudiotracklist.Takealookatchordcharts.Reviewtheglossary

AppendixA

AudioTracksThefollowingisalistofthisbook’saudioaccompanimenttracks,whichyoucanfindonwww.dummies.com/go/musictheory.Youcandownloadthetrackstoyourcomputerandlistentothemasyoureadthebook.

TableA-1TrackListing

Track Figure Chapter Description

1 7 Amajorscale,pianoandguitar

2 7 Aflatmajorscale,pianoandguitar

3 7 Bmajorscale,pianoandguitar

4 7 Bflatmajorscale,pianoandguitar

5 7 Cmajorscale,pianoandguitar

6 7 Cflatmajorscale,pianoandguitar

7 7 Csharpmajorscale,pianoandguitar

8 7 Dmajorscale,pianoandguitar

9 7 Dflatmajorscale,pianoandguitar

10 7 Emajorscale,pianoandguitar

11 7 Eflatmajorscale,pianoandguitar

12 7 Fmajorscale,pianoandguitar

13 7 Fsharpmajorscale,pianoandguitar

14 7 Gmajorscale,pianoandguitar

15 7 Gflatmajorscale,pianoandguitar

16 7 Anaturalminorscale,pianoandguitar

17 7 Aharmonicminorscale,pianoandguitar

18 7 Amelodicminorscale,pianoandguitar

19 7 Aflatnaturalminorscale,pianoandguitar

20 7 Aflatharmonicminorscale,pianoandguitar

21 7 Aflatmelodicminorscale,pianoandguitar

22 7 Asharpnaturalminorscale,pianoandguitar

23 7 Asharpharmonicminorscale,pianoandguitar

24 7 Asharpmelodicminorscale,pianoandguitar

25 7 Bnaturalminorscale,pianoandguitar

26 7 Bharmonicminorscale,pianoandguitar

27 7 Bmelodicminorscale,pianoandguitar


28 7 Bflatnaturalminorscale,pianoandguitar

29 7 Bflatharmonicminorscale,pianoandguitar

30 7 Bflatmelodicminorscale,pianoandguitar

31 7 Cnaturalminorscale,pianoandguitar

32 7 Charmonicminorscale,pianoandguitar

33 7 Cmelodicminorscale,pianoandguitar

34 7 Csharpnaturalminorscale,pianoandguitar

35 7 Csharpharmonicminorscale,pianoandguitar

36 7 Csharpmelodicminorscale,pianoandguitar

37 7 Dnaturalminorscale,pianoandguitar

38 7 Dharmonicminorscale,pianoandguitar

39 7 Dmelodicminorscale,pianoandguitar

40 7 Dsharpnaturalminorscale,pianoandguitar

41 7 Dsharpharmonicminorscale,pianoandguitar

42 7 Dsharpmelodicminorscale,pianoandguitar

43 7 Enaturalminorscale,pianoandguitar

44 7 Eharmonicminorscale,pianoandguitar

45 7 Emelodicminorscale,pianoandguitar

46 7 Eflatnaturalminorscale,pianoandguitar

47 7 Eflatharmonicminorscale,pianoandguitar

48 7 Eflatmelodicminorscale,pianoandguitar

49 7 Fnaturalminorscale,pianoandguitar

50 7 Fharmonicminorscale,pianoandguitar

51 7 Fmelodicminorscale,pianoandguitar

52 7 Fsharpnaturalminorscale,pianoandguitar

53 7 Fsharpharmonicminorscale,pianoandguitar

54 7 Fsharpmelodicminorscale,pianoandguitar

55 7 Gnaturalminorscale,pianoandguitar

56 7 Gharmonicminorscale,pianoandguitar

57 7 Gmelodicminorscale,pianoandguitar

58 7 Gsharpnaturalminorscale,pianoandguitar

59 7 Gsharpharmonicminorscale,pianoandguitar

60 7 Gsharpmelodicminorscale,pianoandguitar

61 9 Intervalswithaqualityoffifths

62 9 SimpleintervalsintheCmajorscale

63 10 TherootofaCmajorchord

64 10 TherootandthefirstthirdofaCmajorchord

65 10 TherootandfifthofaCmajorchord

66 10 Cmajortriad

67 Figure10-33 10 AM,Am,Aaug,Adim,AM7,Am7,A7,Am7(f5),Adim7,AmiMA7onpiano

68 Figure10-34 10 AfM,Afm,Afaug,Afdim,AfM7,Afm7,Af7,Afm7(f5),Afdim7,AfmiMA7onpiano

69 Figure10-35 10 BM,Bm,Baug,Bdim,BM7,Bm7,B7,Bm7(f5),Bdim7,BmiMA7onpiano

70 Figure10-36 10 BfM,Bfm,Bfaug,Bfdim,BfM7,Bfm7,Bf7,Bfm7(f5),Bfdim7,BfmiMA7onpiano

71 Figure10-37 10 CM,Cm,Caug,Cdim,CM7,Cm7,C7,Cm7(f5),Cdim7,CmiMA7onpiano

72 Figure10-38 10 CfM,Cfm,Cfaug,Cfdim,CfM7,Cfm7,Cf7,Cfm7(f5),Cfdim7,CfmiMA7onpiano

73 Figure10-39 10 CsM,Csm,Csaug,Csdim,CsM7,Csm7,Cs7,Csm7(f5),Csdim7,CsmiMA7onpiano

74 Figure10-40 10 DM,Dm,Daug,Ddim,DM7,Dm7,D7,Dm7(f5),Ddim7,DmiMA7onpiano

75 Figure10-41 10 DfM,Dfm,Dfaug,Dfdim,DfM7,Dfm7,Df7,Dfm7(f5),Dfdim7,DfmiMA7onpiano

76 Figure10-42 10 EM,Em,Eaug,Edim,EM7,Em7,E7,Em7(f5),Edim7,EmiMA7onpiano

77 Figure10-43 10 EfM,Efm,Efaug,Efdim,EfM7,Efm7,Ef7,Efm7(f5),Efdim7,EfmiMA7onpiano

78 Figure10-44 10 FM,Fm,Faug,Fdim,FM7,Fm7,F7,Fm7(f5),Fdim7,FmiMA7onpiano

79 Figure10-45 10 FsM,Fsm,Fsaug,Fsdim,FsM7,Fsm7,Fs7,Fsm7(f5),Fsdim7,FsmiMA7onpiano

80 Figure10-46 10 GM,Gm,Gaug,Gdim,GM7,Gm7,G7,Gm7(f5),Gdim7,GmiMA7onpiano

81 Figure10-47 10 GfM,Gfm,Gfaug,Gfdim,GfM7,Gfm7,Gf7,Gfm7(f5),Gfdim7,GfmiMA7onpiano

82 11 KeyofGmajorchordprogressions

83 11 KeyofCmajorchordprogressions

84 11 KeyofFminorchordprogressions

85 11 KeyofAminorchordprogressions

86 11 Authenticcadence

87 11 Perfectauthenticcadence

88 11 Differencebetweenaperfectauthenticcadenceandanimperfectauthenticcadence

89 11 Plagalcadence

90 11 Twomoreplagalcadences

91 11 Deceptivecadence

92 11 Half-cadence

93 12 80beatsperminute(00:00)100beatsperminute(00:12)120beatsperminute(00:20)

AppendixB

ChordChartThisappendixfunctionsasaquickreferencetothechordsonthepianoandguitar.Itcoversallthekeysandshowseachkey’schordstothe7thdegree.Welistthepianochordsfollowedbytheguitarchords.

Thetrickythingaboutdiagrammingguitarchordsisthatthesamechordcanbebuiltinmanyways,inmanydifferentplacesontheneck.Tomakethingseasier,weincludeonlychordsthatdon’tgobeyondtheuppersevenfretsoftheguitarneck.

Forpiano,thekeystobeplayedinthechordareshowningray.Fortheguitar,blackdotsshowyouwheretoputyourfingersonthefrets.An“X”aboveastringmeansyoudon’tplaythatstring.An“O”aboveastringstandsfor“open,”meaningyouplaythestringbutdon’tfretit.Also,foreachguitarchorddiagram,thepitchesforeachopen(non-fretted)stringare,fromlefttoright,(low)E,A,D,G,B,(high)E.

AppendixC

Glossaryaccompaniment:

Theuseofadditionalmusictosupportaleadmelodicline.atonal:

Musicthatisnotinakeyandnotorganizeddiatonically.augmentationdot:

Adotplacedafteranoteorrestthatextendsitsvaluebyhalfoftheoriginalvalue.Seedottednoteanddottedrest.

barlines:Verticallinesinwrittenmusicthatseparatenotesintodifferentgroupsofnotesandrests,dependingonthetimesignatureused.

bassclef:Thelowerstaffinthegrandstaff.ThebassclefestablishesthepitchofthenotesonthelinesandspacesofthestaffbelowmiddleC.

beam:Abarused(insteadofaflag)toconnectthestemsofeighthnotesandsmallernotes.

beat:Oneofaseriesofrepeating,consistentpulsationsoftimeinmusic.Eachpulsationisalsocalledabeat.

bridge:Thecontrastingmusicalsectionbetweentwosimilarsectionsofmusic.AlsosometimescalledtheBsection.

cadence:Theendingofamusicalphrasecontainingpointsofreposeorreleaseoftension.

callandresponse:Whenasoloistisansweredbyanothermusicianorgroupofmusicians.

chord:Thesimultaneoussoundingofatleasttwopitchesornotes.

chordprogression:Movingfromonechordtoanother,usuallyinestablishedpatterns.

chromatic:Amusicalscalewith12pitches,eachonesemitoneapart.Seediatonic.

compoundtime:Ameterwhosebeatcountcanbeequallydividedintothirds(6/8,9/4,andsoon)withtheexceptionofanytimesignaturethathasa3asthetopnumberofitstimesignature(asin3/4or3/8time).

cuttime:Anothernamefor2/2time.

diatonic:Conformingtothenotesfoundinagivenkey.InapiecewritteninCmajor,forexample,theC,D,E,F,G,A,andBarealldiatonicpitches,andanyothernotesusedinthepiecearenon-diatonic,orchromatic.Seechromatic.

dottednote:Anotefollowedbyanaugmentationdotmeansthenoteisworthoneandahalftimesitsnormalvalue.

dottedrest:Arestfollowedbyanaugmentationdotmeanstherestisworthoneandahalftimesitsnormalvalue.

downbeat:Thefirstbeatofameasureofmusic.

duplet:Apairofjoinednotesusedincompoundtimetodivideabeatthatshouldcontainthreeequalpartsintotwoequalparts.

flag:Acurvedlineaddedtothestemofanotetoindicateareducedrhythmicvalue.Flagsareequivalenttobeams.Seebeam.

form:Theoverallshape,organization,orstructureofamusicalcomposition.

genre:Astyleormannerofmusic.

grandstaff:Thecombinationofthebassclefstaffandthetrebleclefstaff.Seebassclefandtrebleclef.

halfstep:ThesmallestintervalinWesternmusic,representedonthepianobymovingoneadjacentkey,blackorwhite,totheleftorrightfromastartingpoint,orontheguitarbymovingonefretupordownfromastartingpoint.

harmony:Pitchesheardsimultaneouslyinwaysthatproducechordsandchordprogressions.

homophony:Layersofmusicalactivity,suchasmelodyandaccompaniment.

improvisation:Spontaneousmusicalcreation.

interval:Thedistancebetweenthepitchesoftwonotes.

key(signature):Thescaledegreeofapieceofmusic,whichisnormallydefinedbythebeginningandendingchordofasongandbytheorderofwholestepsandhalfstepsbetweentonicscaledegrees.(ThekeyofC,forexample,wouldberepresentedbythefirstCofthescaleandtheCanoctaveabovethefirst.)

leadsheet:Ascaled-down,notatedmelodywithchordsymbols,usuallyforrockorjazzmusic,whichamusicalperformanceisbasedon.

measure:Asegmentofwrittenmusic,containedwithintwoverticalbars,thatincludesasmanybeatsasthetopnumberofthekeysignatureindicates.Ameasureisalsocalledabar.

melody:Asuccessionofmusicaltones,usuallyofvaryingpitchandrhythm,thattogetherhaveanidentifiableshapeandmeaning.

meter:Theorganizationofrhythmicpatternsinacompositioninsuchawaythataregular,repeatingpulseofbeatscontinuesthroughoutthecomposition.

middleC:TheCnotelocatedoneledgerlinebelowthetreblestafforonelineabovethebassstaff.Seestaffandgrandstaff.

notation:Theuseofwrittenorprintedsymbolstorepresentmusicalsounds.

note:Asymbolusedtorepresentthedurationofasoundand,whenplacedonamusicstaff,thepitchofthesound.

octave:TwotonesthatspaneightdifferentdiatonicpitchesthathavethesamepitchqualityandthesamepitchnamesinWesternmusic.

pick-upnotes:Introductorynotesplacedbeforethefirstmeasureinapieceofmusic.

pitch:Thehighnessorlownessofatoneproducedbyasinglefrequency.

polyphony:Layersofdifferentmelodicandrhythmicactivitywithinasinglepieceofmusic.

rest:Asymbolusedtonotateaperiodofsilence.

rhythm:Apatternofregularorirregularpulsesinmusic.

scale:Aseriesofnotesinascendingordescendingorderthatpresentsthepitchesofakey,beginningandendingonthetonicofthatkey.

score:Aprintedversionofapieceofmusic.

simpletime:Atimesignatureinwhichtheaccentedbeatsofeachmeasurearedivisiblebytwo,asin4/4time.

staff:Fivehorizontal,parallellines,containingfourspacesbetweenthem,onwhichnotesandrestsarewritten.

syncopation:Adeliberatedisruptionofthetwo-orthree-beatstresspattern,mostoftenbystressinganoff-beat,oranotethatisn’tonthebeat.

tempo:Therateorspeedofthebeatinapieceofmusic.

timbre:

Theuniquequalityofsoundmadebyaninstrument.timesignature:

Anotationmadeatthebeginningofapieceofmusic,intheformoftwonumberssuchas3/4,thatindicatesthenumberofbeatsineachmeasureorbarandshowswhichnotevalueconstitutesonebeat.Thetop(orfirst)numbertellshowmanybeatsareinameasure,andthebottom(orsecond)numbertellswhichkindofnotereceivesthecountofonebeat.

tonal:Asongorsectionofmusicthat’sorganizedbykeyorscale.

tonic:Thefirstscaledegreeofadiatonicscale.

trebleclef:Asymbolwrittenatthebeginningoftheuppermusicalstaffinthegrandstaff.ThetrebleclefestablishesthepitchofthenotesonthelinesandspacesofthestaffexistingabovemiddleC.

trill:Whenaplayerrapidlyalternatesbetweentwonotesawholesteporhalfstepapart.

triplet:Usedinsimpletimetodivideabeatthatshouldcontaintwoequalpartsintothreeequalparts.

turnaround:Achordprogressionleadingbacktothebeginningofthesong.

wholestep:Anintervalconsistingoftwohalfsteps,representedonthepianobymovingtwoadjacentkeys,blackorwhite,totheleftorrightfromastartingpoint,orontheguitarbymovingtwofretsupordowntheneckfromastartingpoint.

AbouttheAuthorsMichaelPilhoferteachesmusictheoryandpercussionsatMcNallySmithCollegeofMusicinSt.Paul,Minnesota.Hehasworkedasaprofessionalmusicianformorethat20yearsandhastouredandrecordedwithJoeLovano,MarianMcPartland,KennyWheeler,DaveHolland,BillHolman,WycliffeGordon,PeterErskine,andGeneBertoncini.

HollyDayisawritinginstructorattheOpenBookWritingCollectiveinMinneapolis.Shehaswrittenaboutmusicfornumerouspublications,includingGuitarOne,MusicAlive!,ComputerMusicJournal,TheOxfordAmerican,andMixdownmagazine.HerpreviousbooksincludeMusicCompositionForDummies,Shakira,TheInsidersGuidetotheTwinCities,andWalkingTwinCities.

DedicationToWolfgangandAstrid,withmuchlove.

Author'sAcknowledgmentsSpecialacknowledgementgoestoallthemusiciansandcomposerswhotookthetimeoutoftheirverybusyschedulestosharetheirthoughtsonwritingmusicwithus:SteveReich,PhilipGlass,IrminSchmidt,BarryAdamson,JonathanSegel,JohnHughesIII,NickCurrie,AndrewBird,RachelGrimes,ChristianFrederickson,PanSonic,MarkMallman,andthelateDr.RobertMoog.Ahugethankstoeachoneofyou.

AbigthankyoualsogoestothestaffatWiley:projecteditorsGeorgetteBeattyandTimGallan;copyeditorSarahWestfall;acquisitionseditorsTracyBoggierandDavidLutton;andtechnicalreviewersKarenLadd.Wethankouragent,MattWagner,aswell.

SpecialthanksgoestoTomDayformasteringandproducingtheaudioforthebookandtorockposterartistEmekforcontinuingtoinspirethroughhisworks.

Publisher’sAcknowledgmentsAcquisitionsEditor:TracyBoggier

AssociateEditor:DavidLutton

ProjectEditors:GeorgetteBeatty,TimGallan

CopyEditor:SarahWestfall

TechnicalReviewer:KarenLadd

ProjectCoordinator:MelissaCossell

CoverImage:©iStock.com/lillisphotography

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