Music theory

Music theory is the field of study that dealswith how music works. It examines the lan-guage and notation of music. It identifies pat-terns that govern composers’ techniques. Ina grand sense, music theory distills and ana-lyzes the parameters or elements of music –rhythm, harmony (harmonic function),melody, structure, form, and texture.Broadly, music theory may include any state-ment, belief, or conception of or about music[1]. People who study these properties areknown as music theorists. Some have appliedacoustics, human physiology, and psychologyto the explanation of how and why music isperceived.

Elements of musicMusic has many different elements. The mainelements are: rhythm, melody, harmony,structure, timbre, dynamics, and texture.Each element—and each of its sub-elements,if any—is discussed below.

MelodyA melody is a series of notes sounding in suc-cession. The notes of a melody are typicallycreated with respect to pitch systems such asscales or modes. The rhythm of a melody isoften based on the inflections of language,the physical rhythms of dance, or simply peri-odic pulsation. Melody is typically divided in-to phrases within a larger overarching struc-ture. The elements of a melody are pitch,duration, dynamics, and timbre.

In the context of theory, a piece of musicmay be melodically based. In this instance, acomposer will first take a melody, and usethat to create his work. A harmonically basedpiece, on the contrary, will focus on a chordprogression, with the melody as a secondaryor incidental factor of composition.

PitchPitch is a subjective sensation in which alistener assigns perceived tones to notes on amusical scale based mainly on the frequencyof vibration, with a lesser relation to soundpressure level (loudness, volume). The pitch

of a tone typically rises as frequency in-creases. At and below 1,000 Hz, the pitch ofa tone gets lower as sound pressure in-creases. Above approximately 2,000 Hz, thepitch increases as the sound gets louder.[2]

The process of assigning note names topitches is called tuning. Historically inWestern music, a number of competing pitchstandards have existed to define the tuning ofan orchestra. "Concert A" was set at 435 Hzby France in 1859[3] while in England, con-cert A varied between 452 and 439 Hz. A fre-quency of 440 Hz was recommended as thenew standard in 1939 and in 1955 the Inter-national Organization for Standardization af-firmed the choice.[4] A440 is now widely,though not exclusively, used as the A abovemiddle C.

The difference in frequency between twopitches is called an interval. The most basicinterval is the octave, which indicates eithera doubling or halving of the base frequency.

Scales and modesNotes can be arranged into different scalesand modes. Western music theory generallydivides the octave into a series of 12 notesthat might be included in a piece of music.This series of twelve notes is called a chro-matic scale. In the chromatic scale, each noteis called a half-step or semitone. Patterns ofhalf and whole steps (2 half steps, or a tone)can make up a scale in that octave. Thescales most commonly encountered are theseven toned major, the harmonic minor, themelodic minor, and the natural minor. Otherexamples of scales used are the octatonicscale, and the pentatonic or five-toned scalewhich is common in but not limited to folkmusics. There are scales that do not followthe chromatic 12-note pattern, for example inclassical Persian, Indian and Arabic music.These cultures often make use of quarter-tones, half the size of a semitone, as thename suggests.

In music written using the system ofmajor-minor tonality, the key of a piece de-termines the scale used. Transposing a piecefrom C major to D major will make all the

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notes two semitones (or one full step) higher.Even in modern equal temperament, chan-ging the key can change the feel of a piece ofmusic, because it changes the relationship ofthe composition’s pitches to the pitch rangeof the instruments on which the piece is be-ing performed. This often affects the music’stimbre, as well as having technical implica-tions for the performers. However, perform-ing a piece in one key rather than anothermay go unrecognized by the casual listener,since changing the key does not change therelationship of the individual pitches to eachother. A key change, or modulation, may oc-cur during a piece, which is more easilyheard as a difference of intervals in sound.

RhythmRhythm is the arrangement of sounds in time.Meter animates time in regular pulse group-ings, called measures or bars. The time sig-nature or meter signature specifies howmany beats are in a measure, and whichvalue of written note is counted and felt as asingle beat. Through increased stress and at-tack (and subtle variations in duration), par-ticular tones may be accented. There are con-ventions in most musical traditions for a reg-ular and hierarchical accentuation of beats toreinforce the meter. Syncopated rhythms arerhythms that accent unexpected parts of thebeat. Playing simultaneous rhythms in morethan one time signature is called polymeter.See also polyrhythm.

In recent years, rhythm and meter havebecome an important area of research amongmusic scholars. Recent work in these areasincludes books by Bengt-Olov Palmqvist,Fred Lerdahl and Ray Jackendoff, JonathanKramer, Christopher Hasty, William Roth-stein, and Joel Lester.

HarmonyHarmony is the study of vertical sonorities inmusic. Vertical sonority refers to consideringthe relationships between pitches that occurtogether; usually this means at the sametime, although harmony can also be impliedby a melody that outlines a harmonicstructure.

The vertical relationship between twopitches is referred to as an interval. A largerstructure involving multiple pitches is calleda chord. In Common practice and Popularmusic, harmonies are generally tertian. This

means that the interval of which the chordsare composed is a third. Therefore, a root-po-sition triad (with the root note in the lowestvoice) consists of the root note, a note a thirdabove, and a note a third above that (a fifthabove the root). Seventh chords add a thirdabove the top note of a triad (a seventh abovethe root). There are some notable exceptions.In 20th century classical music, many altern-ative types of harmonic structure were ex-plored. One way to analyze harmony in Com-mon practice music is through a roman nu-meral system; in Popular Music and Jazz asystem of chord symbols is used; and in post-tonal music, a variety of approaches areused, most frequently set theory.

The perception of pitch within harmonydepends on a number of factors including theinteraction of frequencies within the har-mony and the roughness produced by the fastbeating of nearby partials. Pitch perception isalso affected by familiarity of the listenerwith the music, and cultural associations.

Consonance and dissonanceConsonance can be roughly defined as har-monies whose tones complement and in-crease each others’ resonance, and disson-ance as those which create more complexacoustical interactions (called ’beats’). Asimplistic example is that of "pleasant"sounds versus "unpleasant" ones. Anothermanner of thinking about the relationship re-gards stability; dissonant harmonies aresometimes considered to be unstable and to"want to move" or "resolve" toward conson-ance. However, this is not to say that disson-ance is undesirable. A composition made en-tirely of consonant harmonies may be pleas-ing to the ear and yet boring because thereare no instabilities to be resolved.

Melody is often organized so as to interactwith changing harmonies (sometimes called achord progression) that accompany it, settingup consonance and dissonance. The art ofmelody writing depends heavily upon thechoices of tones for their nonharmonic orharmonic character.

"Harmony" as used by music theorists canrefer to any kind of simultaneity without avalue judgement, in contrast with a morecommon usage of "in harmony" or "harmoni-ous", which in technical language might bedescribed as consonance.

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DynamicsIn music, dynamics normally refers to thesoftness or loudness of a sound or note, e.g.pianissimo or fortissimo. Until recently, mostof these dynamics and signs were written inItalian, but recently are becoming written ortranslated into English. However, to every as-pect of the execution of a given piece, eitherstylistic (staccato, legato etc.) or functional(velocity) are also known as dynamics. Theterm is also applied to the written or printedmusical notation used to indicate dynamics.

TextureMusical texture is the overall sound of apiece of music commonly described accord-ing to the number of and relationshipbetween parts or lines of music: monophony,heterophony, polyphony, homophony, ormonody. The perceived texture of a piecemay also be affected by the timbre of the in-struments, the number of instruments used,and the interval between each musical line,among other things.

Monophony is the texture of a melodyheard only by itself. If a melody is accompan-ied by chords, the texture is homophony. Inhomophony, the melody is usually but not al-ways voiced in the highest notes. A third tex-ture, called polyphony, consists of severalsimultaneous melodies of equal importance.

Form or structureForm is a facet of music theory that exploresthe concept of musical syntax, on a local andglobal level. The syntax is often explained interms of phrases and periods (for the locallevel) or sections or genre (for the globalscale). Examples of common forms ofWestern music include the fugue, the inven-tion, sonata-allegro, canon, strophic, themeand variations, and rondo. Popular Music of-ten makes use of strophic form often in con-junction with Twelve bar blues.

Theories ofharmonizationFour-part writingFour part chorale writing is used to teachand analyze the basic conventions ofCommon-Practice Period music. In the Ger-man musicology tradition referred to as

functional harmony. Johann Sebastian Bach’sfour voice chorales written for liturgial pur-poses serve as a model for students. Thesechorales exhibit a fusion of linear and verticalthinking. In analysis, the harmonic functionand rhythm are analyzed as well as the shapeand implications of each of the four lines.Students are then instructed to composechorales, often using given melodies (as Bachwould have done), over a given bass line, orto compose within a chord progression, fol-lowing rules of voice leading. Though tradi-tionally conceived as a vocal exercise for Sop-rano, Alto, Tenor, and Bass, other commonfour-part writings could consist of a brassquartet (two Trumpets, French Horn, andTrombone) or a string quartet (including viol-in I, violin II, viola and cello).

There are seven chords used in four-partwriting that are based upon each note of thescale. The chords are usually given RomanNumerals I, II, III, IV, V, VI and VII to refer totriadic (three-note) chords which are basedupon each successive note of the major orminor scale which the piece is in. Chordsmay be analyzed in two ways. Case-sensitiveharmonic analysis would state that major-mode chords (I, IV, V7, etc.), including aug-mented (for example, VII+), would be notatedwith upper-case Roman numerals, and minor-mode chords, including diminished (ii, iii, vi,and the diminished vii chord, viio), would benotated with lower-case Roman numerals.Schenkerian harmonic analysis, patternedafter the theories of Heinrich Schenker,would state that the mode does not matter inthe final analysis, and thus all harmonies arenotated in upper-case.

The skill in harmonising a Bach choralelies in being able to begin a phrase in one keyand to modulate to another key either at theend of the first phrase, the beginning of thenext one, or perhaps by the end of the secondphrase. Each chorale often has the ability tomodulate to various tonally related areas: therelative major (III) or minor (vi), the Domin-ant (V) or its relative minor (iii), the Sub-Dominant (IV) or its relative minor (ii). Otherchromatic chords may be used, like the di-minished seventh (made up of minor thirdspiled on top of each other) or the Secondarydominant (the Dominant’s Dominant — a kindof major version of chord II). Certain stand-ard cadences are observed, most notably IIb7– V7 – I. The standard collection of J. S.Bach’s chorales were edited by Albert

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Riemenschneider and this collection is read-ily available, e.g. here; the student is greatlyrewarded by playing them at the piano,singing the lines by themselves, singing themin groups, analyzing them by writing the Keyand the Chords employed and by taking themelody and bass line from any chorale andtrying to fill in the inner alto and tenor parts.Once this has been accomplished the studentcan then begin to complete their own basslines —whilst carefully watching for modula-tions— and then they can fill in the inner altoand tenor parts. Parallel octave and fifth mo-tion is forbidden, and this often proves to bethe pons asinorum of the average musicstudent.

Music perception and cognitionFurther information: Music cognition, FredLerdahl, and Ray JackendoffJackendoff and Lerdahl attempt to develop a"musical grammar." Using Jackendoff’s back-ground as a linguist and Lerdahl’s composi-tional and theoretical background, a series ofgenerative rules are defined to explain thehierarchical structure of tonal music. Therules focus on musical grouping, or methodsin which rhythmic groups of notes, as well asformal hierarchies, are perceived by listen-ers. Three sets of rules are given: "GroupingWell-Formedness Rules," "Grouping Prefer-ence Rules," and "Transformational Rules."These rules are designed to interpret howlisteners group structures in tonal music.These groupings then play into the segmenta-tion of events by listeners, which in turn de-termine the hierarchical structure perceivedby the listener. Although this theory is welldeveloped and complete, it is by far not theonly system designed to discuss music in thismanner, and there is no acceptance of thistheory as being the sole theory by which todiscuss perception of music (see JonathanKramer).

Serial composition and settheoryFurther information: serialism, set theory(music), Arnold Schoenberg, Milton Bab-bitt, David Lewin, and Allen ForteTwelve Tone Serialism is a technique de-veloped by Arnold Schoenberg to order andrepeat all the 12 pitches of the ChromaticScale with specific order. An ordered row ofthe 12 pitches is created, then all possible

transformations are explored. The analytictechniques involve writing a 12x12 matrix ofthe tone row, and all of its forms (Transposi-tion, Inversion, Retrograde, Retrograde In-version) This technique is strongly related tothe composers of the Second VienneseSchool, but also has been incorporated intothe languages of many other composers.Serialism does not always appear in the strict12-note form; many composers have exploredwith serialism using fewer than 12 notes, re-peating tones inside of the row, serialism ofmicrotonal scales. Also, composers such asPierre Boulez and his teacher Oliver Messi-aen explored integral serialism, or the serial-ization of all possible musical parameters(pitch, rhythm, dynamics, etc.). Composerssuch as Igor Stravinsky and Milton Babbittdeveloped personal approaches to Serialism;Stravinsky using a method of Rotational Ar-rays, and Babbitt using Combinatoriality ofthe rows. Set Theory is another approach tounderstanding atonal music that may or maynot be serial. Although more akin to themathematical field of Group Theory thanmathematical Set Theory, the nomenclaturehas become standard inside the musical com-munity. Set theory represents the pitchclasses as numbers to allow a methodology ofexamining music without tonic or triadicfunctional harmony. This technique allows forexploration of the construction of a serialtone row as well as less strict atonal works.This technique has been extended with agreat deal of mathematical rigor to both ton-al and atonal systems by David Lewin in histransformational approach utilizing networksof related sets.

Musical semioticsFurther information: music semi-ology and Jean-Jacques Nattiez

Music subjectsNotationMusical notation is the symbolic representa-tion of music (not to be confused with audiorecording). Historically, and in the narrowsense, this is achieved with graphic symbols.Computer file formats have become import-ant as well [1]. Spoken language and handsigns are also used to symbolically representmusic, primarily in teaching.

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In standard Western music notation, mu-sic is represented graphically by notes placedon a staff or staves with the vertical axisroughly corresponding to pitch and the hori-zontal axis roughly corresponding to time.Note head shapes, stems, flags, and ties areused to indicate duration. Additional symbolsrepresent key, tempo, dynamics, accents,rests, etc.

MathematicsMusic and mathematics are strongly inter-twined. As noted above, the concept of pitchand temperament are both strongly tied tomathematics, and acoustics in particular.Analysis often takes a mathematical route;musical set theory and Transformational the-ory are both steeped in mathematics.

Some methods of composition are math-ematically based. Iannis Xenakis developedseveral methods using stochastic methods.The French school of spectral music usesmathematical analysis of sounds to developcompositional materials.

AnalysisAnalysis is the effort to describe and explainmusic using only the music as a startingpoint. Analysis at once is a catch-all term de-scribing the process of describing any por-tion of the music, as well as a specific field offormal analysis or the field of stylistic analys-is. Formal analysis attempts to answer ques-tions of hierarchy and form, and stylistic ana-lysis attempts to describe the style of thepiece. These two distinct sub-fields oftencoincide.

Analysis of harmonic structures is typic-ally presented through a roman numeral ana-lysis. However, over the years, as music andthe theory of music have both grown, a multi-tude of methods of analyzing music havepresented themselves. Two very popularmethods Shenkerian analysis and Neo-Riemannian analysis have dominated much ofthe field. Shenkerian analysis attempts to "re-duce" music through layers of foreground,middleground, and, eventually and import-antly, the background. Neo-Riemannian (orTransformational) analysis began as an ex-tension of Hugo Riemann’s theories of music,and then expanding Riemann’s concepts ofpitch and transformation into a mathematic-ally rich language of analysis. While both the-ories originated as methods of analysis for

tonal music, both have been extended to usein non-tonal music as well.

Ear trainingAural skills — the ability to identify musicalpatterns by ear, as opposed to by the readingof notation — form a key part of a musician’scraft and are usually taught alongside musictheory. Most aural skills courses train theperception of relative pitch (the ability to de-termine pitch in an established context) andrhythm. Sight-singing — the ability to singunfamiliar music without assistance — is gen-erally an important component of aural skillscourses.

See also• Pitch (psychophysics)

Notes[1] Boretz, Benjamin (1995). Meta-

Variations: studies in the foundations ofmusical thought…. Open Space.

[2] Olson, Harry F. (1967). Music, Physicsand Engineering. Dover Publications.pp. 248–251. ISBN 0486217698.http://books.google.com/books?id=RUDTFBbb7jAC&pg=PA248.

[3] "Revolution in Music: A Brief History ofTuning". http://www.schillerinstitute.org/music/rev_tuning_hist.html. Retrieved on9 January 2009.

[4] Lynn Cavanagh. "A brief history of theestablishment of international standardpitch a=440 hertz" (PDF).http://www.wam.hr/Arhiva/US/Cavanagh_440Hz.pdf.

Sources• Boretz, Benjamin (1995) Meta-Variations:

Studies in the Foundations of MusicalThought. Red Hook, New York: OpenSpace.

• Bent, Ian D. and Anthony Pople."Analysis." Grove Dictionary of Music andMusicians. London: Oxford UniversityPress.

• Jackendoff, Ray and Fred Lerdahl."Generative Music Theory and its relationto Psychology." Journal of Music Theory,1981. New Haven, Yale University Press.

• Kramer, Jonathan. The Time of Music.New York: Schirmer Books, 1988.

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• Lerdahl, Fred. Tonal Pitch Space. Oxford:Oxford University Press, 2001.

• Lewin, David. Generalized MusicalIntervals and Transformations. NewHaven: Yale University Press, 1987.

Further reading• Apel, Willi & Daniel, Ralph T. The Harvard

Brief Dictionary of Music. New York, NY.Simon & Schuster Inc, 1960. ISBN0-671-73747-3

• Benward, Bruce; Jackson, Barbara Garvey;Jackson, Bruce R. Practical beginningtheory : a fundamentals worktext, 8thedition (originally published 1963),Boston : McGraw-Hill, 2000. ISBN0697343979

• Chase, Wayne. How Music REALLYWorks!. 2nd Ed. Vancouver, Canada.Roedy Black Publishing, 2006. ISBN1-897311-55-9 (book)

• Hewitt, Michael. Music Theory forComputer Musicians. 1st Ed. USA.

Cengage Learning, 2008. ISBN13-978-1-59863-503-4

• Lawn, Richard J. & Hellmer, Jeffrey L. JazzTheory and Practice. Alfred Publishing Co.1996. ISBN 0-882-84722-8

• Seashore, Carl, Approaches to the Scienceof Music and Speech, Iowa City, TheUniversity, 1933

• Seashore, Carl, Psychology of Music, NewYork, London, McGraw-Hill BookCompany, Inc., 1938

• Sorce, Richard. Music Theory for theMusic Professional. Ardsley House, 1995.ISBN 1-880-15720-9

• Taylor, Eric. AB Guide to Music. Vol 1.England. Associated Board of the RoyalSchools of Music, 1989. ISBN1-854-72446-0

• Taylor, Eric. AB Guide to Music. Vol 2.England. Associated Board of the RoyalSchools of Music, 1991. ISBN1-854-72447-9

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