SCALES

HARMONY(REVISED MET HOD HARMONY INST RUC T ION)

ELIMINAT ING THE OLD FIGURED BASS SYST EMSEE PREFAC E

NOT ES AND EXERC ISES

DIRK HAAGMANS

T HIRD EDIT ION

PRIC E NET

1 . FISCHER é BRO . NEW YORK

7. 8, 1 0. II, . BIBLE HOUSE (AST OR PLAC E )

PR EFACE .

“Knowing that for almost three hundred years the T horough

Bass (Genera l Bass or Figured Bass ) Method has been genera llyadopted by the entire civiliz ed wor ld as the basis for the study ofHarmony

,i t was perfectly clear to me , when in the year 1 8 8 0 I

published my‘Sketch of a New Method for Harmony Instruction,

’

it would be exceedingly difficult to replace this Thorough Bass(Genera l Bass or Figured Bass ) Method by a radical ly new courseof instruction for the study of Harmony .

”

These are the introductory words embodied in Dr . HugoRiemann

’s preface to the third edition of his wonderful , ultramodern book, “Manual of Harmony,” published in German ,

in theyear 1 8 98 .

Riemann certa in ly was r ight in stating it woul d be exceedinglyd itficu l t to replace the old Thorough Bass System by a radicallynew course of instruction for the study of Harmony . Almosttwenty year s have elapsed since the publication of this marvellousRiemann work with its many new and most beautiful musicaltheories ,—and i t i s astonishing that this book

,conta ining true

revelations respecting Harmony , i s known so l ittle and used ex

tremely seldom by musicians .P robably , the pr incipal reasons why musicians show an averse

ness to Riemann’s new work

,can be assigned—fi rstly , to his theory

of Under tones .

Riemann’s theory of the downward formation of al l minor

chords—for instance , the chord a -c- e a s cons isting of the prime 6,

the dow nward na tura l third c, and the downward natura l fifth a

IIas more or less proved a detr iment to the aim of his work .

S econdly, the ideas and theories expressed by Riemannthroughout this entire work , Manual of Ha rmony , are possiblytoo advanced , and beyond the conception of the average student

T herefore the present work ,“Scales , Interva ls , and Harmony ,

is kep t as simple as poss ible , prog ressing on ly by slowest steps ,while no mention i s made of Riemann

’s theory of“Undertones” or

of the “downward” construction of minor chords .

Trrespective of these two points , it i s a fact that throughout theentire book of Riemann

’

s—Mus ic , in the fullest sense of the word,is the Alpha and Omega

—the quintessence of this work.

E very musician must readily admit tha t any Manua l o f Har

mony in which the Thorough Bass Method is used as the vehicle forthe Instruction of Harmony

,conta ins but little music and almost

noth ing but a very large number of inexpressibly dry rules and laws,and figuratively speaking, an endless array of ar ithmetical problems .

It is safe to conclude that any book of the latter kind—becauseit conta ins so little rea l music—the most unmusica l person , possessing on ly a sufficien t amount of perseverance , will be able to workthrough it and master al l its problems . On the other hand , a

musically gifted student , feeling the lack of rea l music in this book,will find the study very dry and dull beyond al l descr iption ,

—nextto nothing is left him for individua lity or for any musical creationof his own . Almost every note which is written in working out theexercises i s practically prescr ibed by a certa in numera l ; whereas,studying Riemann

’s excellent method of Harmony,even at the

beginn ing—( for instance, E xercise 95 of this book )—the pupil hasoccasion of wr iting something that he may really cal l his own . He

i s a llowed to create and exercise his own individual ity through theRiemann Method which makes the study of Harmony an art , whileany Thorough Bass Method of Harmony Instruction is a science .

Moreover,the student , after studying and working through an

entire course of Harmony according to the pr inciples of the Thorough Bass Method , has not succeeded in solving a l l its theor iesnor has he obta ined even a practica l knowledge of Harmony . He

i s utterly ignorant regarding one of the most difficult points inHarmony ; namely , the formation of a correct Bass-voice , —to saynothing of harmon iz ing a given melody, a process which is entirelyforeign to him. As the name “Thorough Bass” or

“Figured Bass

indicates,the Bass-voice has always been given to him ; conse

quently , l1 e has never written any Bass-voice of his own construc

tion . The great importance of being able to wr ite a correct Bass ,which every musician will cer ta in ly admi t is by f ar the mostdiffi cult of a l l four voices

,—has never been taught him.

In this Book,however

,beginn ing at E x. 1 3 0

,without the aid

of any prescribed figured notation,excepting an occasional guide ,

the pupi l i s compel led to wr ite and find for himself a lmost theentire Bass-voice of every exercise .

T ona l Function”* is the magic word which Riemann has in

troduced ; and , it is Riemann’

s wonderfu l theory of the T ona l

Functions of Chords which conver ts his Manua l of Harmony in to

a work sa tura ted with music.

In accordance with Riemann’

s teachings , Harmony becomes an

ar t for the ea r and sou l and not a science for the eye and brain.

*Compare Note No . 99 , page 60 .

Although I have not had the great honor and benefit of havingbeen a personal pupil of Dr. Hugo Riemann (having studied Har

mony, Counterpoint , Fugue and Composition according to theThorough Bass Method , under Rust, Jadassohn and Reinecke ) no

words can express my highest admiration for his liberal ideas andtheor ies , and I heartily recommend his “Handbuch der Harmonielehre

”

(Third E dition , Breitkopf and Haertel , Leipz ig )—also .his

“Harmony Simpl ified (Augener and Co. ,London ) , and

warmly endor se the careful study of same to every true musician .

New York , Jun e 30 th ,1 9 1 5 .

PREFACE

Note No . 1 .

lI

otes

II otcs

Pi otes

IIotcs

DI otes

bl otes

Il otes

1 2 - 1 5 .

1 6- 1 8 .

2 3 -2 9 .

3 0 - 3 7 .

Note No. 3 8 .

Notes No . 3 9 -4 1 .

Notes No . 42 -43 .

Note No . 41 .

CONT ENT S

PART I

S CALE S

Major Mode and Minor Mode

Major sca les and minor scales ; theirs ignatures ; compar ison of minorsca les ; accidentally ra ised tones inthe Minor Mode . E xercises .

P aral lel scales . E xercises .

Keys with more than seven sharpsor flats . E xercises

PART II

INT E RVALS

Major and minor interva ls ; perfectintervals . E xercises

Augmented and diminished interva ls . E xercises

Complete l ist of a l l twenty- five ih

ter va l s . E xercises

Invers ion of intervals . E xercises .

Interva ls measured downward . E xor

cises

Melodic and harmon ic interva ls .

1 0—1 2

1 2—1 3

1 4—1 9

2 2—24

24- 25

2 5- 2 7

Semitones and Whole- tones . E xer

cises . Compara tive difference between major and minor sca les

The characteristic tone decidingwhether maj or or minor mode ;enharmonic scales ;method of finding harmon ic and melodic minorsca les . E xercises

Note No . 45 .

Notes No . 46-49 .

Notes No . 50 -52 .

Notes No . 53 -60 .

Notes No . 61 -62 .

Notes No . 63 -65 .

Notes No . 66- 76.

Notes No . 7 7 - 8 0 .

Notes No . 8 1 -8 7 .

Notes No . 8 8 -93 .

Notes No . 94-98 .

PART III

HARMONY

E xplanation of letters, figures and

signs 2 9 3 0

Harmony—its meaning. Construc

tion of a chord ; maj or tr iad and

minor tr iadTonic ; Dominant . The pr incipaltr iads + T and

“I'D 3 1 3 2

Key-

proper and key- foreign . Fourpar t wr iting ; range of voices .Doubling of chord-tones ; commontones . Leaps 3 2—3 4Third staff . E xample showing proc

ess of working out a harmonyexercise . E xercises 3 4—3 9Subdominant. The pr incipal tr iads°T and °S . E xercises 3 9—4 1

Cantus Firmus . Repetition of thevery same harmony Furtherinstructions for the working out o f

exercises . E ar tra in ing. E xercises 4 1—47Close and Open Harmony ; mutualdistance permissible between the

diff erent voices . The fina l chord .

E xercises 48—5 1

5 1—54

54 - 57

Accidentally rai sed tones in the

minor mode ; remova l of the MinorDominant [°D ] chord from mod

ern music ; the Major Dominantchord in the minor mode .

E xercises 58—59

Contrary—parallel—and oblique motion . Connecting Dominant and

Subdominant Harmonies . Leadingtone . Changing from Close intoOpen Harmony and vice-versa between chords of the same harmony .

Repetition of h armony and itsadvantages . Leading of the voices,and progressions by leaps . E xer

cises

9 9 - 1 0 0 .

Notes 1 0 1 - 1 0 9 .

Note No . 1 1 0 .

Notes No . 1 1 1 - 1 1 3 .

Notes No . 1 1 4- 1 1 7 .

Notes No . 1 1 8 - 1 2 1 .

Notes 1 22- 1 2 8 .

Notes 1 29- 1 3 7 .

Note No. 1 3 8 .

Notes No. 1 3 9- 1 42 .

Tona l Functions . The only twok inds of Tr iads 60 - 61

The P r incipa l Tr iads ‘T ,"D

,+ S

,

°T, and °S —and their inversions .

Doubling the fifth of a triad . Additiona l rules for the leading ofthe voices 62—64

Consecutive Fifths and ConsecutiveOctaves

Genera l rules for the leading of S oprano, Alto, and Tenor voices . Re

nouncing a common tone 66—67

Changing from Close into OpenHarmony (and vice versa ) betweendifferent ha rmon ies ; mutua l distance permitted between the diff erent voices . Two voice s s ingingthe intervals of a perfect pr ime . 68—7 0

P rogressions by augm ented intervalsrestr icted . Leading tone in theSoprano voice . Contrary and para llel motion between Bass and S o

prano voices . E xercises 70—7 3

The accidentally lowered tone in themajor mode ; the auxiliary °S

chord in the major mode . Ob romatica l ly changed tones ; crossrelation . Further comments re

specting repetition of harmonyE xercises 74- 7 7

Formation of the Bass-voice ; rulesgovern ing the Bass taking thethird or the fifth of a tr iad . Dia

tonic or scale-l ike prog ressions forBass and Soprano voices . P ro

gression of the Leading tone inprominent voices . 7 7—8 2

Conclusion of the study of the P rincipa l Triads

The Dominant-Four-S ix Chord . 8 3 - 8 5

Notes 1 43 - 1 45 .

Notes 1 46- 1 4 7 .

Notes 1 48 - 1 49 .

Notes 1 50 - 1 55 .

Note

Notes 1 5 7 - 1 63 .

Notes 1 64- 1 72 .

Note No . 1 7 3 .

Notes No . 1 74- 1 79 .

Notes No . 1 8 0 - 1 8 2 .

Note No . 1 8 3 .

Notes No . 1 84- 1 8 5 .

Note No. 1 8 6.

Notes No . 1 8 7- 1 8 8 .

Note No . 1 8 9 .

Appendix

No inversions of a Dominant-FourS ix chord,—the pr ime, the onlyinterva l to be doubled ; its progression ; character istic place as

antepenul timate chord 8 5—86

The Dominant-Four - S ix chord in

the minor mode

The progression S (or °S )—D chords .

E xercises 8 7—9 0

Cadences 90 - 92

P er iod.

and Sentence ; Half Closeand Fu ll Close

Harmon iz ing a given melody (FreeHarmony ) . E xercises 94—9 7

P a rallel Chords (secondary tr iads )in the major mode . E xercises 9 8—1 0 2

The Incomplete Tr iad (omitting thefifth )

Respecting the relationship existingbetween two consecutive chordsthe stronger the kinship, the

greater the freedom permissible inthe leading of the voices . A

doubled fifth reached by parallelmotion . E xercises 1 0 3—1 0 7

P ara llel Chords in the minor mode .

The °D and °Dp chords . E xer

cises 1 0 8—1 1 0

The accidentally ra ised seventh and

the non- ra ised seventh in the

1 1 0—1 1 1

The importance of the °Sp chord .

Doubling the third of a triad and

its rules . E xercises 1 1 2—1 1 7

Free Harmony . E xercises 1 1 8 - 1 20

Consonant and Dissonant Chords .1 2 1—1 2 13

Genera l Summa ry of Appendix Notes

SCALES .

NOTE No. 1 .

In modern music , two tone-genders or tone-modes (in German ,

Tongeschlechter ) exist , and they are cal led Maj or and Minor .

In general,the impression on the musica l mind of the Major

gender (or major mode ) is j oyful , festive , an imated , br il liant, light,while the effect produced by the Minor gender (or minor mode )i s melancholic , gloomy , doleful, sad, heavy,—or to quote the wordsof the celebrated theor ist , Mor itz Hauptmann

,

“Like unto thedrooping branches of the weeping willow, in str iking contrast tothe erect tree of l ife , we recogn iz e in Minor the expression ofmourn ing.

NormNo. 2 .

TH E S IGNATURES on ALL FIFT E EN MAJOR S CALES .

(Regarding the number“fifteen compare Appendix Note

C major—No signature,maj or—one sharp ,

F maj or—one flat ,maj or— two sharps , B fla t major—two flats ,maj or—three sharps, E fla t maj or—three flats ,maj or—four sharps , A fla t maj or—four flats ,major—five sharps , 1 ) fla t maj or—five flats ,sha rp major— six sharps, G fla t maj or—six flats ,sha rp maj or—seven sharps, C fla t major—seven flats .

NOTE No. 3 .

The exact series the seven sharps is

F sha rp,

C sha rp,

C sha rp,

D sha rp,

A sha rp,

E sha rp,

B sharp .

T he exact series the seven flats is

B fla t,E fla t,

2 Ma jor and Minor Sca l es

E xe rcise 1 .

the signatures of the following scales

F sharp maj or , A fla t majorD fla t maj or , F sharp ma j or ,A maj or, B fla t maj or ,C sharp major , E maj or ,E fla t major , G fla t major ,B maj or , B major ,A fla t maj or , E fla t major ,F maj or , D major ,C sharp major , C fla t maj or,B fla t major , A maj or ,

D maj or , D fla t major ,G fla t major , F sharp major,E maj or , G fla t maj or ,

C fla t major , C sha rp major,G maj or, C fla t major .

NOTE No 4 .

Although in the Major mode there is on ly one form of maj orscale , in the Minor mode there are three var iations or forms ,resulting in the following three kinds of minor scales

1 . the natura l or origina l minor sca le

2 . the harmonic minor sca le

3 . the melodic minor sca le

and their Signa tures 3

NOTE No . 5 .

Compar ing the three different A minor sca les as il lustrated inNote No . 4 ,

—the signatures of a l l three sca les differ as followsThe scale of Aminor , na tura l , has no signature at al lT he

'

signature of the sca le of A minor , harmonic, is one sharp(G sharp )

And the signature of the scale of A minor , me lodic, is : ascending two sharps (F sharp and G sharp ) and descending no

signature at a l l .Inasmuch

,as the more modern harmon ic and melodic minor

scales are only modification s of the ol d, true, and origina l minorsca le , the signature of the natura l minor sca le i s decisive and au

thoritative for the key . Consequently , the real signature , for instance

,of the key of Aminor i s not one sharp , nor two sharps ,—but

no signature at al l as the natura l minor scale indicates ; and thetones F sharp and G sharp, when appear ing in the key of A minor,are ca lled the accidenta l ly raised tones of that minor key.

NOTE No . 6.

Therefore,every minor key has besides its signature, two acci

denta lly ra ised tones which are the s ixth and seventh tones of theor igina l minor sca le ra ised by a large semitone .*

However,of these two accidentally ra ised tones , the acci

dentally ra ised seventh tone is of f ar greater impor tance than theaccidental ly ra ised sixth tone ; because , the former becomes thehighly impor tant Leading of the key ; and when speakingof the accidentally ra ised tone in minor , the ra ised seventh is

a lways understood .

NOTE No . 7 .

Compar ing any major scale with the natura l minor scale ofthe same letter-name, for instance , the scales of A maj or and

A minor , na tura l

or the scales of F major and F minor , na tura l

*R ega rd ing the term S e in itone and Ha l f -s tep , s ee Notes No. 1 2

a nd 1 3 .

" Rega rd ing the d e s igna t ion “Lea d ing tone , see Note No. 8 3 .

Ma jor and Mil

E xe rci

the signatures of the t

F sharp maj or ,D fla t maj or .A maj or,C sha rp maj or ,E fla t major,B maj or ,A fla t maj or ,F maj or ,C’ sharp major.B fla t major ,D major ,G fla t major.E maj or,0 fla t major ,G major,

OTENo 4 .

Although in the Major modal e , in the Minor mode thensu l ting in the following three

1 . the natura l or origina l

2 . the harmonic minor scc

3 . the melodic minor sca l i

of the same le ttero f such major se

ind ica te the ma insame let te r-name .

mirmr is : th ree m'

the vase of the ( 7

the re. is naught toIn i tsel f the numbers ca le of the same letter-no f C minor‘is th ree flats

T he three rulestmd readily the s ithe follow ing thr

'

Ihe s ignatur e of the s

givengna tnres oee scal es :

it is cvna tu ra lthi rd

,s ixth

,

tones in the major scale areNo. I2 and 1 3) higher thanle tte r- name ; and herefrom

,

de rived :

I. II'

a, major scalesc a le o f the same letter-nf rom the key

-s ignaturel ure o f the sca le o f B(a re of the scale of B

oN o It a major so

o f the same l e tte r-nankey

-s igna ture of suchthe sca le o f A fla t maof the scale of

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4 Major and Minor Scales

it is evident,that the diff erence between the major scale and the

na tura l minor sca le of the same letter-name i s to be found in thethird

,sixth , and seventh tones of such two sca les ,—and these three

tones in the major scale are a semitone or half- step (compare NotesNo. 1 2 and 1 3 ) higher than in the natura l minor scale of the samele tter- name ; and herefrom,

the following practica l rules may bederived :

NOTE No . 8 .

1 . If a maj or scale has sharps, the signature of the minorsca le o f the same letter-name is found by deducting three sharpsfrom the key signature of such major sca le ; for example, the signature of the sca le of B maj or is five sharps— consequently , the signature of the scale of B minor , less three sharps , is two sharps .

2 . If a maj or scale has flats, the signa ture of the minor scaleof the same letter -name i s found by adding three more flats to thekey- signature of such major sca le ; for example, the signature of

the sca le of A fla t maj or is four flats - consequently, the signatureof the scale of A fla t minor, plus three flats, is seven flats .

3 . If a major scale has less than three sharps (as the scales ofC maj or, G maj or and D maj or )— the signature of the minor scaleof the same letter -name is found by deducting the number of sharpsof such major scale from the numera l thr ee, and the result willindicate the number of fla ts belonging to such mino r scale of thesame letter-1 .1 ame For example, the signature of the scale of Dmaj or i s two sharps—consequently, the signature of the scale of Dminor is : three minus two sharps : one flat ; and further, as in

the case of the C major scale, same having no signature at al l ,

there is naught to be deducted,thus the numera l three represents

in i tself the number of flats indicating the signature of the minorsca le of the same letter-name ; therefore , the signature of the scaleof C minor is three flats (compare Appendix Note II) .

NOTE No . 9 .

The three rules given in Note No . 8 will help the student tofind readily the signatures of a l l minor scales , with the exception ofthe following three scales :

The scale of G sharp minor ,D sharp minor ,A sha rp minor .

Therefore , the following Note must'

be committed to memory .

NOTE No . 1 0 .

T he s ignature of the scale of G sha rp minor is 5 sharps,D sharp minor 6 sharps,A sharp minor 7 sharps .

and their Signatures

NOTE No . 1 1 .

THE SIGNAT URES OF ALL FIFTEEN MINOR SCALES .

(Compare Appendix NoteA minor—No signature

,

minor—one sharp ,

minor—two sharps ,sharp minor—three sharps,sharp minor

— four . sharps ,sharp minor

—five sharps ,sharp minor

—six sharps,sharp minor—seven sharps,

Give the signaturesC sharp minor,E fla t minor ,A minor

,

F sha rp minor ,B fla t minor,D‘sha rp minor ,

C minor,A sharp minor,F minor ,E minor ,A fla t minor,B minor ,D sharp minor ,G minor ,A sharp minor,C minor ,

Give the signa tures

D minor—one flat,G minor—two fla ts ,C minor—three fla ts

,

F minor—four flats,

B fla t minor—fi ve flats ,E fla t minor—six flats ,A fla t minor—seven flats .

E xercise 2 .

the following scalesG sharp minor ,B fla t minor ,E minor ,A fla t minor ,F sharp minor ,E fla t minor ,C sharp minor ,D minor ,A sha rp minor ,F minor ,D sharp minor ,G minor ,B minor

,

A fla t minor ,G sharp minor ,D minor .

E xe rcise 3 .

the following scales :D sharp minor ,G fla t major ,C minor ,C sharp major ,B minor ,B fla t maj or ,G sharp minor ,C fla t maj or ,A minor ,E maj or ,

6 Semitones and Whole - tones

NOTE No . 1 2 .

T he distance from any tone to its immediate neighbor,i

. e . ,

C to C sha rp ,

—D to E fla t—E to F ,-is ca l led a semitone or a

hal f-step .

NOTE No . 1 3 .

There are two different kinds of semitones (or hal f- steps )La rge semitones (or Large hal f-steps ) and

Sma ll semitones (or Sma ll half- steps ) .

1 . A semitone (or ha lf-step ) is cal led large , i f it is composedo f two tones which have the same letter-name ; for instance , F to

F sha rp ,—D fla t to D na tura l ,—A sha rp to A doubl e sha rp .

2 . A semitone (or ha lf-step ) is called small , i f it is composedo f two tones which have consecutive letter-names ; for instance ,D sharp to E ,

—B to C ,— E fla t to F fla t , and G doubl e sha rp to

A S harp,etc . (compare Appendix Note III ) .

NOTE No . 1 4 .

The sum of two consecutive semitones (of which one is a largeand the other a small semitone ) i s ca lled a whol e-tone or whol estep . Whol e- tones (or whole- steps ) are C to D ,

—E fla t to F ,

B sharp to C doubl e sha rp .

E xe rc ise 4 .

Name the following tones (or steps ) ; whether whole-tone ,l arge semitone , or small semitone

Semitones and Whole-tones 7

What whole-tonelarge semitonesmal l semitonewhole-tonel arge semitonesmall semitonewhole-tonel arge semitonesma ll semitonewhole-tonelarge semitonesmall semitonewhole-tonelarge semitonesmall semitonewhole-tonelarge semitonesma ll semitonewhole-tonewhole-tonelarge semitonesmall semitonewhole-tone

*Al though in practica l mus ic trip le ch roma t ic s ig ns do not exis t,t heore tica l ly they may b e used .

E xercis e 5 .

from C sha rp,

B fla t,A sharp,

8 Major and Minor Scales

What is a large semitone fromsma ll semitonewhole-tonelarge semitonesmall semitonewhole-tonel arge semitonesma ll semitonewhole-tonelarge semitonesmal l semitonewhole-tonelarge semitone

NOTE No . 1 5 .

E xamples of the four different kinds of scales :

A Major :

A Minor, natura l :

A Minor, harmonic

A Minor, melodic

Hi 2Y2 3 3i 43i 5 V1 7 32 8 8 Y1 7 71 6&5K4 3fi 3 3422 31 1

The comparative difference between these four kinds of scalesi s to be found in the diff erent places of the whole-tones and semitones

Major and Minor Sca les 9

Ma jor

Minor (natura l) 1 2 3 4 5 6 7 8

Minor (ha rmon ic) —1 2 3 4 5 6 1 7 m 8

N. a .

Minor (melodic) 1 3 4 5 6 7 8

NOTE No. 1 6.

The character istic tone deciding whether a scale (or key )i s major or minor is the third tone of the sca le—the third being theonly tone which , without exception , is always different in majorand minor .

NOTE No . 1 7 .

In accordance with the modern equa l ly tempered sys tem oftuning , the word “enharmon ic” means difl erent names for thesame pitch ; i . e .

,enharmonic tones are F sharp and G fla t; C and

B sharp,—and enharmon ic scales are the sca les of C sha rp maj or

and D fla t major ; and the scales of E fla t minor and D sharpminor ; etc .

NOTE No . 1 8 .

Although the student is cautioned not to foster the idea thatthe minor mode has been der ived from the major mode (an ideawhich is most absurd and absolutely wrong ) the following expedients regarding minor scales may be of grea t help to beginners .

1 . In order to find a certa in harmonic minor sca le,take the

major scale of the same letter-name , lower its third and its sixthdegrees a large semitone and the result will be the harmonic minorscale .

2 . In order to find a certa in me lodic minor sca le , take theharmonic minor scale of the same letter -name, and—ascending,r a ise its sixth degree a large semitone , and descending, lower itsseventh and its [ra ised ] sixth degrees a large semitone , and theresult will be the melodic minor scale .

Carefully noting the above instructions , the student wil l experience no difficu lty in finding a l l harmon ic and melodic minorscales with the exception , however , of the three minor scales given inNote No . 9 . These three scales , namely °

The scale of G sharp minor ,D sha rp minor,A sharp minor ,

may be found by means of their respective enharmonic (compareNote No . 1 7 ) scales—to wit ,

1 0 P ara llel Scales

A fla t minor ,E fla t minor ,B fla t minor .

(Also compare Note No .

E xe rcise 6.

Wr ite or recite the following scalesC minor , harmon ic , E fla t minor , melodic,G minor , melodic, G sharp minor, harmon ic ,A sharp minor , harmon ic , D sharp minor , melodicC sharp minor , melodic, E minor , harmon ic ,B fla t minor , harmon ic, Afla t minor, melodic .

NOTE No . 1 9 .

PARALLE L SCALE S (and para llel keys ) * are one majora nd one minor sca le (or key ) which have the same signature ; f orinstance , the sca les (and key s )—A minor and C maj or, or thes ca les (and keys )—F sharp major and D sharp minor , etc .

NOTE No . 2 0 .

In order to find the parallel sca le (or parallel key ) of a certa inmajor sca le , take the sixth degree of this maj or sca le , and this tonewill be the key-note or fundamenta l tone of the paral lel minor sca le(or para llel minor key ) .

In order to find the parallel scale (or parallel key ) of a certa inminor scale , take the third degree of this minor sca le, and this tonewill be the key-note or fundamenta l tone of the para llel major scale(or para l lel major key ) .

E xercise 7 .

What i s the para llel scale of E maj or,( C C‘ ( C C‘F ”l if t/OT

( i C‘ B major I( t ( C ( C C‘G minor

D major ,F sharp minor,G major ,C minor,F sharp major ,B fla t minor ,C fla t major ,

*For va rious rea sons the more modern express ions “P a ra l le l sca l e s

a nd“P a ra l le l k eys ” a re f a r be tter and more adequa te than the old name s ,

“R e la tive minor” and

“Re la t ive ma j or.”

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1 2 Scal es

sca le ha s for its signature—5 fla ts ,cc cc cc c c sharps ,

7 sharps,c c c c c c3 flats ,6 flats

,

1 sharp ,

cc c c cc4: sharps ,5 flats

,c c c c cc flats ,—5 sharps ,

- 1 sharp,flats ,

—2 flats ,6 sharps,2 sharps ,6 flats

,c c c c cc3 flats ,7 sharps,3 sharps ,flats ,

( C5 flat s,sharps ,

6 sharps ,flats

3 flats ,

5 sharps ,c c c c c c7 sharps ,c c c c flats ,flats ,

—3 sharps,—5 sharps ,2 flats "

NOTE No . 2 1 .

Although in practica l music no signatures of more than sevensharps , or more than seven flats are used , —theoretically , sca les withmore than seven sharps or seven flats do exist ; for example, thes ca le of D sharp major i s

And the signature of this sca le (or key ) of D sharp major is n inesharps , or strictly speaking , two double sharps and five single sharps(compare Appendix Note IV ) .

Scales 1 3

NOTE No . 22 .

Another simple and practical method of finding the signatureof even the most unusua l sca le or key

,is to take the enharmon ic

sca le (or key ) and deduct its number of sharps or flats from thenumera l twelve— (the sum total of the two signatures of any twoenharmonic sca les is a lways twelve )—and the resul t will indicatethe number of flats or sharps of the scale (or key ) desired. For

exampleQues . What is the signature of the scale (or key ) of D fla t

minor "

Ans . The enharmonic scale of D fla t minor i s the scale ofC sharp minor—and the signature of C sharp minor is four sharps ;subtract four from twelve , the result being eight—consequently , thesignature of the scale (or key ) of D fla t minor i s eight flats, orr ightly sa id , one double flat and six single flats .

Give the signatures

E xercise 1 0 .

of the following scalesC fla t minor ,G sharp maj or ,F fla t minor ,A sharp maj or ,G fla t minor ,F fla t maj or ,E sharp minor .

PAR T II.

INTERVALS .

NOTE No. 2 3 .

In musica l terminology the word INTE RVAL means thedistance between any two tones—and an interva l takes its namefrom the number of letter -names or degrees it embraces ; i . e . ,

the interva l from C to D is a second ,cc c c cc

Dc cFc c third

,

E A fourth ,B F fifth .

(For the present a l l inter vals are figured upward .

E xe rc is e 1 1 .

NOTE

Any interva l of a second being identica l with a whole-tone (ora whole-step ) i s ca lled a maj or second ; for example , major secondsa re : A to B ,

—F sharp to G sharp .

—B fla t to CAny interval of a second being identica l with a small semitone

(or smal l ha l f- step ) i s cal led a minor second ; and , minor secondsa re : E to F,

—C sharp to D,—F to G fla t

, etc .

NOTE

Seconds and Thirds

E xe rcise 1 2 .

Any interval of a third composed of two whole-tones (or twowhole-steps ) i s cal led a maj or third ; for example, maj or thirds a re ;F to A

,

—D fla t to F ,

—E to G sharpAny interva l of a third composed of one whole-tone and one

small semitone is ca lled a minor third ; and , minor thirds are :4 to C,

—D sharp to F sharp,—C to E fla t, etc .

What

E xe rcise 1 3 .

third of F sha rp ,

second F fla t.third A double sharp,second C sharp,

third B doubl e fla t.second G sharp,

second E double fla t,third C doubl e sharp,

second F double fla t,third E sharp ,

1 6 Fourths and F ifths

minor secondmajor thirdminor secondmaj or s econdminor thirdminor secondmajor thirdminor thirdmajor secondminor third

NOTE No. 26.

The interva ls of a four th and a fifth as they are found in anymajor scale , figured from the key-note or fundamenta l tone of thesca le to its fourth or to its fifth degree are cal led a perf ect fourthand a perf ect fi f th— (a maj or fourth or a minor fourth and a majorfifth or a minor fifth do not exist ) . To find the perfect fourth ofF

,take the four th degree of the scale of F major , which is B fla t

and this tone B fla t, will be the per fect fourth of F .

To find the per fect fifth of F sharp,take the fifth degree of the

scale of F sharp maj or , which is C sharp, and this tone C sharp,

will be the perfect fifth of F sharp .

E x e rcis e 1 4.

G double fla t,A sharp,

D doubl e fla t,E double sharp,

C fla t,B sharp,

E sharp,

F fla t,‘

D double sharp,

G doubl e fla t"

F doubl e fla t,F doubl e sharp,

B double sharp,

B double fla t,A doubl e fl a t"

Sixths and Sevenths 1 7

E xe rcis e 1 5 .

Name the following intervals

NOTE No. 2 7 .

T he basis of measurement for interval s i s the maj or s ca l e,

as in any major sca le a l l intervals figured upward from the keynote or fundamenta l tone of the sca le a re cal led either perfect ormajor ; f or example, the differen t interva ls in the sca le of B majora re :

Perf ec t maj or maj or perf ect pe r fect maj or maj or per f ec tprime s sec ond third four th f i f th s ix th s ev enth oc tav e t t

Consequently, in order to find, for instance , the major s ixth of

C sharp,take the C sha rp maj or scale and the sixth tone (or de

*A l though in f a ct the re ex is ts no interva l or d is tance be tw een tw o

tone s of the same p i tch , y e t in mus ica l terminology th e repe t it ion of the

very same tone is ca l led a perf ec t prime .

”

” T he expre s s ion “e igh th” is not us ed in re f erring to th is interva l ,

but the word “Oc tave” is used ins tead .

1 8 Interva ls

g rce ) of this scale will be the major s ixth of C sharp ; namely,A sharp

In order to find the major seventh of D fla t, take the D fla tmaj or scale and the seventh tone (or degr ee ) of this sca le will bethe major seventh of D fla t; namely, C na tura l .

NOTE No. 2 8 .

No defini te names will be used f or intervals larger than one

octave , and the names Ninth , Tenth , E leventh , etc. , are not appliedspecifica lly to the interva ls themselves , as will be seen later .

Any interva l larger than one octave takes its name from theinterva l acquired by removing either the upper tone or the lowertone of the interva l in question within the limiting range of oneoctave ; thus , a l l of the following intervals are ca lled T hirds rc

gardless of the distance interven ing between same :

NOTE No. 2 9 .

Any major interva l reduced by a large semitone , becomes a

minor interva l ; for instance , the major s ixth, C sha rp to A sharp ,

will be changed into a minor sixth either by ra ising the lower toneof the interval , C sharp, into C doubl e sharp, or by lower ing thehigher tone of the interval , A sharp, into A na tura l .

E xe rcis e 1 6.

major third ofminor sixth A fla t,perfect fourth E sharp,

minor second D doubl e fla t,major seventh B

per fect fifth F fla t,maj or second G doubl e sharp,

per fect octave D fla t,minor third F

major sixth B fla t,perfect prime G sharp,

minor seventh C fla t,major th ird D fla t,minor sixth B sharperfect fourth E fla t,minor second doubl e sharp,major seventh A doubl e s t,

per fect fifth E

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2 0 Intervals

Wha t perfect fourth of

augmented octave F fla t,dimin ished fifth E ,

augmented pr ime D doubl e fla t,dimin ished fourth A

perfect fifth C fla t,dimin ished octave F double sharp,

augmented fourth G fla t,augmented fifth F sharp,

per fect four th E fla t,augmented octave G sharp,

diminished fifth C fla t,augmented pr ime G sharp,

dimin ished four th C doubl e flat,augmented fifth C fla t,perfect fifth B ,

dimin ished octave E

augmented fourth C fla t,augmented fifth E fla t,perfect four th G doubl e

augmented octave B doubl e fla t,dimin ished fifth A sharp,

augmented pr ime B fla t,dimin ished four th D sharp,

augmented fifth B fla t,per fect fifth A flat,dimin i shed octave sharp,

augmented four th E fla t,augmented fifth G double sharp"

NOTE No.

A major second en larged by a large semitone , becomes an

augmented second (a diminished second does not exist ) —cousequently, there are three different kinds of S econds

Maj or, minor, and augmented .

NOTE No. 3 2 .

A major third enlarged by a large semitone , becomes an

augmented third - and a minor third reduced by a large semitone ,becomes a dimin ished third ; consequently , there are four differentkinds of Thirds

Maj or , minor , a ugmen ted , and diminished .

Augmented and D iminished 2 1

NOTE No. 3 3 .

Regarding Fourths and Fifths—there a re three different kindsof each

P erfect, augmented and diminished .

(Compa re Notes No . 26 and

NOTE No. 3 4 .

A major sixth enlarged by a large semitone , becomes an augmented sixth,—and a minor sixth reduced by a large semitone ,becomes a dimin ished sixth ; consequently , there are four differentkinds of Sixths—S imilar in classification to the four kinds of thirds—VIZ . ,

Major , minor , augmented,and diminished .

NOTE No. 3 5 .

A minor seventh reduced by a large semitone , becomes a

dimin ished seventh (an augmented seventh does not exist ) -con

sequently,there are thr ee different kinds of Sevenths :

Maj or, minor , and diminished.

NOTE No. 3 6.

There are thr ee different kinds of Octaves— correspondinglythe same in class ification as fourths and fi f ths—and they a re :

P erfect, augmen ted, and diminished .

NOTE No . 3 7 .

Regarding pr imes— there are on ly two different kinds ofP rimes , perf ect and augmen ted ,

—and as stated in Note No . 3 0,a

dimini shed prime does not exist .

E xe rc is e 1 8 .

W hat is the diminished seventh of

augmented seconddimin ished thirdaugmented sixthdimin ished sixthaugmented thirddiminished seventhaugmented seconddimin ished th irdaugmented sixthdiminished sixthaugmented third

( C ( C

( C ( C( C ( C

Interva ls

hat Is the dimin i shed seventh of

( CC C

CC

CC

( C( C

( C

( CC CC C( C( C( C

66

NOTE

augmented seconddimin ished thirdaugmented sixthdimin ished sixthaugmented thirdd lminished seventhaugmented seconddimin ished thirdaugmented S ixthdimini shed sixthaugmented thirddimin ished seventhaugmented seconddimin ished th irdaugmented s ixthdimini shed sixthaugmented third

( C( C

( C

( C

( C( C

COMP LETE LIST OF ALL TWENTY-FIVE INTERVALS .

T wo kinds,—P erfect and augmented .

T hr ee kinds,—Major, minor, and augmented .

F our kinds,—Major, minor, augmented, and dimmished .

T hree k 1 nds, —P erfect , augmented , and d imin ished .

T hree kinds, —P er fect, augmen ted , and dimimshed .

Four kinds, —Major, minor , augmented, and d 1m1 n

ished .

SEVENTHS : T hr ee kinds , —Major , minor, and dimin ished .

OCTAVES T hree kinds , —P erfect , augmented, and dimin ished .

(Compare Appendix Note V . )

E xe rc is e 1 9 .

W I“

°

Iat is the diminished fifth of C sha rp,

( C

( C( C

augmented octave B fla t,dimin ished sixth E fla t,major third E sha rp,

minor sixth C fla t,augmented second D sha rp,

perfect fourth F fla t,dimini shed seventh A sharp,

augmented pr ime G fla t,minor second B sharp,

perfect octave E fla t,( C

augmented third B sharp,

sha rp,

doubl e fla t,doubl e sha rp,

doubl e fla t,doub l e sha rp,

doubl e fla t,fla t,doubl e sharp,fla t.doubl e sha rp,

doubl e fla t,double sha rp"

Interva l s

ha t 1 s the dimin ished th ird of

maj or s ixthaugmented fifthminor seventhmajor secondminor thirdaugmented s ixthdimin ished fourthdimin ished octaveperfect pr imeaugmented fourthmajor seventhperfect fifthdiminished fifthaugmented octavedimin ished sixthmajor thirdminor s ixthaugmented secondperfect fourthdimin ished seventhaugmented primeminor secondaugmented thirddimin ished thirdmajor sixthaugmented fifthmajor secondminor seventhminor thirdaugmented sixthdimin ished four thdimin ished octaveaugmented fourthmaj or seventhper fect fifthdimin ished fifthaugmented octavediminished sixthmajor thirdminor sixthaugmented secondperfect fourthdimin ished seventhaugmented pr imeminor secondaugmented th irddimin ished third

s . ( c

( C ( C( C s .

’

( C CC

( C n

( C ( C( t ( C( C ( C( C ( o

( C ( C

( C ( C( C ( C( c ( C

( C ( C( C ( CC C

C C ( 5

C C

( I

( C ( C

( C ( C( C ( CC ( C

( C ( 6

A sha rp ,

C doubl e sha rp,

D doubl e fla t.D double sha rp ,

F double sha rp ,

A doubl e fla t,G doubl e sha rp,

B doubl e fla t,E doubl e sha rp ,

C double fla t .D doub l e sha rp.

B double

A doubl e sha rp,

24 Inversion of Interval s

Wha t i s the major six thaugmented fifthmajor secondminor seventhminor thirdaugmented sixthdimin i shed four thdimin ished octaveaugmented four thmajor seventhperfect fifth

( C ( C( C

cc ( C

CC CC

INVE RSION OF INTE RVALS .

NOTE No. 3 9 .

Inverting an interva l means to transpose either the lower toneof the interva l a perfect octave higher—or to transpose the uppertone of the interva l a perfect octave lower , the result in both casesbeing exactly the same as f ar as the interva l or distance is con

cerned .

However , inverting an interval larger than an octave , it i snecessary first of al l to remove the upper or lower tone of suchinterva l within the l imiting range of one octave (compare NoteNo. before it is possible to proceed with the inversion of same .

NOTE No. 40 .

To find the inversion of a cer ta in interval , subtract the specificnumer ica l denomination (number-name ) of such interva l fromNINE and the result wil l be the Inversion ; i . e .

The invers 1 0 n of a third will be a sixth ;The invers ion of a fourth will be a fifth ;The inversion of an octave will be a pr ime , etc.

NOTE No. 4 1 .

A maj or interva l , when inver ted , becomes a minor interval,A minor interva l , when inverted , becomes a maj or interval ,An augmen ted interva l , when inverted, becomes a diminished

interval,*A diminished interval , when inver ted , becomes an augmented

Interval ,bu t

A perf ect interval , when inverted, rema ins a perfect interval .

*I an a ugmented oc ta ve cannot be inverted . Also compareNote No. 3 0 .

Inversion of Intervals 25

E xe rcis e 20 .

What 1 nversion of a perfect fifth ,a maj or seventh ,an augmented fourtha dimin ished octave ,an augmented sixth

,

a minor third ,a dimin ished fourth ,a major second ,a minor seventh ,

an augmented fifth ,a major sixth ,a dimin ished third ,a minor second ,an augmented pr ime ,a dimin ished seventh ,

a perfect fourth ,

an augmented second,

a minor sixth ,

a major third ,an augmented third ,a dimin ished fifth ,a perfect octave ,a perfect pr ime ,a diminished sixth "

NOTE No . 42 .

So f ar a l l interva ls have been figured upward ; however , in theexercises following

,i t i s pla inly indicated that the downward

interva l i s required as well .

NOTE No . 4 3 .

GENERAL INSTRUCTIONS FOR FINDING INTERVALS Dow xwxnn.

1 . Smal l interval s , as pr imes , seconds , and thirds , count thenumber of steps (or tones ) downward .

2 . For intervals larger than a’ third , use invers ions ; for

example , i f the augmented S ixth downward of F sha rp is requi red ,

take the invers ion of this interval , which is the d iminished thirdupward , and transpose the acquired tone a perfect octave lower .

E x e rc is e 2 1 .

l l ha t i s the perfect fifth downward of E sha rp,

major seventh F fla t,augmented fourth B sha rp,

( C ( C

26 Intervals , Upward and Downward

What d im . octave dow nwa rd ofaugmen ted sixthminor thirddimin ished fourthmaj or secondaugmented thirdminor seventhaugmented fifthmaj or sixthdimin ished thirdminor seconddimin ished sixthaugmented pr imedimin ished seventhperfect fourthaugmented secondminor s ixthmajor thirdaugmented octavedimin ished fifthperfect octave

E xerc ise 22 .

W hat is the p er fect fifth zip -and dow nwa rd of F fla t,major seventh zip-and downwa rd of A

augmented four th np -and dow nwa rd of D doubl e fla t,dimin ished octave up-and downward of B sharp,

augmented third up-and downward of B fla t,dimin ished four th up-and downward of E fla t,augmented sixth up- and downward of A sharp,

minor third up-and downward of G fla t,major second up-and downward of C double sharpminor seventh up- and downward of D

augmented fifth up-and downward of D fla t,major sixth up-and downward of E doubl e fla t,

dimin ished third up-and downward of G sharp,

minor second up-and downward of F sharp,

diminished sixth up-and downward of B sharp,

augmented pr ime up-and downward of A fla t,diminished seventh up-and downward of C sharp,

perfect fourth up-and downward of fla t,augmented second up-and downward of B sharp,

minor sixth up-and downward of G fla t,major third up-and downward of D doubl e fla t,

augmented octave up-and downward of E sharp,

dimin ished fifth up-and downward of A fla t"

Q

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2 8 Melodic and Ha rmon ic Interva l s

NOTE No. 44 .

Just as the musica l sense of Melody is successive tones

(usually of different pitch )

Ad i g l o BE ETHOVEN

e t c .

and the musical sense of Harmony is simul taneous tones (usual lyof diff erent pitch )

thus a lso, a melodic interva l is an interva l whose tones are pro

duced by a single part , successiv’

elyxfl ‘3

1and a harmon ic interva l intervfihwhose tones are produced bytwo individua l parts, si neously z

v

PART III.

HARMONY.

NOTE No . 45 .

E e ANAT ION or LETTERS, FIGURES AND S IGNS To BE USED In

CONJUNCTION WITH THIS COURSE OF HARMONY STUDY.

*

I . The capital letter s T , D , and S are Function-letters .and they are the abbreviations denoting the three Tonal Functions :

T onic,Dominan t, and

S ubdominant.

(Compare Note . No.

0

II . A Figure above a function-letter refer s to the Sopranovo1 ce .

A Figure helow a function - letter refers to the Ba ss-voice .

III. Arabian figures indicate maj or tr iads ,Roman figures indicate minor tr iads .

IV . T he short perpendicular l ines between function- letters(D T ) are the bar - lines .

V . The sma l l ita l ic letters a , b, c, d, e, f , and g are Chordletters

,and they indicate the pr ime of the chord required ;

thus , in E xercise 59,the letter f indicates the major tr iad

f -a -c, and the letter bb in the same exercise indicates the major

triad bb-d-f . Also compare par t IX of this Note .

VI. If in exercises where “Cantus Firmus (compare Note

No . 67 ) i s given , a note appears without a letter or without( for instance , the two notes bb in E xercise 59 ) it indicates tha t amajor triad is requ ired and that the note itself is the prime of thechord ; consequently , the first and third chords in E xercise 59 are

bb-d-f .

T he g rea ter part of th is high ly pra ctica l and S imp le se t of le tters ,figures and s igns (wh ich a l so we ow e to R iemann

’

s beaut i ful sy s tem o f

Ha rmony S tudy ) is in i ts e l f quite a new d epa rture in the s tud y of

Harmony—entire ly d ifi eren t , and f a r superior to the ol d figured and

p rescribed method known a s the“T horough B a ss

”or

“Figured B ass

”

Nota t ion .

3 0 E xplanation of Letters, Figures and Signs

VII . If in exercises where “Cantus Firmus is given

, a noteis accompan ied by a chord-letter ( for example , the second, s ixth and

seventh notes in E xercise the letter indicates the prime ofthe chord ; consequently , the second and sixth chords in E xercise5 9 are f -a - c, and the seventh chord is bb-d-f .

VIII . The “D itto sign means the repetition of the im

mediately preceding harmony ; hence, in E xercise 59,the barmo

nies of the third,fourth and fifth chords are exactly the same ,

namely , bb-d-f ,—regardless of the position of the respective chordsin question .

IX . In addition to Arabian and Roman figures , indicatingmaj or and minor tr iads respectively, the signs and will beused :

the Sign denotes a maj or triad , andthe sign denotes a minor tr iad .

Where no figure is given and neither “I' nor0 i s noted , it i s

a lways understood that the maj or tr iad is requ ired.

X . In a l l exercises where “Cantus Firmus is given ,figures

above the staff refer to the Soprano-voice and figures be low thestaff refer to the Bass- voice .

XI . A tie between two figures (as in E xercise 1 2 1 ) means toreta in the common tone (compare Note No . 58 ) in the very samevoice to which these two figures refer .

XII . The word up or down between two figures indica tes the upward or downward progression of that voice to whichsuch two figures refer .

XIII .Regarding the designation D2, see Notes No. 1 3 9

- 1 42 .

XIV . The Sign added to a figure ( for example, Dg> )C

means to lower the natural or norma l 1 nterva l (compare AppendNote V I ) referred to by a large semitone ; thus :

In the key of C maj or D2mean s the chord g- c-e,—wh1 l e

in the key of C minor D2> means the chord g- c- eh.

XV. The letter s T p, Dp, Sp ,

°T p,°Dp,

and °Sp are tl1 <

abbreviations denoting :T onic-para l l e l chord,Dominant-para l l e l chord ,

and

S ubdominan t-para l l e l chord .

(Compare Notes No . 1 70 , 1 72 , and

Major and Minor Triads 3 ]

NOTE No . 46.

In music , the word Harmony means the science of chordshow to construct them and how to connect them mutua lly .

NOTE No . 4 7 .

A chord is the s imultaneous sounding of three or more tonesof d ifferent pitch , constructed in accordance with the laws of

Harmony .

NOTE No . 48 .

The very s implest and most elementary combination of tonesca lled a chord , is found by taking any tone as basis and adding toit

,either its maj or or minor third , and its perfect fifth ; for

example

Therefore,chords constructed in this manner cons isting of

pr ime , major third (or minor third ) and perfect fifth, a re ca lled

TRIADS” ; and a tr iad takes its name from the tone upon whichit has been bu ilt . The different names of the above S ix tr iads are :

Triad of C ,

Tr iad of E ,

Tr iad of F sharp,

Tr iad of B fla t,Tr iad of A sharp,

Triad of F fla t.

NOTE No. 49 .

A triad consisting of pr ime, major third and perfect fifth iscalled a

“major triad , while a tr iad consisting of prime, minorthird and perfect fifth is ca lled a

“minor tr iad” ; consequently, thesix triads wr itten in Note No . 48 are known as

The C maj or triad ,

E minor tr iad ,

F sha rp major triad,B fla t minor triad ,

A sharp maj or triad,F fla t minor triad .

NOTE No . 50 .

From a harmonic point of view , the most important and

strongest rul ing tone of any piece of mus 1 c —1 r respect 1 ve of whethersuch composition i s a sonata , study, or any other form or var 1 a

3 2 Ton ic and D ominant Harmon ies

t ion—is ca lled the The Ton ic is a lways identica l withthe lowest or fundamenta l tone of that very scale out of which a

p iece of music has grown or developed .

NOTE No. 5 1 .

T he second most impor tan t and strongest ruling tone of anypiece of music is ca lled the

“DOMINANT ” ( the word Dominant

mean ing dominating—next to Tonic ) and the Dominant of any

p iece of music is found by taking the perfect fifth of the Ton ic ;consequently, in the keys of both C maj or and C minor the Ton icis C and the Dominan t is G, and in the keys of both A fla t maj orand A fla t minor the Ton ic is A fla t and the Dominant is E fla t.

THE P RINCIPAL TRIADS +T AND +D .

NOTE No . 52 .

Adding to the Tonic and to the Dominant of any key theirrespective key-

proper (compare Note No. 53 ) thirds and fifths , theresult is :

The Ton ic chord (or Ton ic tr iad ) and

The Dominant chord” (or Dominant tr iad ) ,for example , in the key of D fla t major, the Ton ic chord is db-f—ab,and the Dominant chord in the same key is ab-c- eh.

NOTE No . 53 .

The express ion hey-

proper (in German,l eitereigen ) refers

to any of the seven tones belonging to the scale of tha t key inwhich a piece of music is written , and the expression hey

-foreign (in German ,

leiterfremd ) refer s to any tone not belongingto the scale of a cer ta in key .

NOTE No : 54 .

Al l exercises must be worked out in four-part wr iting”

Soprano , Alto, Tenor , and Bass— same to appear on two staves ;on the upper staff (with treble clef ) Soprano and Alto voices , andon the lower staff (with bass clef ) Tenor and Bass voices

*Compa re the. l a t te r part o f Append ix Note XV , b eg inning a t Amos t beauti ful thes is”

Four -

part Wr iting 3 3

keeping in mind that in al l exercises the natura l relative positionof the higher and lower parts must be respected, i . e. , a lower partmust never cross a higher par t.

NOTE No . 55 .

Confine the four voices (Soprano , Alto , Tenor , and Bass ) as

far as possible to their own range . Regarding S oprano and Bassavoid the use of ledger- l ines , but if necessary

,never use more

than one ledger-l ine above the upper staff or below the lower staff ,then , with the help of the rules to be given in Note No . 56 respecting the mutual distance permissible between the four voices, themiddle-voices (Alto and Tenor ) will find their proper range.

NOTE No . 56.

For the present, in al l exercises up to E x. 8 2 inclusive , thedistance permitted between Soprano and Alto

,and be tween Al t o

and Tenor must be either a third or a fourth, never more or less ;the on ly restr iction though regarding the distance between Bassand Tenor voices is that these two voices are never a llowed to bemore than two octaves apart from each other . For example, a l l

of the following positions are perfectly correct :

NOTE No . 5 7 .

Inasmuch , as al l exercises must be worked out for four parts(S , A, T, and B ) , and a tr iad conta ins only three tones of differentpitch , one tone of the tr iad must be sung by two voices , must—as

it is termed , be doubl ed, and this “doubling” may be done in theprime (in unison ) , octave , double octave (or tr iple octave ) .

For the present, doubl e on ly the prime of a chord ; do notdouble either the third or the fifth

3 4 Common Tone

NOTE No . 58 .

If two different chords conta in one or more tones of exactlythe same pitch , this tone (or tones ) i s cal led a common tone ;

for instance,in the following example the common tones are ia

dicated by a tie :

NOTE No . 59 .

For the present , if two successive chords of different harmon ies have a common tone

,this common tone must be reta ined in

the same voice and Indicated by a tie

NOTE No. 60 .

Never let any voice proceed by a leap larger than one octave ;for the present , this rule appl ies especially to the Bass-voice .

NOTE No . 61 .

In order to simpl ify the work dur ing the first few weeks , whenworking out the exercises , a third staff must a lso be used directlyabove the two staves on which the exercise will appear whenfinished—this third staff to be u sed solely to wr ite the desiredTon ic , Dominant , and Subdominan t chords in pla inest form.

Furthermore , this practice will help the student to become thoroughly famil iar with the Tona l Functions (compare Note No . 99 )of the different keys .

NOTE No . 62 .

E xAM P LE SHOWING THE P ROCESS To BE FOLLOWED IN WORKINGOUT THE E XERC ISES .

E x. 24, on page 3 8 , as indicated, must be worked out in the

key of F maj or .

P roceed to wr ite the Signa ture of this key on each of the threestav es ; a l so the sign (If, (indicating gtime) on the two l owerstaves , and copy the question of E x. 24 above the third staff

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3 6 Connecting Ton ic and Dominant Tr iads

3

Ex .2 4 . T 11)

Next Alto and T enor must be added , and“ following the rul es

given in Note No . 56, there will be no question or doubt that theAlto-voice must take the note F in the first space of the treble Clef(w ith stem turned downward ) , and the Tenor -voice takes the fi f thof the chord , the note C, on the first ledger- l ine above the staff inthe bass clef (with stem turned upward )

f

Ex .2 4 . T I1

)

The position of the first chord now is settled , and as the wordHarmony” means the science of cons tructing chords and con

nectiny them mutual ly, the next step will be to have the T chordfollowed by— or connected with—the D chord in the proper way.

The figure 1 below the letter D decides that the Bass-voicemust sing the pr ime of the chord, which is C

Write the pr ime of this chord , the note C,in the second space

f or the Bass-voice (with stem turned downward ) °

Unles s specia l d irect ion f or Rhy thm is noted . it is understood tha tin a l l exerc ises where the tona l functions a re g iven, every funct ion-le tter—excepting the very l ast—represen ts the chord in ha l f notes d bwhi le theve ry l a st function -letter of every exercise represents the chord in wholenotes a .

Connecting Ton ic and Dominant T riads 3 7

3

Ex . 2 4 I P

The next important question is : which is the common tonefound in this D chord and the preceding T chord "

”

Answer : T he tone C ,—and following the rule given in Note

No . 59 , this common tone must be reta ined in the same voice ;therefore , wr ite the note C ( the fifth of this D chord ) on the firstledger - l ine above the Staff for the Tenor - voice

,and indicate this

common tone by a tie , thus connecting it with the preceding noteC of the Tenor-voice :

Ex .2 4 . T 11)

And, further adhering to al l rul es given 54 - 60

,

E xercise 24 , worked out , will be as follows :3

Ex .2 4 . T D

T he principa l Triads +T and +D

E xercise s 24-42 .

MAJOR.

3

Ex . (in fi ’ ) (b T D T1

Ex . 2 5 . (in B ) (b T1

Afl a t ) (BT1

Ex . 3 2 . (in

Ex . 3 3 . (in 1 7 ) (h T D T1 1 1

Ex . 3 4 . (in Uf l a l l (h

Ex . 3 5 . (in B ) (is

E x . 3 6 . (in

T he principal Tr iads °T and °S 3 9

5

V E x . 3 7 . (in A ) e T D | T1 1 1

Ex . 3 8 . ( in

E x . 3 $l . (in 6’sha rp )¢T D T

1 1 1

Ex . 4 0 . (in B f l a t )

b .Ex . 4 1 . (in F sha rp )¢E . 4 2 .

'

A l l T D Tb x (1 1 1 f a )¢1 1 1

TIIE P RINCIPAL TRIADS °T AND °S .

NOTE No . 63 .

From Notes No. 50 and 5 1 it is known tha t in any piece of

music the most important tones a re the Ton ic and the Dominan t ,and next to these two tones , the third important tone is the

“S U 3

DOMINANT” ; the Subdominant of any key is found by takingthe perfect fourth of the Ton ic . Consequently , in the keys of bothB fla t maj or and B fla t minor ,

the Ton ic is B fla t,the Dominant is F ,

the Subdominant is E fla t.

NOTE No . 64 .

Adding to the Subdominant of any key its key-

proper thi rdand fifth

,the result will be :

The “Subdominant chord (or Subdominant triad ) .

For instance , in the key of C minor , the Subdominant chord isf -ah-c; and in the key of C maj or the Subdominant chord is f -a -c .

NOTE No . 65 .

In E xercises 4 3 - 58 , not Arabian ,but Roman figures a re found

accompanying the function- letters T and S ; consequently , minortriads (compare Note No . 45 , part III ) are required.

T he process of working out these new exercises is exactly thesame as in the foregoing E xercises 24-42 inclus ive .

40 T he principa l Triads °T and 08

E xe rcis e s 43 -58 .

MINOR.

1 e f s TEx . 4 3 . (1 n EI I I

III

(t T TI I I

VIII

Ex . 4 5 . (in F sha rp ) (13 T TI I I

Ex . 4 6 . ( in

III

Ex . 4 7 . (in (1: T S TI I I

Ex . 4 8 . (in

Ex . 4 9 . (in

III

Ex . 5 0 . (in A ) (B T S TI I I

VIII

E x . 5 1 . (1 n C ) (I3 TI H

mH

v-l

E 1 143 , w ork e d out as examp l eV-T S

/

I I

Cantus Firmus 4 1

V

Ex . 5 2 . ( i 1 1 D sha rp ) (b TSI 1

“

Ex . 5 3 . (in

Ex 5 4 (in A sha rp ) (I"T"1;

e f s TEx 5 5 . ( 1 n B )I I I

Ex . 5 6 . (in

Ex . 5 7 . (in SIV

Ex . 5 8 . (i n Osha rp ) T I"NOTE No . 66.

A second ser ies of exercises, qu ite different in nature to E xercises 24-58 , now follows .

In these exercises not the function-letters T ,D

,

°T and °S

are given but instead the complete part of one certa in voice(Soprano, Alto, Tenor, or Bass ) , called

“Cantus Firmus,” i s noted

(compare Note No . and the pupil has to supply to each and

every one of these exercises the three respective other voices , whichwill result in four-part music .

NOTE No . 67 .

The expression “CANTUS FIRMUS” [C . F . ] signifies theGiven P art ; the word “Cantus” implying Melody—and the word“P irmus” mean ing fi rm ; steady ; unchangeable ; consequently , theexpression

“Cantus Firmus” means unchangeable melody , or as

it i s cal led in the study of Harmony, “Given P art .”

NOTE No . 68 .

Supplementing Note No . 59,regarding the rule to reta in

a common tone in two successive chords— this rule refers only tosuccessive chords of different harmon ies .

If, however, a chord is followed by the same ha rmony aga in ,

that is , i f the very same chord is instantaneously repeated (for

42 Cantus Firmus

instance , a B fla t maj or chord followed imm ediately by anotherB fla t maj or chord ) , it is a lways a llowable and genera lly advisablef or the present , even compulsory—to a lter the position of thechord and not reta in any common tone at a l l

no t g ood

NOTE No . 69 .

Al though the distingu ishing character istic of a Bass-voiceis to move and not to reta in a common tone

,occa siona lly, the

Ba ss-voice may be susta ined from a strong [accented ] beat to a

weaker beat, ' but never from a weak beat to a stronger beat

not. g ood g ood

In general,the Bass-voice prefers to make a leap of a perfect

octave— which a t any t ime is al lowed— instead of reta ining a com

mon tone .

W hen two voices written on the same staff ( i . e . , Sopranoand Alto

,or Tenor and Bass ) sing the very same tone , and this

tone has the va lue of a whole note,the note must be wr itten twice

see il lustra tion at N . B . :

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44 The principal Tr iads + T and +D

E xe rc ise s 59-82 .

CANTUS FIRMU S IN SOP RANO .

MAJOR.

E x .60 .

E x .61 .

Ex. 62 .

EX . 5 9 , Cantus F irmus in S opr ano .w ork e d out a s e x ampl e

T D T

Ex .60 ,Cantus Firmus in S opr ano,

w ork e d out a s exampl e

Ex .64 .

Ex .65 .

Ex .66 .

Ex .6'

7 .

Ex .68 .

Ex .69 .

Ex. 7 0 .

E X 65 , Cantus Firmus -in S opr ano ,w ork e d out a s exampl e

T he principa l Triads °T and “S

T he pr incipa l Tr iads + T—+D and °T—°S

CANTUS P IRMUS IN ALTO .

MAJOR.

E x . 7 1 .

a a

Ex .7 2 .

Ex. 7 3 .

MINOR.

c a t: 0 c a l) o

od lt o og fi o

E x . 7 6 .

Ex . 7 1 , Cantus Firmus inAl to .w ork ed out as exampl e

T D T

T he principa l Triads + T—+D and °T—°S

CANTUS FIRMU S IN TE NOR.

MAJOR.

Ex . 7 9 .

MINOR.

Ex . 8 0 .

o bi: o e e l» o

Ex . 8 1 .

Ex.

c al) o ab o e l:

Ex. 7 7 , Cantus P irmus in T enor ,w ork ed out as examp l e

4 8 Close and Open Harmony

NOTE No . 7 7 .

A chord is sa i d to be in CLOSE HARMONY when the

three upper voices (Soprano, Alto , and Tenor ) a re a rranged insuch a manner that they lie close together

,leaving no room for any

other tone of the same harmony , either between Soprano and Alto,or between Alto and Tenor :

Thus f ar, a l l Harmony exercises up to E x. 8 3 have beenworked out in what is called C lose Harmony .

NOTE NO. 7 8 .

A chord is sa id to be in OP E N HARMONY when the threeupper voices are ar ranged in such a manner that there is room f or

one or more tones Of the same harmony to fall in between eitherS oprano and Alto

or between Alto and Tenor :

Mutual D istance between Voices 49

or in both cases

Also compare -the latter par t of Note

NOTE No . 79 .

E xercises 8 3 - 94 must be worked out in Open Harmony,but

for the present , when wri ting in open harmony, the distance between Soprano and Alto , and between Alto and T enor must bee ither a fifth or a s ixth

,not more or less, thus leaving room for

on ly one harmony tone to fa ll in between both S oprano and Alto,

and between Alto and Tenor :

T he distance between Bass and Tenor (regardless of whetherthe chord is written in open or close harmony ) has no res tr ictionwhatsoever

,excepting as stated in Note No. 56, these two voices

a re never a l lowed to be more than two octaves apart from eachother .

NOTE No . 8 0 .

The final chord of any piece of music will have a most satisfactory effect if the Soprano- voice sings the octave (double octave ,or tr iple octave ) of the prime of the chord , a lthough at any time ,the fina l chord may al so appear with either the third or the fifthin the Soprano-voice .

50 E xercises in Open Harmony

E xercis es 83 -94.

e i D I T 5 ID 3 T

Ex . 8 3 ,w orked out as e xampl e

3

T D T .

5. D 3

Ex. 8 5 ,worked out a s exampl e

VOS OT

VUI

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52 Connecting Dominant and Subdominant Harmon ies

NOTE NO. 8 2 .

If two successive chords have no common tone at al l ( forexample , connecting Dominant and Subdominant chords or viceversa ) and both chords have the prime in the Bass-voice , f or thepresent , wr ite the s econd chord as follows

First : the Bass- voice, progressing by a step of a second

,

Second : the Soprano-voice, proceeding in contrary motion to

the Bass-voice,

Third : the Alto-voice,

Fourth : the Tenor-voice .

S ee illustration below showing the progression —Bass-voice at

a,—Soprano-voice at b,—Alto-voice at c,

—and Tenor-ve ice at d

The P rogression of S -D chords in 0 major

S D 4 8 D

The P rogression of D -S chords in C major

NOTE No . 8 3 .

In regard to Melody, a highly important tone in any key isthe “LEADING TONE ” (in French, Note sensible ) .

T he Leading tone of a key (major or minor ) is found bytaking the major seventh of its Tonic or fundamenta l tone.

The natura l progression of the major seventh of any keyis to proceed , or—to “lead” to the key-note or ton ic ; therefore ,the major seventh of any key‘is known by the character istic name“Leading tone .

”

Leading-tone Step P rogression 5 3

NOTE No . 8 4 .

If a voice can progress by a leading-tone step (a progressionof a sma ll semitone or minor second ) this progression is, specia llyto be recommended . For the present , leading-tone steps in the

major mode are only possible between the third of the D chordand the pr ime (or octave ) of the T chord and vice versa , and

between the third of the T chord and the prime or octave ) ofthe S chord and vice versa.

CLOSE OR OP EN HARMONYad libitum.

NOTE No. 8 5.

From now on,beginn ing at E x. 95 , no directions for close or

open harmony will be given ; the pupil must decide for himselfwhether or not an exercise should be started in open or in closeharmony; In genera l , it will be advisable to use Open Harmonywhen the Soprano-Voice sings tones of high pitch, and to use CloseHarmony when the Soprano-voice sings tones of low pitch ; forexample,

Open harmony Close harmony

NOTE No . 86.

Between two successive chords of the same harmony changingfrom open into close harmony (or vice versa ) i s not on ly a llowedbut Often advisable (though not compulsory ) , bear ing in mind tha tif Close harmony is used , the distance permitted between Sopranoand Alto and between Alto and Tenor must be either a third or

a fourth (compare Note NO. 7 7 —and if Open harmony is used ,the distance between Soprano and Alto and between Alto and Tenormust be either a fifth or a sixth (compare Note No .

54 Leading of the Voices

NOTE No. 8 7 .

But,for the present, between two successive d ifferent har

mon ies a change from close into open harmony (or vice versa ) i snot a l lowed .

NOTE No . 8 8 .

Although for the present it is imperative to fol low strictlythe rule given in No te No. 59—i. e .

,

“if two successive chords ofdifferent harmonies have a common tone , this common tone mus tbe reta ined in the same voice”—every advantage should be takeno f the grea t l iberties a llowed when the same harmony appear stwice in succession ( indicated by as in this case , not only theSoprano but any or a l l voices occasiona lly may proceed by boldestleap, thus breaking the possible monotony of a Soprano-voicepivoting on on ly two or three different tones .

NOTE No . 8 9 .

Never let a voice make two successive leaps in the same direction ; for instance , as in the following example at N . B .

,

S T D S T D

but at any time, without the s l ighest hesitation a leap of a perfectfourth followed by a leap of a perfect fifth (or vice versa ) i sa llowed in the same direction , and especia lly for the Bass-voice :

Leading of the Voices 55

NOTE No . 90 .

If a voice occasionally makes a leap, it will be best afters uch leap, to insure and promote

'

a smoothly flowing, melodiousprogression ,

tha t the voice proceeds in the opposite direction of

the leap and if possible by a step of a second,—in order , so tospeak,

“to fill up the gap (See Note No . 1 1 1 , part I )

NOTE

Avoid giving the Soprano-voice too many common tones ;f or an Alto or Tenor voice, common tones are special ly,

to be

recommended and the reason for this will be given later in NotesNo. 1 0 7 and 1 1 2 .

NOTE No . 92 .

As a genera l rule it is a lways advisable to connect chordsof diff eren t harmon ies in the most natura l manner , letting a l l

voices proceed to the nearest possible tone of the subsequent newharmony .

NOTE No. 93 .

In E xercises No . 95- 1 1 0,al l figures have been omitted , and

the pupil is a t l iberty to use his own discretion regarding thearrangement of the three upper voices , following closely in struotions given in Notes No . 8 6- 8 8 ; with regards to the Bass-voice ,compare Notes NO. 60

,69 , 8 9 and 90 .

Now , for the first time the pupil has the opportun ity to br inginto evidence his musica l knowledge

,showing his ability and sense

for melody -writing,and creating a melodious

,smoothly flowing

Soprano-voice .

56 T he P rincipa l Tr iads + T ,+D

, and + 8

E xe rcis e s 95-1 04 .

MAJOR .

S ID IT S ID IT S IT

Ex . 96 . (m4 ) e T D I S T I

Ex . 9 7 . (summer IS T IS IDT I S IDT I S IT

Ex . 9 5 ,w orked out as exampl e in three diff er ent w ay s

T he P r incipa l Tr iads + T ,

"I' D,and + 8 5 7

Is . . ID IT I S IDT I D IT

Ex . 99 (in d f l a tHBT IS D IT ID IT IS D IT S IT

Ex. 1 0 0 . (inUsfia rp )¢T S I D Is IDT I DIS ID T

Ex . 1 0 1 . (in (BT I D I S I D IT IS DIT S IT II

E rr/1 0 2 . (in E )¢T S I. . DIT I D I S D I T I I

(me me) e T ID T II

S ID IST I D IS ITD IT II

THE +D TRIAD IN THE MINOR MODE .

NOTE No . 94 .

According to Notes No . 5 and 6,every m inor key has two

accidenta lly ra ised tones—the highly important major seventh or“Leading tone ,” and the secondary important major sixth,

*and

this peculiarity of possessing two accidenta lly ra ised tones is an

essential , character istic qua lity of the modern minor mode .

NOTE No . 95 .

Centuries ago composer s introduced the Leading tone intothe old , or igina l minor mode solely to acquire the more melodiousleading- tone step between the seventh and eighth degrees of thenatura l minor sca le . Later , however , composers also ra ised thesixth tone of the ol d

,origina l minor sca le by a large semitone

in order to avoid the more or l ess unmelodic progression of an

augmented second between the sixth and seventh degrees of thissca le .

NOTE No . 96.

The introduction of these two accidentally ra ised tones in theminor mode has effectuated a great change ,

in some of its harmon ies , but pr incipally it has affected the Dominan t chord , forinstance , in the key of A minor

,the Dominant chord before the

introduction of the leading tone w as e-g-b and after the introduc

tion of the major seventh [or l eading tone ] it had to appear as

e-gii- b.

NOTE No . 9 7 .

Nowadays , with very few exceptions ,” composers absolutelyignore the key-proper Dominant chord of the old , origina l minormode ; the old , subdued, more or less gloomy minor Dominantchord has entirely disappeared from modern music and in its placethe bright maj or Dominan t chord predominates ; consequently, thethree most impor tant chords in modern minor music are the °T“I'-D and 0 8 chords , and herefrom it follows :

Tha t in any two keys of the same letter-name (namel y , one

major and one minor key ) the Dominant tr iads are a lways exactlya l ike ; for exampl e , in both the keys of G major and Of G minor the

Dominant tr iads are d—ffi-a .

K now n a s the D or ian S ix th , compa re Append ix Note V II I .

For ins tance , in Dvoi-ék’s New W orld S ymphony . firs t move

ment , second theme in G minor . repea ted l v . the minor D ominant chordappears , a l so in the s econd movement of th is symphony , s econd theme in

C sha rp minor .

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60

TONAL FUNCTIONS .

NOTE No . 99 .

Although every chord in music has but one fixed and unchangeable name ( for instance , the following chords :

can only be named the C maj or triad ,the F minor tr iad ,the D sha rp maj or tr iad ,the E fla t minor triad ) ,

any one tr iad (compare Note NO. 1 0 0 ) can express different characters , emphasiz ing the diff erentia l equation of musica l color and

thereby changing its typica l individua lity ; but, these different characters which a certa in tr iad can express , do not ar ise from the tr iadi tself but from the surrounding chords which are immedia telyconnected with it. This may be proved by the following two verysimple examples

E xample a . E xample b.

When E xample a is played, the second chord makes a distinctlydifferent impression from the two other chords : the third chordgives the musica l mind satisfaction and perfect rest, whi le the second chord, instead of giving rest and satisfaction , str ives for con

tinuation to the 0 maj or chord .

In E xample b the very same G maj or chord of E xample a isf ound , but when E xample b is played , this very same G maj or chord(which in E xample a produced in the musica l mind a longing forthe progression to the C major chord ) , now has changed its character—its color , giving complete satisfaction and rest . Although ,both times

,in E xamples a and b, the very same chord has been

played , and the fixed and unchangeable name of this chord is the

Tona l Functions 61

G maj or tr iad, it is evident that one tr iad can produce diff erenteff ects , expressing different characters or colors, but this variabilityof the individua l ity of a tr iad is not caused by the very chord itself,but as said before , by those chords which surround it or are immediatel y connected with it, and these character istic differentials arecalled the TONAL FUNCTIONS of a tr iad .

T here are on ly Three kinds of Tona l Functions, and they are

Dominan t ,

Subd ominant .

Al l chords (even the strongest and sharpest dissonant chords )a re to be conceived and expla ined as Ton ic

,Dominant

,or

Subdominant ( indicated by T ,D

,S ,

°T or08 ) or as modifications

of one of these three tonal function s ( indicated by

Dg,T p ,°sp, D

7,SVI

,et c

to be studied and expla ined later ) .

E xample showing the maj or chord (or tr iad ) l n its threedifferent Tona l Functions :

T ' T

NOTE No . 1 00 .

There are on ly Two kinds of tr iads , the Major tr iad and the

Minor tr iad, and as stated in Note No . 49 , a major tr iad consistsof pr ime, major third and perfect fifth , while a minor tr iad con

sists of pr ime , minor third and perfect fifth (compare AppendixNote IX ) .

(52

THE PRINCIPAL TRIADS, +T ,

“I' D,+ S

,

°T ,

°S,AND

THE IR INVE RSIONS .

NOTE No . 1 0 1 .

Whenever a chord appear s with prime in the Bass-voice, thechord is sa id to be in fundamenta l position ,

—and thus far a l lchords have been wr itten in fundamenta l position .

NOTE No . 1 02 .

The Bass being the deepest voice , the foundation on which,so

to speak , a chord is resting, genera lly takes the pr ime of the chord ;but , the Bass may a lso take the third or the fifth of a triad , thoughthese two latter cases are subj ect to certa in rules .

NOTE No . 1 0 3 .

Whenever the Bass-voice has any other interva l but the pr imeof a chord ( irrespective of the arrangement of a l l other voices ) ,the chord is called inver ted ; i. e . , i f the Bass has the third of thechord , the position is ca lled the first inversion

and if the Ba ss has the fifth of the chord , the p osition i s ca lled thesecond inversion :

(Compare Appendix Note X . )

NOTE No . 1 04 .

In al l exercises hitherto,the pr ime of a chord has been the

only interva l to be doubled,but from now on

,beginn ing at E x. 1 1 1 ,

either the prime or the fifth of a tr iad may be doubled, provided the

Doubling the Fifth of a Tr iad 63

doubled fifth is reached by contrary motion or by oblique motion ,

but , for the present, between chords of diff erent harmon ies nevera rrive a t a doubled fifth by means of paral lel motion :

not good

D T

However, when the very same harmony is repeated, a doubledfifth may be reached by para llel motion :

And,if absolutely necessary, the very first chord of an exercise may

appear with doubled fifth but never double the fifth in the fina lchord of any piece of music . The final chord

,having Ton ic sign ifi

cance , must a lways be in fundamenta l position and here the pr imeis the only interva l which can be doubled .

NOTE No . 1 05 .

When writing for four par ts (S oprano , Alto, Tenor , and Bass )g enera l ly the bes t in ter va l to be doubl ed wil l be the P rime of a

chord ; the next best interva l to be doubled will be the F ifth of achord ; and lastly, the Third of a chord which is the least desirableinterval to be doubled, being subject to cer ta in restr ictions to bediscussed later .

For the present , double either the pr ime or the fifth of a tr iad,but do not doubl e the third .

NOTE NO. 1 0 6.

If the Bass-voice has the fifth of the chord,it is genera lly

advisable (not compulsory ) to double the fifth

64 Leading of the Voices

NOTE No . 1 0 7 .

One of the most importan t laws of Harmony is that everyvoice Should progress natura l ly , smoothly and fluently .

The middle- voices more or less keep a l l parts together, general ly moving within a very small range

,while the Soprano and

Bass voices are permitted greater .freedom.

Therefore , i t depends entirely upon the leading [or progress ion ] of the voices whether it is best to double the pr ime or the fifthof a chord .

NOTE No . 1 0 8 .

Although the Bass at any t ime is allowed to proceed by a leapof a perfect octave—leaps of a sixth , and especial ly leaps of a

seventh between chords of different harmon ies must be avoided bythe Bass . Whenever there is a possib ility of the Bass proceedingby a leap of a sixth, in genera l , it will be better to proceed insteadby a leap of a third [which is the inversion of a sixth ] in the oppos ite direction .

NOTE NO. 1 0 9 .

Connecting chords of diff erent harmon ies , never let al l voicesproceed in parallel motion as follows :

However , when the same harmony is repeated , a l l voices may

proceed in para llel motion ; for example , the following progressionsa re a llowable

Consecutive Fifths and Consecutive Octaves 65

NOTE No . 1 1 0 .

It is strictly forbidden to let two voices progress in fifths orin octaves , either in para llel motion or in contrary motion

very bad not a l l ow ed

Such faulty and absolutely unpardonable progressions are

known by the name Of “Consecutive [or para llel ] F ifths and Oc

tavesf’

But if a chord of the same harmony is repeated an octavehigher or an octave lower in exactly the same position,

the aforesa id progressions are a llowed ; for example,

It is scarcely necessary to add tha t Con secutive P r imes are

just as bad as Consecutive Octaves , and the following progress ionunder no circumstance l s a llowed :

(Also comDare Appendix Note XI . )

66 Leading of the Soprano-voice

NOTE No . 1 1 1 .

GENERAL RULES FOR THE LEADING OF THE S OPRANO-VOICE .

I . First of a l l the excellent words of Riemann may be quotedIn progression by . seconds rests the actual healthy life of melody( therefore , the sca le is rea lly at a l l times the norma l basis of mel

ody ) and this is appl icable even to the freest, boldest melody forma

tion . Leaps are not , indeed , excluded in melody ; on the contrary ,

they form the most eff ective factors (vigorous arousing, sudden collapse of energy, but they enta il subsequent complete, or , atleast , partial , fi lling up of the gaps by means of single- step prog ress 1 ons.

”

II . If the Soprano proceeds by making a leap downward , itwill be best to have the chord preceding the leap in Open harmonv

and the chord following in Close harmonyI f the Soprano proceeds by making a leap upward, i t is advis

able to have the chord preceding the leap in Close harmony and the

chord following in Open harmony. For example :

III. If the S oprano proceeds ascending through four tonesor more (compare E xercise 1 1 1 , measures 1 - 3 ) genera lly , it will bebest to begin in Close harmony , permitting the Bass to star t ratherhigh and progressing in opposite direction to the Soprano-voice .

If the Soprano proceeds descending through four tones or

more (compare E xercise 1 1 2 , measures 1 -2 ) it will be advisable tobegin in Open harmony, and in this case, permitting the Bass tostar t rather low

,advancing a lso in contrary motion aga inst the

S oprano-voice .

IV . In order to give more var iety to the Soprano-voice , occasional ly, it i s a l lowed to depar t from the rule—“Reta in common

tones in the same voices” ; for instance,b e tter

Can tus Firmus

in Ba ss :

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68

CHANGING FROM CLOSE INTO OP E N HARMONY (ANDVICE VERSA ) BE TWE E N DIFFE RENT HARMONIE S .

NOTE No . 1 1 4 .

Heretofore , a change from open into close harmony and viceversa was permitted only between two chords of the same harmony(compare Notes NO. 8 6 and but from now on , a change fromopen into close harmony and vice versa may be made without hesitation between any two chords , provided the leading of the voices doesrequire or permit such change , a lways bear ing in mind that a

smooth and natura l leading [or progression ] of a l l voices is one

of the pr incipal laws of Harmony °

Changing from open into Changing from close intoclose harmony : open harmony :

T S T T D T S T S

NOTE No . 1 1 5 .

From now on (beginn ing at E x. 1 1 1 ) the distance betweenSoprano and Alto voices may also be less than a third or more thana sixth , though never more than an octave

not g ood

The distance between Alto and Tenor voices may also be lessthan a third

* R e g a rd ing S op rano and Al to s ing ing the interva l of a pe rf ec t

prime ,compare Note s NO. 1 1 5 and 1 1 6.

Distance permissible between Voices 69

and , if necessary , these middle-voices may a lso be one whole octaveapart—never mor e, provided the distance between Tenor and Bassvoices is a rea l third (not a tenth )

not g ood

The reason for this last restr iction is that ofsound produced by two low voices singing the small interva l of athird, covers more or less the empty space of an octave betweenTenor and Alto voices .

NOTE No . 1 1 6.

Two voices may s ing the interval of a perfect pr ime

but never let any two voices continue to sing a pr ime in two suc

eessive chords , asr

otherw 1 se, four-par t muSIC will appear as three

part music ; for Instance ,

not al lowed

7 0 Leading of the Voices

NOTE NO. 1 1 7 .

Whenever in an exercise the figure 1 or I refers to the S opranovoice ( for instance , the tenth chord in E x . 1 2 1 ) it is self understoodthat the Soprano has actua lly to sing the P r ime of the chord and

not the Octave of the pr ime ; hence, the tenth chord in E x. 1 2 1 mustbe wr itten :

T T

and not

NOTE No . 1 1 8 .

With the only exception of the augmented prime (compareAlto and Bass voices respectively in the very first music exampleof Note No . it i s str ictly forbidden to let any voice proceedby an augmented interva l (see working-out of E x. 1 1 1 , on page 7 1 ,the fourth and fifth chords ; a lso compare Appendix Note XII ) .

NOTE No . 1 1 9 .

Whenever in the progression D—T (or D—°T ) the leading toneappears in the Soprano- voice , the leading tone must proceed upward(compare Note NO.

NOTE No . 1 20 .

In genera l,i t will be safest and best (and sometimes necessary

in order to avoid mistakes ) to let Soprano and Bass voices move incontrary motion, even if both voices proceed by leaps .

This does not mean that it is forbidden for Soprano and Bassvoices to move in para llel motion, but never between chords ofdifferent harmon ies have the Soprano and Bass voices progress inparal lel motion by leaps in both voices .

No objection can be made if Soprano and Bass voices move inparallel mot ion in thirds or in sixths , even if occasional ly bothvoices proceed by leaps

T D T S T

T he P rincipa l Triads and their Invers ions 7 1

NOTE No . 1 2 1 .

It may be advisable to remind the pupil that the rule given inNote No . 8 2 on ly refer s to chords in fundamental position ; wheninversions are used it is not necessary to adhere to the instructionsspecified in this note .

E xer cis es 1 1 1 -1 23 .

CANTUS FIRMUS IN SOP RANO .

MAJOR.

1 3 1 1 3 1 1 3 5 1 3up3 1 1 1

E x . 1 1 2 .

1 5 3 5 1 3 3 3 1 1 1 1 1

E rr/1 1 3 .

E x .1 1 1 , Cantus P irmus in S opr ano ,w orked out as ex amp l e

T D s T S D T D T S D

1 3 1 1 NB.3 1 1 3 5 1 3 1 1 13 3 1 1 1

At MB .the pr ogr e s s ion in the B a s s -v oice w ou l d

b e ve ry bad on account of the a ugme n ted four th (compar e Not e N9

1 1 8 1 .

7 2 The P rincipal Tr iads and their Inversions

MINOR.

E x . 1 1 4 .

E x . 1 1 5 .

c g f c

I 5 11 1 1 V III 1 1 1 1

CANTUS P IRMUS IN ALTO .

MAJOR.

Ex . 1 1 6 .

d b cb d b

Ex . 1 1 7 .

b . . b e ll 0 e f f]1 1 3 5 1 1 1 3 5 1 3 g 1

BKAI4 ,Cantus P irmus in S opr ano,w ork ed out as ex ampl e

I III 5 I 1 1 3 1 1 1 1 1 V III 1 1 1

*It is se l f und erstood , especia l ly as no chord -let ter is g iven , tha t thesecond and f ourth chord s in E x . 1 1 6, a re the chord s d b-f -ab. CompareNote No. 45 , p art VI .

Ex. 1 1 8 .

Ex . 1 1 9 .

E x . 1 2 0 .

Ex . 1 2 1 .

BL 1 2 2 .

The P r incipal Tr iads and their Inver sions 7 3

MINOR.

I 3 I I 3 1 I III 5 I III I T I I

CANTUS FIRMU S IN TE NOR.

MAJOR.

1 3 1 3

MINOR.

I III V III 1 1 11 1 1 3 1 1 1 1 1 1 1 1

74

THE AUXILIARY °S CHORD IN THE MAJOR MODE .

NOTE No. 1 2 2 .

Just as the MINOR mode has the accidenta lly ra ised seventh(the impor tant leading tone ) the MAJOR mode sometimes appear swith a character istic accidenta lly lower ed tone , and this acciden

ta lly lowered tone in the Maj or mode is the sixth of the majorscale

,lowered by a large semitone

,giving the Major mode a new

and third leading- tone step ; for example , in 0 major fromA fla t to G and vice versa .

NOTE No . 1 23 .

This accidenta lly lowered sixth in Major most probably hasbeen instituted by the old composers of church-music

, aga in , in

order to acqu ire a new leading tone progression—but now ,in the

Major mode—viz ., between the two chords accompanying the

Amen ; for instance, in C major :

A men men .

NOTE No . 1 24.

Although the accidentally ra ised seventh (the leading tone ) inthe Minor mode has absolutely removed the old minor Dominantchord (in the key of C minor, the chord g-bb-d ) from modernmusic , the accidenta lly LOWERED SIXTH in the Major mode hasnot had the power to displace the old major Subdominant chord .

The old,or iginal major Subdominant chord has always ma inta ined

its place as third pr incipa l chord in the Major mode, yielding onlyin impor tance to the T on ic and Dominant chords .

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7 6 Cross Re l ation

In other words,if in two successive chords a tone is chromati

ca lly changed,this chromatic change must be made in the same

voice ; and at the same time, it will be advisable (not compulsory )to reta in a l l common tones .

NOTE No . 1 2 8 .

Aga in , the pupi l is reminded of Note No . 8 8,to take every

a dvantage of the oppor tun ity which is offered whenever the sameharmony appears twice in succession ( indicated by The sec

ond chord certa inly should never be wr itten a t random, but , quoting Riemann :

I f the same harmony appears twice in succession a changeof position of the chord should deliberately be made use of in orderto ga in a good prog ression to the following ; the student should insuch cases a lways find out which position i s rendered desirable bythe Bass-tone required for the next chord .

”

E xe rcise s 1 24-1 29 .

MAJOR.

Ex . 1 2 4 , worked out a s exampl e5

T .S‘

T T D T S D T S D T1 1 5 1 3 5 3 1 1 1

Formation of the Bass-voice

8 8 v°

e f zambT S S D1 3 m 1

5

E x . 1 2 7 . (m4 )¢T S T D S1 I 3 1 3 up3 3

3

ST S D T |S . . SD TD

1 1 3 I 1 3 13

doq~

3 8

1 1

51

131“

3 fD§

°l mID

'

gf"TII

FORMATION OF THE BASS -VOICE .

NOTE No . 1 29 .

While inregard to Melody , the Soprano or highest voice as a

rule is the pr incipa l or leading voice,—in regard to Harmony , byf ar the most important or leading voice is the Bass or lowest voice .

NOTE No . 1 3 0 .

AS stated in Note No . 1 0 2 , the Bass , being the lowest voice ,f orms the foundation and is that particu lar voice on which a c hordr ests .

In Harmony,the Bass takes an exceptiona l position , f ar

more and quite differen t to a l l other voices ; and therefore , ion of a per fectly correct Bass-voice is cer ta in lymore than tha t of any other voice .

Al though the Bass as a rule likes to take the pr ime of a

chord (compare the Bass-voice of E xercises 1 1 1 it may

7 8 Formation oi the Bass-voice

a lso take any other interva l of a chord, provided this interva l isr eached and l ef t by a s tep of a second

T D T ° S D S D S T D T D

1 5 3 1 1 3 1 1

NOTE No . 1 3 2 .

Occasiona lly the Bass-voice may take or leave the Third of a .

chord by a leap

but,it is Str ictly forbidden for the Bass , when a change of harmony

takes place, to proceed even by smal lest leap from or to' the fifth

of a tr iad—con sequently

NOTE No . 1 3 3 .

The Fi fth of a tr iad can be used in the Bass only when itenters and leaves by a step of a second ; at the same time, if pos

Formation of the Ba ss-voice 79

s ible, avoid having the Fifth in the Bass return to the very sametone which it has just left

not v e ry od much b e tte rM

T D T T D T

The reason why the Bass-voice cannot take the fifth of a tr iadby a leap will be expla ined after the study of the “

Dominant-FourS ix chord .

” Moreover,i t is prohibitive for the Ba ss a t any time

to take the fifth of a tr iad in two successive chords .

NOTE No . 1 34 .

The rules given in Notes No . 1 3 2 and 1 3 3 refer on ly to chordso f different harmon ies

,for , if the same harmony is repeated, oc

c asional ly, as an exception, the Bass-voice may take or leave theF ifth by a leap :

T ° S D T D T U S . . U T

a t the Bass takes the Fifth by a leap, and

a t the Bass leaves the F ifth by a leapbut , on a strong (or accented ) beat, the Bass-voice is never a l

l owed to take the F ifth of a tr iad -by a leap, even though the sameharmony is repeated :

° T D ° T

In genera l,the pupil is cautioned to make a most restr icted

use of the second inver sion of a tr iad ( i . e . , fifth in the Bass ) .

8 0 Formation of the Bass-voice

For instance, take as example any of Beethoven’s Sonatas and closeobservation will Show

‘

that on ly by gr ea tes t er cep tion a tr iad appea rs with F ifth in the Bass . E ven ILL/ 8 1 1 0 11 exceptiona l cases theprogression of a l l voices leading to a tr iad in its second inversionmust be as smooth as possible . Also

,compare the smooth progres

s ion of a l l voices leading to triads in their second inversion in theworking-out of the following exercises

E xercise 1 1 1 , worked out on page 7 1 ,( 6

1 1 4,

c c c c u < 4

1 24, 76—and others .

NOTE No . 1 3 5 .

The very fir st chord of an exercise (or of any piece of music )may appear with the thif d

i f

in s the Bass-voice (compare E x . 1 3 0 ,worked out on page 8 1 ) though never with the fif th in the Bass,w hile the fina l chord mu st a lw ay s app ea r in fundamenta l p osit ion, T or T and fur thermore, it will be advisable and more satis

1 I

factory to have the chord preceding thd fina l chord a lso in fundamenta l position ; thus :

1I

D T”or S or S T lletc.

\ 1 1 1 1 , I I

(Compare Note No .

NOTE No . 1 3 6.

Also, regarding the Bass-voice,special stress should be laid

on Riemann’s excellen t words quoted in Note No . 1 1 1 , part I

,

“In progr ession by s econds r es ts the actua l hea l thy lif e of

me lody, and the sca l e is r ea l ly a t a l l times the norma l basis of.melody.

Therefore, relative to the diff erent Notes referr ing to a per

f eet l ead ing of the voices, it may be well to say, that particular lyf or Bass and Soprano voices , occasionally diaton ic progressions[scale like motion ] are highly recommendable ; compare the Bassand Soprano voices of E xercises 1 3 0 and 1 3 1

,the first five and

four measures respectively, worked out on page 8 1 , also compareBass and Soprano voices of measures 2 to4 of Wagner’s P reludeto “

Die Meistersinger .

”

NOTE No . 1 3 7 .

Supplementing Note No . 1 1 9,i t is necessary to add , that

whenever the leading tone in the progression D—T or D—°T ap

pears in a more prominent voice , i . e ., Soprano or Bass—the

leading tone must proceed upward ; however , in a middle-voice ,Alto or Tenor

,the leading tone in the progression D—T or D—°T

may proceed either upward or downward .

Ton ic, Dominant , and Subdominant Harmon ies 8 1

E xe rcise s 1 3 0 -1 3 9 .

Ex . 1 3 0 .

(in fi '

fimaj or ) (3T D IT S‘

IT S IT D IT

Ex . 1 3 1 .

i

(mamm) OS I° T DI° TDI6T ° S I D I ° S I D IOT I If

Ex . 1 3 2 .

D IT I D I IT S IOS D

Ex . 1 3 3 .

I° T .Dl° T I° S D I0 T II

O, k d t'

m—IeEms W e

T

o

iia

fie

s

mirps T D T S T ° S D T

d t,1Igx 'mi ’m idi;T

ou

DaL

gii

iimgrbs D °T ° S D ° T

The ha l f not e b e l ow th e func t ion l e tt e r ° S (0 S ) ind ic a tes

that this chor d mus t ap D e ar in ha l f not e 8

8 2 Tonic , Dominant , and Subdominant Harmonies

Ex . 1 3 4 .

I S I D IT ° S ID T IS ° S

Ex . 1 3 5 .

I° S I D I° T ID°T I° S ID . .I° T I I

Ex . 1 3 6.

IS DiT D l T I° S D IT I° S

Ex . 1 3 7 .

(in p : I D I ° S I° T ID ° T I° S D I° S D I° T II

Ex . 1 3 8 .

I D I T I ° S B IT II

Ex . 1 3 9 .

DI° T ID IoT II

NOTE No . 1 3 8 .

h

/Y

E xercise No . 1 3 9 practical ly concludes the study of al l P r incipa l Triads, and the chords thus f ar studied, the TONIC , DOM INANT

, and SUBDOMINANT tr iads (as they appear either in the majoror in the minor mode ) are the pr incipa l and most important chordsin music ; they are , so to speak, the three mighty pillars on whicha l l music rests—the foundation or generating centre of al l musica lcreation ; they are the source from which a l l harmon ic combinations have ar isen

,as al l of the infin ite number of chords which

can possibly be constructed, have their direct or indirect root inone of these three leading chords or , as they are ca lled , “P r incipalTr iads, i . e .

,Tonic

,Dominant, and Subdominant, and this w il l

be shown and proved later , as gradually, the study of more com

plicated chords is reached.

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8 4 T he Dominant-Four-S ix ch 'ord

This disguised Dominant chord , in fact, belongs to a class ofdissonant chords (compare Note NO. 1 8 9 ) ca lled Suspensions ,

”

and a lthough the study of Suspensions” will not be taken up

until much later , it i s str ictly necessary to define and expla in thisdisgu ised Dominant chord without further delay , as even at thevery beginning of the study of Harmony this new chord is indispensable .

NOTE NO. 1 40 .

Therefore , if at the close of a musica l phrase (compare NoteNo . 1 50 regarding the word Cadence ) the penu ltimate chord isthe “

Dominant chord ,” this Dominant Chord very often is preceded by a chord which appear s to the eye as a Tonic chord in itssecond inversion (i . e . , fifth in the Bass—compare illustration ofNote No. 1 3 9 ) however , the ear decides that this chord formationcannot be a Ton ic chord—but

,tha t this very chord is a Dominant

chord of which the third and fifth have been r eplaced (or sus

pended ) by the fourth and s ixth .

NOTE No . 1 4 1 .

The chord formation which ar ises from a D chord of whichthe third and fifth have been suspended by the fourth and sixth, isknown in the more modern study of Harmony by the name Of theDOMINANT-FOUR-S IX CHORD.

NOTE No . 1 42 .

As in any key , the Dominant our-S ix chord,” and the T on icchord in its second invers ion look exactly a l ike , the car a lone hasto decide how these chord formations should be classified ; for instance , the tona l functions Of the following phrase

certa inly are not

T D IT I S ID T I. . IS° S IT D I T II

as erroneously given in most books on Harmony (even in the well

The Dominant-Four-S ix Chord 5

known Manua l of Harmony of my highly esteemed teacher , P rof.Jadassohn ) , but most decidedly they are :

T U IT I S ID T I IS OS ID Z D IT II

(Compare Appendix Note XIII . )To the eye the four th and thirteenth chords of the above exam

ple may look a like (both being g -c- e ) but the ear perceives the grea tdiff erence in character of these two chords : the four th chord is the0

,maj or triad (T chord ) with the fifth in the Bass , while the

thirteenth chord is by no means a C maj or tr iad , but the G maj ortriad (D chord ) of which the third and fifth have been suspendedby the four th and sixth , and the tona l function of this latter chordis known as the Dominant-Four -S ix chord

,indicated by D 2.

NOTE No . 1 43 .

Suspended tones (better call ed “Suspen sion s can never bedoubled , and therefore, in the Dominant-Four - S ix chord the pr ime

‘

is the on ly interva l which can be doubled—never double ei ther thef ourth or the sixth of this chord .

Furthermore, there are no inver sions of the Dominant-FourS ix chord, and same is u sed

,without exception, in fundamenta l

position on ly .

NOTE No . 1 44 .

The Dominant-Four - S ix chord is a lways fol lowed (and forthe presen t immediately ) by the actua l Dominant chord . Boththe Dominan t-Four -Six chord and the subsequen t D chord can

only be used in fundamental position (prime in the Ba ss )while the four th and sixth of the Dominan t-Four -S ix chord andthe third and fifth of the subsequent D chord may be given to anyof the three upper voices

D2 D DZ D“

D2 D

After a Dominant-Four-S ix chord one or more voices (even

Zhe r

giddl e-voices ) may proceed by leaps—as shown in E xamples

an e .

8 6 T he Dominant-Four - S ix Chord

In E xample e, consecutive octaves appear in contrary motionbetween Bass and Soprano , but no possible obj ection can be madeaga inst same as here the consecutive octaves occur on account ofthe tran sposit ion of the pr ime and the octave into a lower and

higher octave (compare Note No . the tones e fla t in bothchords are the pr ime and the octave of the two chords.

NOTE No . 1 45 .

As stated above , the Dominant-Four-S ix chord must be followed by the actua l

'

Dominant chord, and in turn this actualDominant chord for the present must be followed by the Ton icchord

,therefore it is evident that the character istic place of a

Dominant-Four- S ix chord is always the third chord from the end

of a phrase or musical sentence , and as regards Rhythm , at a l l timesi t must appear on a beat s tronger than the beat on which the subsequent D chord enters.

NOTE NO. 1 46.

As expla ined in Notes NO. 1 3 9- 1 4 1,a Dominant-Four-S ix

chord is a Maj or Dominant tr iad of which the third and fifth havebeen suspended by the four th and sixth ; therefore , it would beentirely wrong to indicate the Dominan t-Four -S ix chord whenappear ing in the minor mode by Dii

i as the Dominant triad in any

minor key is a lways a Maj or triad ; consequently, the DominantFour-S ix chord in the minor mode must a lso be indicated byArabian figures

,and the figure 6 must be accompan ied by the

sign

The explanation for this is that in the minor mode the fifthof the D chord by no means can be suspended by the natura l ornorma l sixth (compare Appendix Note VI ) , but by the key-properminor sixth , hence the figure 6 of a Dominant-Four-S ix chord inthe minor mode must appear with a decrescendo Sign ,

which Signaccording to Note NO. 45

, part XIV ,indicates that the

natura l or norma l interval (not the key—proper interva l ) must belowered by a large semitone ; consequently, the proper indicationfor the Dominant-Four - S ix chord in the Minor mode must be6>D4

0

Furthermore , a l l rules given for the Dominant-Four - S ix chordin the Major mode also hold good for the Dominant-Four-S ixchord in the Minor mode . (Also compare Appendix Note XIV . )

NOTE No . 1 4 7 .

Never doubl e the fifth in a D chord if same has been immediately preceded by the Dominant-Four-S ix chord .

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8 8 The Dominant-Four - S ix Chord

E xercis es 1 40 -1 55.

Ex . 1 40 .

(ia aj orflbD IT IS T IOS D IT IS D IT OS IDZ D IT II

I"

Ex . 1 41 .

(in UII film .) (bS II5

) I° T ° S ID I° T . . I° SDI° T ° S ID2

> '

D I° T II

I”

1 1 1 1 4 42 .

5

(in A l: maj or )¢TS I° S T I D S IT ID T IS OS ID"D I T I I

Ex . 1 4 3 .

IDOT ID I° T II

Ex . 1 40 , w ork ed out a s ex ampl e1

D T S T ° S D T S D T ° S D2D T

E 1 4 41 , w or lir

fiad out a s examp l e

S D ° T ° S D ° T ° S D°T ° SD2

>D T

The Dominant-Four- S ix Chord 8 9

Ex. 1 .44

(inF IImaj or )¢TD IT IS D IT IPS D IT S IDa D I T I I

Ex . 1 45 .

(in a ll mahfi)¢ I° S DI°T D I° T I° S I D2> D IOT II

Ex . .1 46

(inGIvmaj or )¢T I D I S ID T IS OS IT S IDZ D IT

o f“

f"

.

ID I° T ° S ID IOT ID2> D I° T

(ia aj q r ) (bS D IT IOS D IT IS D I'

T IS D I T

Ex . 1 4 9 .

o S ID

Ex . 1 5 0 .

(inF maj or )¢S IT D I T I S I T IDT IDT IDZ D IT

f

(m z a .MS T ° S ID° T I° S I° T I D

E l i -1 5 2 ° 3 down 3 3 8 d W I IT S IDT ID IT S

°

II

SDIT S IDZ D IT II

9 0 Cadences

Ex . .1 5 3

(ia s OT OS IDOT I DIOT OS II

D I OT IDZ

>D IOT II

Ex . 1 5 4 .

ID T I S D IT ID T ID IS ° S IT II

Ex . 1 5 5 . 5

(in Abmm (DD IT ID°T I° S IOT I° S DIOT OS IDZ>DI° T II

CADE NCE S .

NOTE No. 1 50 .

A “CADE NCE ” i s a series of chords , which expresses conclusion

,occurr ing at the end of a mus ica l phrase or per iod , and giving

the musica l mind complete satisfaction and rest .Therefore , the closing chord of a cadence can on ly be the

Ton ic chord in fundamenta l position , appear ing at a point strongest as regards rhythm and metre .

NOTE No . 1 5 1 .

There a re thr ee different kinds of cadences known as

1 . The “Authentic” or“Dominan t Cadence

,

”

2 . The P lagal,” a lso “Subdominant” or “Amen Cadence .

3 . The“P erfect or

“Complete Cadence .

NOTE No . 1 52 .

An Authentic [or Dominant ] Cadence is a cadence in whichthe final chord is preceded by the D chord :

D T | | or D °T | |

A P laga l [a lso Subdominant or Amen ] Cadence is a cadencein which the fina l chord is preceded by the S or

°S chord :s T | | or

°S T | | or08 1

°T | |

A P erfect [or Complete ] Cadence is a cadence of which thelast three tona l functions are Subdominant, —Dominant, —Ton ic,thus

S D I T | | or°s D T | | or

°S D 0T"(Compare Appendix Note XVI . )

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‘LO10 Cadences

° T D ° T ° S ° T °S D2

>D ° T O S ° T

In order to give cadences greater volume of tone,thereby

strengthen ing the effect , they may a lso be played with doubledBass and Soprano voices . Hence

,the foregoing cadence may be

played (as in the key of E minor ) , as follows

f° T D or os ° T os D2

>

D ° T ° s °T

It i s true , in the two examples at f , the Dominant-Four-S ixchord appear s in these cadences as apparently the fifth chord fromthe end, and not , as stated in Note No . 1 45

,as necessar ily the third

chord from the end ; but the fact is that in this instance the seventhmeasure of this cadence actual ly concludes the phrase or musicalsentence, while the eighth and n inth measures on ly constitute an

extension or coda ; consequently, as shown in the above illustration , a fter the perfect or complete cadence there follows still ahother—a plaga l cadence .

“T h is doubl ing of B a ss and S oprano voices certa inly must not beregard ed a s

“f aul ty consecut ive octaves” nor a s f aulty d oubl ing of the

th ird ” (mea sure 5 , chord 1 ) because, notwithstand ing tha t more than

f our tones a re hea rd s imul taneous ly , the mus ic is on ly f or f our ind iv idua l pa rts , of wh ich two parts , S oprano and B a ss , have been s trengthened by doubl ing .

P eriod and Sen tence 93

NOT E No . 1 56.

P ERIOD AND SENTENCE .

The student , no doubt , has noticed tha t a l l Harmony exercises( except the very simple E xercises No . 24-94 ) have a length of

e ight measures .

In fact , the smallest division possible in order to express a

c omplete musica l idea usua l ly consists of at lea st eight measures .Hence , any independent musica l par t which represents in itself a

w hole— a total ity,genera lly involving such smallest

,complete

musica l idea of at least eight measures in leng th , and ending witha Ton ic chord in fundamenta l position (which gives the musica lmind rest and satisfaction ) is called in musica l terminology a

Such P er iod of eight measures usual ly consists of. two sub

d ivis ion s or section s of four measures each,which stand to each

o ther , so to speak, as question and answer (com‘pare Cantus P irmu s

o f E xercises No . 1 56

The first four measures of a per iod ( the ques tion ) constitutewhat is cal led the first sentence , and the second four measures( the answ er ) constitute the second sentence consequently, a

p er iod consists of [at least ] two sentences .

In accordance with the laws of Metre it is best to end everys entence (especia lly if the la st measure of a sen tence conta in s on lyone chord ) with a chord in fundamenta l position , and with raree xceptions , the chord closing a first sentence will a lways be a Domin an t chord (seldom a Subdominant or a Ton ic chord ) because a

D ominan t chord , more than any other chord, possesses the qua lityo f question ing character in the strongest degree .

If the final chord of a sen tence is a Dominant Chord in fund amenta l position ,

such sentence is sa id to end with a“Ha l f

C lose” ; but, if the final chord of a sentence is a Ton ic Chord in

fundamenta l position ,same is sa id to end with a

“Fu ll C lose”

( compare Appendix Note XVII )

*Compa re the firs t e igh t mea sures of the s low movement of a lmosta ny sona ta by B ee thoven , Moz art , Hay dn , K uh l au , e tc .

M “Ins tea d of the word S entence”a lso th e word “

P hra se is of ten

us ed ,bu t a s the term “

P hra s e” app l ie s to some th ing quite d iff erent inmus ica l terminology—the d es igna t ions “firs t” and

“second s entence,” with

r e g a rd to the d i ff erent sect ions of a period , may be bet ter than “firs t”and

“second phra se .”

94 1 4 17

FRE E HARMONY .

NOTE No . 1 5 7 .

Free Harmony, this expression is used to define a new ser iesof exercises , tha t is , exercises f or

“Harmoniz ing

”

a melody whichappears without any indication of tona l funct ions , or chord- lettersand signs ; consequently , in these new exercises the pupi l mustdeterm ine the best and most appropr iate harmony for each and

every tone of a “Cantus P irmus .

NOTE NO. 1 58 .

It is needless to say that in Free Harmony exercises onlythose chords can be used which have been studied hitherto—and

therefore, in the maj or E xercises NO. 1 56 1 65 On ly the + T,+D

,

+ S,D2 ,

and occasionally,the °S chords can be introduced, while

in the minor E xerci ses NO. 1 66- 1 75 on ly the °T,+D

,

0 8,and

D2> chords are a llowed .

NOTE NO. 1 59 .

In al l Free Harmony exercises , if the in itial chord enters onthe first [accen ted ] bea t of the measure, such harmony must bea Ton ic chord ; but , if the initia l chord of an exercise enters on an

unaccented beat (up-beat [in German—Auftakt ] ) this first chordmust be a Dominant (or a Subdominant ) chord (compare E xercises 1 3 1 , 1 3 5 , 1 3 6, while the fina l chord Of any piece of

music must a lways be a Ton ic chord.

NOTE NO. 1 60 .

From wha t has been sa id about the D2 and D2> chords inNote NO. 1 45, it is obvious that the D2 and D2

> chords can

never appear at the beginn ing or in the middle of a sentence ; ifthe D2 or D2

> chord is introduced at al l , it can on ly be used as

third chord from the end of a per iod and must a lways be followedby D and T (or

°T ) chords ; while, regarding metre the D 2 (or

D2 chord can only appear on an accented beat of a measureand the subsequent D chord on a beat less accented .

NOTE No . 1 61 .

The D2 or D2> chord ga ins con siderably in strength and

e ffectiveness if it is immediately preceded by the S or0 8 chord

(compare Notes No . 1 52 and 1 54 about Cadences ) , but specia lcare must be taken never to have the D2 or D2

> chord immediately preceded by the actual D chord .

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9 6 Free Harmony

Ex . 1 5 9 .

E x. 1 6 0 .

EXAM .

3 15 1 62 .

E x i1 63 .

E x . 1 64 .

E x . 1 65 .

MINOR.

Ex . 1 66 .

E XJGG, w orked out a s examp l e° T ° S ° T OS D

'

° T D ° T ° S D2>D °T

Ex4 67 .

Ex4 68 .

Ex4 69 .

Exd 7 0 .

Fkfl 7 2 .

Ex4 7 3 .

Ex4 7 4 .

Ex 1 7 5 .

Free Harmony 9 7

98

PARALLEL CHORDS

(SECONDARY TRIADS )

IN THE MAJOR MODE .

NOTE No . 1 64 .

SO f ar,on ly the first, fifth, and four th tones (or degrees ) Of a

sca le have been used for the formation of chords ; and tr iads bu ilton the first, fifth , and fourth tones of any major or minor scale areca lled

The P r incipal T r iads of the key in question , known by thenames

T on ic Tr iad,

Dominant Tr iadSubdominant Triad.

NOTE No. 1 65 .

If the key-proper third and the key-proper fifth are added tothe second, third , s ixth, and seventh tones of any maj or sca le , theresult will be , for instance , in C major :

Analyz ing these four new tr iads built on the tones d, e, a, andb, the pupil will notice that the three chords, d-f - a ,

and e-g-b

,and

a -c- e, consist of pr ime, minor third and perfect fifth ; consequently ,these three new triads

,notwithstanding the fact that they are

found in the key of C maj or , are minor tr iads belonging to thatmaj or key .

But, analyz ing the chord bu ilt on the seventh tone of a majorsca le (in C maj or , the chord b-d-f ) , it will be seen that this chordconsists of pr ime, minor third and diminished fifth, and therefore ,according to Note NO. 1 0 0 (and see Appendix Note IX ) , thischord formation is no tr iad at a l l but a

“dissonant” chord,which

will be studied later under the Chapter of“D issonant Chords .

NOTE No . 1 66.

In contradistinction to the three pr incipal tr iads of any majorkey

,the new tr iads, built on the second , third and sixth tones Of

any maj or scale, are generally known as the Secondary Tr iads”of the key ; and in importance and use these Secondary T r iads areextremely infer ior to the P r incipal Triads .

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1 0 0 P arallel Chords in the Major Mode

In example a , the chord at N .B . certa inly looks l ike a d minortr iad built on the second tone of the sca le , but this chord , as re

gards i ts Tona l f unct ion , most decidedly gives the ear the impression of a Subdominant chord, and it cer ta in ly would not be toof ar-fetched to ca ll this chord the Subdominant tr iad of C maj or,modified by replacing the fifth of the tr iad by the key-proper sixth(compare Appendix Note XVIII ) .

In example I) , the chord at N .B . has the appearance of beingan e minor triad built on the third tone of the sca le , but aga in , re

garding its Tonal ' function , the car will assign to this chord theDominant function , and (as in the case of the modified Subdominant chord ) i t wil l conceive this e minor tr iad as the Dominanttr iad of C maj or , modified by replacing the fifth of the tr iad bythe key-proper sixth .

NOTE NO. 1 69 .

From the examples and explanations given in Note No. 1 68 ,

it is evident , tha t m the Maj or mode a pr incipa l tr iad occasiona llycan be replaced by the respective second ary tr iad ; for example, inthe key of C major—the f maj or [pr incipal ] tr iad occasiona l lymay be replaced by the d minor [secondary ] tr iad, and the 9 major[pr incipa l ] tr iad occasiona lly may be replaced by the e minor

[secondary ] tr iad , thus substantiating the connection between a

P r incipa l tr iad and its substitute Secondary tr iad,and s tanding to

each other in exactly the same r e la tion as any maj or sca le (or key )to the para l l el minor sca le (or key ) .

In view of these facts it must be admitted that Riemann mosta ssuredly has instituted and given the most appropria te name ,“PARALLE L CHORDS ,

” to those minor and major tr iads whicha re general ly known by the name of “secondary tr iads” ; and as

,for

example , the sca le of D minor is the parallel scale of the F majorscale ; and the scale of G maj or is the para l lel scale of the E minorscale : so a l so, the d minor triad is the parallel chord of the f ma jortriad , and the 9 maj or triad is the parallel chord of the e minor

tria d , consequently

NOTE No. 1 70 .

P a ra llel Chords are two triads (one major and one minor )standing to each other in exactly the same relation as two para llelscales . For example :

The para llel chord of the d maj or tr iad is the chord b-d-ffli,and vice versa

the parallel chord Of the 6 minor tr iad is the chord d-ffl-a

The para ll el chord of the a fla t maj or triad is the chord f—ab-c,and vice versa :

the para llel chord Of the f minor triad is the chord ab-c—eh.

P ara l lel Chords in the Major Mode 1 0 1

NOTE No . 1 7 1 .

In Note No. 1 69 on ly the para llel chords of the D and S tr iadshave been discussed, but with regards to the T chord , it is clearthat on account of the un ique character istic of the Ton ic function ,

a Ton ic chord in fact can never be actua l ly r eplaced ; neverthe

less,thq para llel chord of a Ton ic chord (for instance , in the key

of E fla t maj or , the chord e- eb-g ) may be introduced as a subs titute for the Ton ic chord and P ARTICULARLY in a DECEP TIVECLOSE (compare Appendix Note XV I)

T S DTp S ps T T Tp DZD ' N.B .

a t N .B 1 nstead of the expected T chord, the “P arallel chord appears , l

which changes the “authentic cadence into a

“deceptiveclose” involving an indispensable continuation (compare Appendix Notes XV I and XVII ) .

NOTE No . 1 72 .

These P arallel chords in the Major mode are indicated byfunction-letters T ,

D , S , to which the sma l l letter p [parallel ]been added as follows —T p, Dp, Sp . For E xample ,

In the key of C major , T p denotes the chord a -e-e,66 66 66 66

Dp66 66

e_g-b,

66 66 ‘6 SpB major , T p

{4 c c c c Afla t maj or , DP5: ( 6

F sharp major , S p

E xe rcis e 1 76.

Wr ite the following chords :Dp in the key ofT p

65

SP66 66 66 66

T p66 66

Dp66 66 66

T I)66 66

1 0 2 P aral lel Chords in

Sp in the key of

Dp66

Sp66

Sp

66

66

66

66

66

66

66

‘6

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

( 6

66

66

66

66

66

66

( 6

66

( 6

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

66

the Major Mode

D fla t major ,A major ,B maj or .

G lla t major ,C sha rp major ,E fla t maj or ,

C sharp ma jor ,F sharp major ,0 fla t major ,E major ,B fla t major ,F maj or ,B fla t major ,D major ,G fla t major ,F major,A major,D fla t major,G major ,A fla t major ,C major ,D major ,E fla t

.

major ,

0 fla t maj or7 sharp ma j or ,4 fla t maj or ,

Dfla t major ,C’ majorG major ,F sharp ma jor ,0 fla t maj or ,A ma jor ,C sharp maj or .

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1 04 Voices P rog ressing by Leaps

and D2 [or D2>] chords) 3 m iddle-voice sometimes may p roceed

by a leap of a fourth

NOTE NO. 1 75.

For melodic reason s,a Soprano-voice occasionally may progress

by a leap of a minor seventh,— (never a maj or seven th)bear ing in mind that after a leap it is a lways advisable to proceed in the opposite direction of the leap and best of a l l by a

step of a second .

NOTE NO. 1 76.

Al though , according to Notes No . 1 44 and 1 45 , the Dominant-Four - S ix chord must a lways be followed by the actual Dchord

,it is a lso permissible that the D2 (not the D 2> ) chord

may be followed immediately by the Dp chord . In this case ,however

,the Dp chord must appear with its third (which is the

prime of the principa l chord ) in the Bass , and fur thermore , i twill be advisable to double the third (compare Note No . 1 8 6,

par t VI, respecting rules govern ing the Doubling of the Third ;a lso compare the penultimate chord of E xample I) in Note No .

NOTE No. 1 7 7 .

Beginn ing at E x . 1 7 7 , if str ictly necessary a doubl ed fifthmay a lso be reached by para llel motion , provided one of thetwo voices progresses by a step of a second—or even better

,by a

semitone :

P arallel Chords in the Major Mode 1 0 5

NOTE NO. 1 78 .

It is understood that in al l exercises where no figure is givenfor the Bass-voice ,—the Bass is perfectly free to take the pr ime ,or the third , or the fifth of the chord in accordance with the rulesgiven in Notes NO. 1 3 2 , 1 3 3 , 1 3 4 and 1 49 .

The designations °a,

°e,

0b, or T , S ,Dp, etc .

,r efer to the

chord in.genera l and not to its fundamental position or any of

its invers 1 ons .

NOTE NO. 1 79 .

In order to simpl ify the study of P ara llel chords dur ingthe first few weeks

,it will be necessary to wr ite on a third staff

(directly above the two staves on which the working-out of theexercise will appear ) the pla in chords to be used in such exer

cise this entire third stafi to be prepared before the actual working

- out of the exercise .For example, compare E x . 1 7 7 , worked out at the bottom of

this page .

E xe rcis e s 1 77 -1 88 .

MAJOR.

CANTUS FIRMU S IN SOP RANO .

N.B —B efor e w orking ou t E xer cises 1 7 7 - 1 8 8 , consu l t ca refu l lyNote No. 1 8 6

,— the in troduction ; par t I

—VI ; a lso par t X .

Ex . 1 7'7 .

w orked out as exampl e

Ex.1'

7 9 .

Ex . 1 8 0 .

Ex . 1 8 3 .

P ara llel Chords in the Major Mode

CANTUS P IRMUS IN ALTO .

o bi» O Obb

CANTUS FIRMU S TE NOR .

3 III III 5

obl» g’o abo

d a d og o f bl: o

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1 0 8

PARALLEL CHORDS

(SECONDARY TRIADS )

IN THE MINOR MODE .

NOTE NO. 1 8 0 .

I f the key-proper third and the key-proper fifth are addedto every tone of any na tura l minor scale ,—the result in A minor ,f or instance

,will be as follows

° S °D

(Regarding the 0D chord, compare Note No .

Here aga in,four new chords are found , built on the tones

b, c, f , and 9 . For the present, the chord built on the tone I)will be ignored for reasons given in Note No . 1 65 , last paragraph .

In view of the explanations given in Notes No . 1 67- 1 7 0 , the

three rema in ing [maj or ] tr iads can on ly be conceived as the three“

para llel chords in the minor mode,namely

The maj or tr iad built on c, as the parallel chord of the °T chord,( 4 c c a

f :c c OS chord,

g ,

°D chord,*and these three new chords are indicated by the function -letter s0T

,

08,and °D to which the sma ll letter p has been added . For

example,

inAminor in 0 minor

NOTE NO. 1 8 1 .

Special attention shou ld be given to the fact thatcation °T p should be r ead as :

“The P ara llel chord of the °T chord

the indication °Sp should be read as

The P ara llel chord of the 0S chord”;

and the indication °Dp should be r ead as

“The P ara llel chord of the °D chord .

*Compare Note NO. 1 8 2 .

P arallel Chords in the Minor Mode 1 0 9

S ince the parallel chord of a minor,tr iad must a lways be a

maj or tr iad (just as the para llel chord of a maj or tr iad musta lways be a minor triad ) , the indications °T p,

°Sp , and °Dp,

without exception , denote major tr iads , notwithstanding the minors ign 0

affixed in front Of the function- letter (compare the firstpar t of this Note ) .

Consequently,the indications T p , Dp , and Sp (or if speci

fi ed with as follows -+ T p ,+Dp , and +Sp ) a lways require a

minor tr iad, and the indications °T p, °Sp, and °Dp a lways re

quire a major tr iad .

NOTE NO. 1 8 2 .

Although the old °D chord has been entirely removed frommodern minor music , and on ly by greatest exception is thischord ever used any more in modern music (compare Note No .

the para llel chord, the °Dp chord , ( for instance , in the keyof A minor , the chord g-b-d ) is still used and met with sometimes .

E xe rcis e 1 89 .

Wr ite the following chords .

°T p in tl“

1 e key Of°Dp

66 66 6‘

°T pc c c c

°Dpcc c c

°T pcc c c

Ospc c c c

GDP66 66

°T pc c c c

°T pc c c c

OSc c c c

OI)D cc c cP

1 1 0 P ara l lel Chords in the Minor Mode

66 66

66 66

66

66 66

66

66 66

66 66

66

66 66

66

66 66

66 66

66 6‘

NOTE NO. 1 8 3 .

Inasmuch as the accidental ly ra ised tone in the minor modehas been introduced by composers solely in order to acquire themore melodious leading-tone step progression from the seventhto the eighth tone of the old

,or igina l minor sca le, the appear

ance of the accidentally ra ised tone in minor accordingly i s

most prominent in the progression D—°T (oroT—D ) ; for ex

ample , in the key Of A minor :

D ° T ° T D

A minor,

E minor,F sharp minor ,D minor

,

“

B fla t minor ,E minor,B minor

,

D sharp minor ,A sharp minor ,E fla t minor ,C sharp minor ,E minor ,G sharp minor ,A minor ,A sharp minor ,0 minor ,G minor

,

D minor ,B fla t minor ,F sharp minor,E fla t minor ,1 ) sharp minor ,A fla t minor ,E minor ,E minor .

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1 1 2 Doubling the Third of a T riad

NOTE NO. 1 8 6.

DOUBLING THE THIRD or A TRIAD .

In a l l exercises hitherto either the P r ime or the Fifth of

a chord ha s been the on ly interva l to be doubled,and thus f ar

it has been str ictly forbidden to double the Third of a tr iad .

But, with the introduction of para llel chords , a lso this lastinterdiction ceases to exi st ; however , (with very few exceptionswhich will be given later in this Note ) the rule given in NoteNo . 1 0 5 ,

—namely

When wr iting f or four par ts (S oprano , Alto , Tenor , and

Bass ) g enera l ly the bes t in terva l to be doubl ed w il l be the P rime

of a chord ; the next best interva l to be doubled will be the FIFTHof a chord ; and lastly , the THIRD of a chord which is the leastdesirable interva l to be doubled”—must, never theless be heeded .

RULES IN REFERENCE TO DOUBLING THE THIRD .

I . On account of the fact that in the major mode the thirdof any para llel chord is the prime Of the respective principa l chord ,the

“third” of a T p, Dp , and Sp chord may therefore be doubledat any time and without any restr iction i f the leading of the

voices does require or permit it . S ometimes, indeed, there are

cases where the doubling of a. third in a Tp, Dp , and Sp chordis f ar more preferable than the doubling of either the prime

or the fifth,for instance

,in a cadence (compare the chords a t N .B .

in E xamples a and b of Note NO. 1 68 , and par t IX of this Note ) .

II . T he “third may be doubled in a + T,

°T, or

+ 8 chord,

provided the doubled third is reached either by contrary or byOblique motion but never reach a doubled third Of a + T ,

°T,or

+ S chord by pa ra llel motion

g ood

AD ° T

Doubling the Third of a .T riad 1 1 3

However, there is one exception to this rule , namely,—whenthe same ha rmony is repeated the third Of a + T

,

°T , or+ 8 chord

may be doubled in para ll el motion :

III . A Leading tone, when appearing in a +D or a°S

chord , can never be doubled ; and therefore, it is s trictly forbidden to doubl e the third of any +D or

0 8 chor d .

IV . If absolutely necessary the third may a lso be doubled inthe very first chord of a piece of music, provided this chord isnot a +D or a

°S chord .

V .

’ Never double the third in a final chord (compare thelatter part of Note NO .

VI . Whenever the fina l chord is preceded by the Dp chord ,it is best and most effective to have the Dp chord with doubledthird—the Bass taking one of them and with pr ime in Soprano,wh ile the fina l chord is wr itten with Octave in Soprano, thusrefra in ing from keeping any common tones ; f or example, in

G maj or :

Also , if the Dp chord appear s as antepenu l tima te chord” ,

it will be advisable. to double the third of this Dp chord , givingone of the thirds to the Bass-voice .

1 1 4 Doubling the Third Of a Triad

VII . As stated in par t I of this Note , the third of any T p,Dp, or Sp chord may be doubled ; however , it is well to avoiddoubling the third of a

°T p, or a°Dp chord*,

but if absolutelyunavoidable the third of a

°T p , or a°Dp chord can be doubled

on ly by reaching the doubled third in contrary motion ; on theother hand

VIII. The third may be doubled in a°Sp chord .

IX . Specia l a ttention must be given whenever the chordprogress ion D—°S p , or °Sp

—D appea rs, as it is well n igh impos1 1 1 1

s ible to have a faultless connection between the D and °Sp chords,1 1

or between the °Sp and D chords un less the °Sp chord appears1 1 1

with doubled third ; for example , in the key of A minor '

Very b ad

D Osp° Sp D

‘T he reason f or th is cannot be g iven unt il la ter w hen the s tudy of

Intra Dominan t Chord s” ( compare Append ix Note XX I ) is reached .

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1 1 6 P aral lel Chords in the Minor Mode

E xe rcis es 1 90-1 97 .

MINOR.

CANTUS P IRMUS IN SOP RANO .

Ex . 1 9 0 .

3 of o c

1 1 5 1 1 v

a 3 30 0 3 e t2>g t

CANTUS PIRMUS IN ALTO .

Ex . 1 9 2 .

Ex. 1 9O,w orked out as examp l e

1 1 5 1 1 V

P ara llel Chords in the Minor Mode 1 1 7

CANTUS P IRMUS IN TE NOR .

Ex .1 9 3 .

Ex . 1 9 4 .

Vup 3

(in 1 4) ID I° T

Ex . 1 9 5 .

mm 5 8 V

(in F IIMBT S IODpD IT ° S p ID

8

I° T D I° S p S ID2>D I° T

Ex . 1 9 6 .

(ia )¢T Iospos rRD IOT

os I° T II1 1

E x .

’

l 9 4 ,w or ked ou t a s ex amp l e

T o

sp D l

’

l‘ °

Dp°

nospD1

0 T

1 1 8

FRE E HARMONY .

INTRODUC ING P ARALLEL CHORDS.

NOTE No. 1 8 7 .

Before working ou t any of the following Free Harmonyexercises , aga in a schedule mus t be wr itten on a third sta ff ofa l l the different chords which may be used in each exercise , according to the key . For example , the schedule for E xercise 1 98 will be

T D S 0 5 D2 Tp . Dp Sp

and the schedule for E xercise206 will be

0 T D OS D2> ° Tp

°DpOsp

NOTE NO. 1 8 8 .

At least thr ee parallel chords must be introduced into eachand every one of the following exercises .

E x ercis e s 1 98 -2 1 2 .

CANTUS FIRMU S IN SOP RANO .

MAJOR.

Ex . 1 9 8 .

E x .

’

l 9 8 , w ork ed out a s examp l e

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1 2 0

Ex .2 0 7 .

Ex .2 0 8 .

Ex .2 0 9 .

Ex .2 1 0 .

Ex.2 1 1 .

Ex .2 1 2 .

Free Harmony

1 2 1

CONSONANT CHORDS AND DISSONANT CHORDS .

NOTE No. 1 8 9 .

With the exception of the Dominant-Four - S ix chord as in

the major and minor mode,on ly

,the two differen t kinds of

tr iads , Major T riads and Minor T riads,have been studied in

Book I of this course of Harmony instruction .

Al l possible chord formations which are or can be used inmodern mus 1 c may be d 1 v1 ded into two ma in division s cons istingof two classes as follows :

1 . Consonant Chords .2 . D issonant Chords .

Dissecting the word Consonant (or as noun—Consonance ,der ived from the Latin , Consonantia ) agreemen t—concord— con

gruity is the essentia l musica l requ isite between tones soundingsimultaneously, thereby producing a harmon ious , pleasing and

satisfactory eff ect .

On the other hand,analyz ing the word Dissonant (or as

noun—D issonance,from the Latin

,Dissonantia ) same tends in

the opposite direction , evincing want of agreement—discordanceincongruity—thus exer ting momentar ily between the simultaneous sounding of tones less closely r elated a more or less displeasing and unsympathetic vibration Of harmony .

However,these definitives want of agreement—discordance

incongruity” as applied to D issonant Chords must not be misconstrued ; by no means are these expression s used to convey theimpression that acoustically such chords create a positively disagreeable

,badly sounding

, or unharmon iou s effect . Quite the con

trary, such unyielding qua lities in Music could not possibly exist,and the chords to which these expressions have been appl ied abso

lutely need a cont inuation and resolution into another chord .

E very Dissonan t chord mus t progr ess or resolve into a new

harmony , and if this new harmony in turn is another D i ssonan tchord , aga in it involves a fur ther continuation,

and so on,until

at last a Con sonan t chord has been reached .

O f these two division s of chords,the first class, the Consonant

Chords is comparatively very smal l,compr ising only of al l

maj or and minor triads ; but, the second class , the D issonantChords

,i s very large, in fact

,endless

,—embracing a l l possible

chord forma tions in music exc luding major and minor triads .

1 2 2 Consonant Chords and D issonant Chords

T he cla ss of Dissonant Chords may be subdivided into twoparts, i . e . ,

1 . Mild D issonances,

2 . Sharp D issonances.

TO the cla ss ofMild Dissonan ces belong , for examp le , such chordsas the D2 and D 2> chords, the Dominant-Seventh chord (as inthe key of C maj or , the chord g-b-d-f , tona l function indicated byD 7 ) , the Subdominant- Sixth chord* (as in the key of C major , thechord f—a -c-d or the chord f-ab-c-d [S V 1 ] ) and others to bestudied later .

To the class of Sharp Di ssonances belong, for example , suchchords as the large Seventh chord* (as in the key of C major , thechord c-e-g

-b [T 7 < ] and the chord f -a - c- e and the smal lS ixth chord (as in the key of C minor , the chord c-eh-g-ab [SVI

>

and an endless number of more complicated chords—also, to fol lowlater .

Compa re Append ix Note XVIII .

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APPENDIX.

The following E xpl anatory N otes and Amendments have beenspecially prepared for the more advanced studen t with the viewof defining in deta il some of the Notes conta ined in the generaltext of Book I .

T o NOTE No. 1 , PAGE 1 .

Although it may be cla imed that in the modern E qually tempered Tone-system

” there are on ly twe lve major scales which are

absolutely different as regards pitch , but for the sake of completeness a l l fif teen sca les which can be practica lly used , are givenhere . Moreover , the compromise construction of keyboard-instruments natural ly reduces a l l sca les to an arbitrary form

,called

“tempered,”

and when i t is cla imed tha t there are only twelve

major scales , i t is impossible to decide just which three scales toe liminate—and

,irrespective of the limit which has accordingly

been set , in practice such sca les as the scales of F sharp maj or or

G fla t maj or , and the sca les of C sharp major or D f la t major , andthe scales of B maj or or 0 fla t maj or cannot be omitted as eachand every one of these six scales (and keys ) have exactly the samer ight of existence .

On instruments not arranged or tuned in accordance with theE qually tempered Tone- system”

as,f or instance , the violin , it

is possible to demonstrate and express to a fineness tones of en

harmonic pitch; therefore , on the violin and s imilar instruments,

between such sca les as the F sharp maj or sca le and the G fla t maj ors cale

,and the sca les of C sharp major and D fla t maj or , and the

s ca les of B maj or and 0 f la t major there is certa in ly a decided'

d ifference regarding absolute pitch, tone color , as well as finger ing.

However, at some defin ite point a l imi t must be reached re

g arding the number of different scales , and it is well to place thisl imit at a point where a scale is going to conta in more than sevensharps or flats—therefore , the student should be taught that thereare fif teen different major scales (and keys ) and fif teen differen tminor scales (and keys ) which can be practical ly employed in

modern mus ic (also compare Appendix Note IV ) .

1 26

T o NOTE NO. 8,P AGE 4 .

The experience of many years of piano and harmony instruction has shown that pupils become more or less confused whentaught the Signatures of minor sca l es by referring to the so- ca lled"relat ive” maj or s ca les ; and, for example, in order to find the sig

nature Of the A minor scale they are referred to the G maj or scale .

It i s indeed surprising that nowadays so many instructor spersistently adhere to this Ol d method of teaching Sca les

,i . e . ,

in the following order0 major,A minor ,G maj or ,E minor ,D maj or ,B minor

, etc . ,

as this method positively cannot give the pupil a cl ear and d istinctidea respecting the

“Character istic D iff erences” existing betweenthe Maj or and Minor Modes .

It is a fact,that in con sequence of teaching Scales in this

absurd order, pupils receive a confused impression with regards

to major and minor scales, and almost without exception ,if told

to play, for instance , the F maj or sca l e and to follow same immediately by the E minor sca le—for the latter , they will hunt forthe so-ca lled “

relative” minor scale of the F maj or sca le and playinstead the D minor sca l e, bel ieving it to be the actua l E minorsca le . This fa llacy of teaching Sca les has developed in the pupil

’

s

musically ill- tra ined mind the impress ion to regard the so-ca lled“relative” minor scale Of a cer ta in major sca le as the minor scaleof the same letter-name.

Consequently,any compar ison between a major scale and

a minor sca le of exactly the same key—signature (as the scales of

C major and A minor,or the sca les of B maj or and G sharp minor ,

etc . which sca les in the more modern theory of Music are knownas P ara llel Sca les” —compare Notes No . 1 9 and 2 0 ) Should beentirely abandoned as i t is aga inst al l reason ing to speak of“comparison

” between two subjects which in every respect are

decidedly different in nature or character .

Therefore,the compar ison of a major scale with the minor

scale of the same letter -name ( for example , comparing the G maj orsca le with the scale of G minor ) gives the pupil a clear and trueinsight into the “

Character istic D ifferences existing between theMajor and Minor Modes ; and , in order to enable the pupi l noton ly to learn but to actual ly hear and fee l this vast and r eal difference

,they should be taught the major and minor scales in the fol

lowing manner

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1 2 8

T O NOTE NO. 2 1 , P AGE 1 2 .

E ven practica lly, composer s occasionally use keys which havemore than seven sharps for their S ignatures, for instance, Bach 1 1 1

his C sharp maj or fugue of the Well - tempered Clavichord, Book I,sometimes modulates into the keys of G sharp major and of Esharp minor ; Haydn in his C sharp minor piano- sonata ,

last movement in the Tr io , also introduces the key of G sharp maj or ; Chopinin the Romance of his E minor concerto likewise uses the keyOf G sharp maj or , and even the key of D sharp maj or .

T o NOTE NO. 3 8,PAGE 2 2 .

Regarding this complete l ist of interva ls it is necessary toadd , that in fact , there are three more interva ls which , though ap

pearing extremely seldom, do exist, and they a re

1 . The Double Augmented P r ime,

The Double Augmented Fourth,and

3 . The Double D imin ished F ifth .

.N

A double augmented pr ime is found by en larging an augmented pr ime by another large semitone

pe r fe c t prime s augment ed prime s doub l e augmented prime s

9

Amelodic* double augmented pr ime appear s in Chopin S“Va

ria tions Br illantes,” op. 1 2 , 2 l st measure of the introduct ion ; a lso,the following writing is orthographically perfectly correct

the interva l G fia t—G sharp between Al to and Soprano being a

harmonic* double augmented pr ime .

*Reg a rd ing the d es igna tions me lod ic interva l and harmonic l nte rva l ,” compa re Note NO. 44 .

1 2 9

A double augmented fourth is found by enlarging an augmented fourth by another large semitone :

er f e c t f ourths augmente d f our ths doub l e augmented fou r ths

Al so compare the following w ritingé harmonic double ang

mented four th between Alto and Soprano :

A double dimin ished fifth is found by reducing a dimin ishedfifth by another large semitone :

pe rf e c t f if ths diminished f if ths doub l e d iminished f i f ths

Also compa re the following wr iting—melodic double diminished fifth in Soprano :

A double augmented interva l , when inverted,becomes a

double dimin ished interva lA double dimin ished interva l , when inverted , becomes a double

augmented interva l .

1 3 0

T o NOTE No. 45, PART XIV, PAGE 3 0 .

The natura l or normal prime isThe natura l or norma l secondThe natura l or norma l thirdThe natura l or norma l four thThe natura l or norma l fifthThe natura l or normal sixthThe natura l or norma l seventhThe natura l or norma l octave

As the study of Overtones (compare Appendix Note VII )teaches us, the natura l or norma l seventh of a certa in tone is notits maj or seventh but its minor seventh, specia l attention Shouldbe given to this fact, that later , when the figure 7 is met withoutadded sign, the na tura l or minor seventh is a lways understood andrequired ; hence, the Dominan t-seventh chord will be indicatedthus : D7—while the sharply dissonan t interva l of a major or large

seventh will be indicated with ra ising sign as follows : T 7 <or S 7 <

Ov er tones (Al iquottones or P ar tia l tones ) is the musica l termappl ied to a harmon ic ser ies of collateral tones of different pitch ,which

,when heard collectively produce a vibrant sound con

st ituting what is called an actua l “tone” . The strongest and mostprominent factor in such over tone ser ies is the lowest or fundamenta l tone—and , a musica l sound takes its name from the lowestof its overtones .

Thus the complex vibration of any sound known as tone is

in fact the sonorous sounding-body Of a number of par tia l or

upper tones which, though gradual ly dimin ishing in strength as

they r ise in pitch, blend with the lowest tone in mathematicalpropor tion or ratio .

A str ing touched by a bow, a hammer , or a finger , does notvibrate on ly as a whole but also in its a l iquot parts or segments

,

and the vibration of the proportionate par ts of a str ing producessimultaneously with the lowest or fundamenta l tone also the

octave,twelfth

,fifteenth

,seventeenth

,etc .

,Of such lowest tone .

For example , when the lowest str ing on a Violoncello or thecorresponding same str ing in a pianoforte or other instrument isbrought into vibra tion

,the following overtones are sounding :

per fect pr ime,maj or second,maj or third ,per fect four th,perfect fifth

,

major sixth ,Minor sev enth ,

perfect octave .

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1 3 2

VIII .

T o NOTE NO . 94,P AGE 58 .

Introducing the ra ised Sixth in the minor scale , the minorsca le resembles to a certa in extent the old Dorian Church mode

[scale ] , and therefore this raised Sixth in the minor scale is knownby the name Of the Dorian S ixth.

T o NOTE NO 1 0 0,P AGE 61 .

Many old books on Harmony cla im tha t there are four kindsOf tr iads , citing in addition to the maj or and minor tr iads , a

diminished triad , that is, the chord formation :

and an augmented tr iad, the chord formation

but of these two terms, the designation dimin ished triad is by a l l

means radica l ly wrong—the so- ca lled diminished triad is no tr iad

at al l , and the SO- ca lled augmented tr iad is a modified, a ltered

maj or or minor tr iad, to be studied later under the chapter of“Altered Chords —Book II.

The foundation of Harmony,or rather , of al l modern music ,

is to be found in the pla in tr iads ; and just as there a re on ly twodiff erent modes or genders in modern music (maj or and minor

modes ) so a lso there are on ly two kinds of tr iads—maj or and

minor tr iads .Triads are (as expressed in modern musical terminology ) the

only Consonant chords*—and a tr iad a lways has the power of ap

pearing as an absolute , independen t chord , qual ified to be a rulingfactor and acting as pr incipa l chord among others , for instance,as a Ton ic chord , and as the agent of this Tona l function givingthe musica l mind satisfaction and rest .

Compare Note NO. 1 8 9 .

1 3 3

For this reason,the so—ca lled dimin ished tr iad is no tr iad

a t a l l , but a der ivation of another more complica ted and D issonantchord to be Studied later . (Also compare Note No .

Regarding the SO- ca lled “dimin ished triad,

” Riemann in hiswonderful

,ultra modern book on Harmony , says .

T his chord former ly caused much doubtfu lness , irresolutiona nd obscurity in the theory of harmony, because, in blind forma lism,

it was g rouped beside the maj or and minor chords in a

third c lass by those who thought it necessary to r egard as pri

mary a l l chords tha t cou l d be r epresented as consis ting of‘thirds ’

p laced over one another .

”

As the modern theory‘

of chords is not at al l found on the

principle of -building up by“thirds” (the chord c- e-g does not ap

pear as the combination Of two thirds of different S iz e,c- e and

e -

g , but as the combination of a [major ] third c- e and [perfect ]fifth c—g ) , so b-d-f does not appear comparable with c-e-g or a—c- e

but rather with g - b-f (a Dominant-seventh c hord withou t its fif th ) ,in as f ar as both formation s ar ise from the omission of an easilydispen sable tone in the chord of the Dominan t- seventh .

T he S ubdominan t- six th chord (compare Appendix NoteXVIII ) without its fifth ( for example , in the key of A minor , thechord d- f - b ) is on ly apparently similar to the Dominant—seventhchord without its prime (as in the key of C maj or , the chord b- d-f ) ,but the great diff erence in Tona l function between these tw ochord formations may be proved by compar ing the following twophra ses :

It is truly r idiculous to cal l the two chords at N .B . dimin

ished triads” with the tone I) as root or principa l tone . By a l l

means the second chord in the A minor example is the chordd -

‘

f -a—b** with fifth omitted

,and the four th chord in the C maj or

example is the chord g -b- d-f with prime omitted.

*R eg a rd ing the d e s igna t ion D2>

, s ee Notes NO. 1 3 9 -1 42 .

a” Compa r e Append ix Note XV III .

1 3 4

With regards to the augmented tr iad - the thesis given inmany Ha rmony books tha t “the augmented triad is found on thethird degree Of the harmon ic minor sca le

,

” conveys but little froma purely musica l point of view and is only in par t correct ; forinstance , if in the key of A minor, the so-ca lled augmented triad

,

the chord formation c-e-gt] appears, not the tone c but the tonee will be found as the root of the chord

,this tone e being the orig

ina l fundamenta l tone—and the only tone which in “

perfect fourpar t wr iting

”can be doubled . Hence

,this chord is not an aug

mented triad built on the third degree of the harmonic minorsca le , but i t is the Maj or Dominan t triad (built on the fi fth degreeof the minor scale ) of which the per fect fifth (the tone b ) hasbeen r ep laced by the minor sixth (the tone 0 )

and the musica l ear must readily perceive and admit,that the

second chord in this phrase, as stated before, i s not to be consideredan augmented triad built on the tone 0 .

To NOTE No. 1 0 3 , PAGE 62 .

In al l books on Harmony which advocate the “Figured Bass

or“Thorough Bass Me thod” ( for instance, Jadassohn

’

s and Richter ’s ) the first inversion Of a tr iad , i . e .

,when the third of the

t riad is in the Bass , i s ca lled a“Chord of the Sixth,” and the sec

ond inversion of a tr iad—when the fif th of the tr iad is in the

Ba ss,is ca lled a Chord of the Fourth and Sixth .

”

But in this course of Harmony instruction the designationsChord of the Sixth” and

“Chord Of the Four th and Sixth” are

more proper ly used for other chord formations, as will be shown

later (compare Notes NO. 1 3 9- 1 42 and Appendix Notes XIII and

XVIII ) .

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1 3 6

It is a fact,however, that on the organ when the mixture

stop is used, each and every tone played i s accompan ied by itsperfec t fifth and a continuous progression of consecutive fifths isthe resu lt ; but, as on the organ when a melody is harmon iz ed

,not

only one but each and every tone Of every voice is accompan ied byits perfect fifth , this , natura lly sends forth a volume or fullnessof sound [tone-production ] which yields a perfect blending of al lvoices , and in turn removes the disagreeable effect caused by twovoice-parts proceeding in fifths . And thus , on the organ . whenthe mixture- stop i s used, the tone-volume brought into play on

account of a l l voices progressing in fifths,creates and emits a

r ichness of tone-color swelling into proportions of sublime grandeur .

T o NOTE NO. 1 1 8 P AGE 70 .

Regarding Melodic augmented and Melodic dimin ishedInterva ls,

” Riemann says :

Al l augmented and dimin ished part progressions necessitatea subsequent semitone step, the

‘augmented’ ones fur ther away in

the direction of the melodic interva l a lready made ( for which rea

son they a lmost without exception contradict the melody pr inciplementioned in Note NO. 90—turn ing after leaps—and are therefore bad ) , the

‘dimin ished’ ones,on the other hand , turn ing aga in

(by which mean s they atta in a specifica lly melodic character ) .

But melodic dimin ished interva ls are good , only on the supposit ion tha t a turn ing semitone step follows ; if the latter does not

follow or is impossible , the melodic dimin i shed interva l a lso isbad. The first con sequence of this is that a melodic diminishedinterva l must be excluded in cadences .

1 3 7

XIII .

T o NOTE NO. 1 42 , P AGE 84 .

Regarding this very interesting chord , which in older Harmonybooks most erroneous ly is a lways known a s a

“Ton ic chord in the

second inversion ,

” but to which Riemann has given its rea l Tona lFunction

,the new and on ly true

,authentic name- The Domi

nant-Four- S ix Chord”—a most excellent E ssay, entitled Die

Haup tkadenz im,

W andel der Z eiten , by Ma rtin Frey , appearedin the German semi-monthly “

Die Musik” (Heft 4 . Z weites NOvember-Heft , 1 3 Jahrgang 1 9 1 3

In this exceedingly well wr itten essay , Martin Frey payshighest tr ibute to the Gen iale P f adfinder in dem Reiche der Har

monieen ,

”P rof. Dr . Hugo Riemann , for having found and estab

l ished the true or igin of thi s chord in question,and the reading

and further study of this essay is warmly recommended to a l l ultraconservative musicians who still adhere to the ol d faulty theorytha t this chord is a T onic chord with fifth in the Bass .

XIV .

T o NOTE NO. 1 46,P AGE 8 6.

Not until now , having studied the Dominan t-Four -S ix chord,

could a more deta iled explanation be given of Notes NO. 1 3 2 and

1 3 3 ; namely, why the Bass is never a l lowed to take the F ifth of atr iad by a leap .

Whenever a voice takes a tone by a leap ,such tone accord

ing ly becomes more prominent , more emphasiz ed than if samewere reached by a s tep of a second .

If the Bass were to take the fifth of a tr iad by a leap :

T D MB .

1 3 8

the chord at N .B most decidedly would lose its color or individualcharacter, forfeiting in this case its Subdominant function on ac

count of the prominence of the bass-tone taken by a leap. T he

car doubtlessly would refuse to accept this F maj or tr iad as theSubdominant chord of the key of C major (which it is intendedto be) ; but instead it would readily take this chord as the D2chord of the new key into which it is expected to modu la te, and

the ear natura lly would expect the following progression after thechord noted above at N.B

which is a modulation into the key of F major .

This,however

,is not intended to be the case, for the F maj or

tr iad at N .B . shou ld appear as the Subdominant chord of the or ig i1nal key , and therefore either the pr ime or the third must be givento the Bass-voice .

This Mi srepresentation of the Tona l function of a chord”is

the impor tant reason why the Bass is never a llowed to take thefifth of a tr iad by a leap.

T o NOTE NO. 1 48 P AGE 8 7 .

Although in any piece of music the Ton ic chord is a lways themost impor tant and leading chord, second to none , it is interestingto prove that in one respect at least both the Dominant chord and

the Subdominant chord are more powerful than the T onic chord ;namely,

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1 40

i s followed by

XVII.

T o NOTE No. 1 56 P AGE 9 3 .

A Ha l f C los e ar ises,if the last chord of a sentence [ or

phrase ] is a Dominan t Chord in fundamen ta l position and usua llyfol lowed by at least four or more measures

S D T S T D

Neither a Deceptive close nor a Half close can ever be used as

the fina l ending or conclusion of a piece of music—consequently ,they appear on ly at the end of intermediate parts as

,the non-ap

pearance of the Ton ic chord at the close—also,the question ing

character of the Dominant function compels a further continuation .

A Ful l C lose ar ises,i f the last chord of a per iod is a

T onic Chord in fundamenta l position .

1 4 1

XVIII .

T o NOTE NO. 1 67, P AGE 99 .

Relative to the D eg re e of Re lat ionship man ifest betweenP r incipa l tr iads and Secondary triads, it is s ingular that a l l leadingbooks 0 1 1 Harmony fa il to give to this important subject any ex

pl icatory analysis in fact , the mutua l kinship emanating from the

succession and intermingling of these harmon ies and the reciproca lconcordance of one with the other is a subject entirely obscure and

foreign to such theorists as Jadassohn ,P aul

,Richter and others .

However,the great ingenuity of Riemann aga in asserts itsel f

and with the introduction Of his theory of P ara l lel Chords , subs tantiating the mutua l relationship between P rincipal tr iads and

certa in Secondary triads , it _is obvious,that a l l unknowingly

,ig

norance in genera l on this point has heretofore caused much uncer

ta inty and irresolution .

E ven,at the present time , as long as musicians continue

to be strict adherents Of the methods and theories expoundedin older books of Harmony instruction

,this uncerta inty will pre

va il , and in consequence of same,a doubtful solution with refer

ence to the constituent elements of var ious chord format ions willpersist .

In order to prove conclusively the exact extent of this relationship existing between P r incipa l triads and Secondary tr iads ofa maj or key, the following merits thorough examination .

For the sake of simpl icity, the key of C maj or will be useda s the basis f or this analysis .

Hence , careful scrutiny will reveal to the Student the sames triking similar ity between Ton ic tr iad and the secondary triad

built on the S ix th deg ree as between Ton ic

t riad and the secondary tr iad bui lt on the third deg ree

for, in both ca ses , these secondary t riads ha ve tw o ton e s in com

mon Wi th the Ton ic chord .

Likewise comparing the Subdominant tr iad and the secondary

tr iad built on the second deg ree w ith the S ub

1 42

d ominant tr iad and the seconda ry tr ia d built On the six th deg ree

v i sibly , same disp lay ma rked simil itude .

Here aga in , both these secondary tr iads have two tones incommon with . the Subdominant chord.

Although , the above four examples appear a l ike in kind, theydiffer in degree ; and , as soon as the ear becomes the judge, i t isevident tha t the mutua l relationship existing between the twochords at a , and between the two chords at c is much stronger thantha t between each of the two groups of Chords at E xamples b and

d . This may be proved by the simultaneous sounding of a l l of thediff erent elements belonging to such two chords—hence

,the simu l

taneou s sounding of the two chords at a produces the mild dissonance

while,the s imultaneous sounding of the two chords at b produces .

the sharp dissonance :

Thus a lso , the combined harmony of the two chords at 0 yieldsthe mild dissonance :

while the combined harmony of the two chords at d yields thesha rp dissonance

Therefore , this is proof that the degree of relationship betweeneach of the two groups of chords at a and c is much stronger harmoniously than that between each of the two groups of chords atb and d .

The chord formations at f and h are known as Large Seventhchords” (or specifically as the Ton ic- Seventh chord and the Sub

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1 44

f sha rp, has been added in order to strengthen its Subdominantfunction— (just as the chord g -b—d -f in the key of C maj or is inrea l ity the major tr iad g -b-d in order to strengthen its Dominantfunc tion

,the na tura l * seventh may be added )—consequen tly, the

Subdominant chord of the key of E minor (considering the firsttwo measures after the fanfare- introduction as belonging to thekey of E minor and disregarding for the present the theory of

Intra i s a - c-e to which, as stated before , the natura l

S ixth has been added , producing the Subdominant- Sixth chord , the.chord a -e- e- f fl; (as in the key Of E minor ) .

However,this does not mean that the chord format ion a - c-e-f f]:

(or any of its invers ions ) is a t a l l times pos itively a SubdominantSixth chord , f or a s stated in Note NO. 9 9

,the Tonal function of

a chord depends not upon the very chord itself, but upon thosechords by which it is immediately surrounded or connected ; as, inthe following phra se :

the third chord in this case is not a Subdominant- Sixth chord withthe tone a as pr ime, but most decidedly this chord forma tion i s theDominant-Ninth chord Of the key Of G maj or wi th

“

pr ime”

omitted ( to which chord Riemann has given the appropriate name

of“Dominant-Third-Ninth chord , or br iefly the “Three-Nine

chord” ) and , in this chord , the tone f sharp is indisputably themost impor tant tone .

Another str iking example of the Subdominant-S ixth chord isfound in the very first measure of Beethoven’s S onata

,op. 3 1 ,

No . 3,in E flat major

This chord is not a Seventh- chord with f as prime or fundamen ta l tone

,but it is unquestionably the Subdominant-Sixth chord

*Compa re Append ix Note V I .

w “Compa re App end ix Note XX I .

1 45

of the key of E fla t maj or with the tone a fla t as pr ime and root ofthe chord.

*

The very Simplest and best expedient to prove that in thesetwo examples (Mendelssohn

’s Wedding Ma ren and Beethoven’

s

Sonata , op . 3 1,No . 3 ) the tones f sharp and f (in the chords

a -c- e-f f] and ah-c- eb-f ) are not the primes or roots of these chords ,is to play both of

‘these chords as follows :

In the Mendelssohn example , omitting a lternately the tonesa and fit in the chord a - c- e-f if ; and l ikewise

,in the Beethoven

example , omitting alternately the tones a b and f in the chorda -c-ebb

Hei'c

ef rom i t can be judged which of the two tones in each of

these examples can best be omitted without absolutely changingor destroying the intended eff ect—the character istic color or T ona l

function of the chords in quest ion .

I t will be evident that as f ar as harmony is concerned theMendelssohn chord will lose cons iderably less of its color by omitting the tone f sharp than by omitting the tone a , and theBeethoven chord wil l a lso lose cons iderably less of its character byomitting the tone f than by omitting the tone a fla t, thus provingthat the tones a and a fla t respectively a re the most importantelements of the chords under discussion , and that these tones (aand a fla t ) from a harmon ic viewpoin t must positively be consid

ered as the two pr imes or roots on which these chords have beenbuilt .

Although the Subdominant-Sixth chord in the examples givenabove of Mendelssohn and Beethoven appears in both cases as firstor in itia l chord , the most characteristic place of the SubdominantS ixth chord is in the perfect or complete cadence—compare thefollowing Subdominant- Sixth chords in Beethoven ’

s piano-sonatas :

Opus 2,No . 1 (F minor ) , first movement , second mea sure from

the end,Opus 1 0 , NO. 3 (D major ) , second movement, measures 2 0 , 2 5,

59 , 64 and 7 1 ,Opus 1 3 , (C minor ) , Introduction , measure 1 0 , and second move

men t , twen ty-fi rst measure ,Opus 2 7 , NO. 2 \ (C sharp minor ) , first movement, thirteen th ,

measure .

As Riemann himself wr ites : Centur ies ago, the cel ebratedFrench musician

,Jean P hilippe Rameau ( 1 68 3 a lready

speaks of the chord d-f -a -c in the key Of C maj or as l’

accord de la

S ix te aj oute’

e and Riemann absolutely ignores the old idea of

even modern conservative musicians that the theory of chords isfound on the pr inciple of building up by T hirds .

*B y w ay of p arenthes is it may be s ta ted here tha t B ee thoven’s

w rit ing Of the notes g fla t in the fourth and fi f th mea sures is not

orthog raph ica l ly correct, same should rea d f sha rp ins tea d of 9 fla t .

1 46

XIX .

T o NOTE NO. 1 8 3 , PAGE 1 1 0 .

It is true , however , that the accidentally ra ised tone in modernminor music is used as an element in a ser ies of more compl icatedchord formations ; for example , in the key of A minor , the chordsc- e-gft, and especially gfl-b-d are met with occasiona l ly

,but when

ever these chords are introduce d, for instance, the chords at N .B

° T N.B .

OT 0 8 D2>

N.B .

it is well to keep in mind tha t these chord formations are by no

means triads (compare Note No . 1 0 0 ) but“D issonant chords”

which will be studied in Book II .

T o NOTE NO. 1 84, PAGE 1 1 1 .

The reason why the °T p and the °Dp chords seldom appearany more in modern minor music is that each of these two chordsconta in as an element the seventh tone of the old natura l minorsca le in its origina l , non

- raised form ; and the appearance of thisnon-ra i sed seven th as an actua l element of a chord in the minormode disturbs more or less the character istic tona lity of the ModernMinor Mode.

XXI .

T o NOTE NO. 1 86, P ART VII , P AGE 1 1 4 .

The study of Intra Dominant Chord s has not been discussedin this first book , but will be introduced in Book II of this courseOf Harmony Instruction,

however , the student may be interestedto know that Riemann has given the most ingenious name of“Intra Dominan t Chords” to any key

-for eign chord which has“PD relationship with any chord of a certa in key.

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XXII .

A most interesting, highly elevating musica l divers ion maynow be attempted by the more advanced and ta lented pupil , and

with the guidance Of the teacher , the instruct ive study of ha rmonica l ly ana lyz ing some of the simpler works of the Classics may be

introduced at this time .Beginn ing with Kuhl au

’

s beautiful Sonatinas , a l l harmon iesmust be ana lyz ed and tona l function ascribed to each and everychord ; thus, giving the student an excellent opportun ity to pract ically employ such knowledge of harmony as he has acquired so f ar

from the study of Book I of this course of Harmony Instruction .

It is natura l tha t the piano pupil , having devoted many yearsto piano-study pr ior to taking up the study Of Harmony, is moreor less better acqua inted with tona lity and the rudiments of modu

la tion . NO matter what he is playing, whether a Simple Cz ernyStudy

,a C lementi S onatina, or even one of the greater works of

Bach,Beethoven , or Wagner , he should at a l l times be perfectly

conscious and mindful of the key in which he is performing,making note on the pr inted score respecting the modulations fromone key to another .

First of al l,however , it will be necessary that the teacher con

veys to the pupil a genera l idea of the“Dominant- Seventh chord ,”

of“P assing- tones ,” “Auxil iary- tones (also ca lled “

neighborand

“Accented Auxiliary- tones (the latter, in fact, beingidentica l with “

unprepared suspensions

As an example , take the first movement of Kuhl au’s S onatina ,

op . 55 , NO. 2 .

This composition i s wr itten in the key of G maj or ; therefore ,write at the beginn ing of this piece, in the first measure , G maj or .

This key of G major preva ils throughout the first eight measures

,and in the ninth measure (a lthough the key-signature of G

maj or is reta ined ) a new key , the key of D major begins to rule .Wr ite in the n inth mea sure D maj or , and this key of D major

extends throughout measures n ine to twenty inclus ive .

In the twenty-fi rst measure, the tone C sharp yields to C na t

ura l , con sequently at this point the composer leaves the key of Dmaj or and returns to the pr incipa l key of G major .

Write in the twenty-fi rst measure G major , and this key ofG major continues to rule until the very end of the first movement .

Not unti l the modulations of an entire movement have beensettled

, and the pupil is thoroughly famil iar with the diff erent keysused , can he proceed to wr ite (above the staff ) the tona l functionsof each and every harmony. For illustration , the tonal funct ionsof this entire first movement are as follows

1 49

T s sp ng D T D7 T

D7 T

D7 T D7 T

D7 T sp D7 T

S Sn D T D7 T D7 T

This first movement gives an excellent proof of the fact thatof the three tona l functions Ton ic

,Dominant , and Subdominant

,

the first two functions , TONIC and DOM INANT take a decidedly moreprominen t place and appear f ar Oftener than the Subdominantfunction . Further itemiz ing the harmonics of this fir st movement,the result will be as follows :

T on ic function ruling in more than 24 measures ,Dominant function rul ing in more than 2 0 measures

,and

Subdominant function ruling in only 3 measures .

Whenever the pupil meets a chord which has not been studiedas yet ( for instance , in the second movement of this same Sonatina ,

s ixth measure,the chord on the third beat c- eh- a in the key of

G major ) , for the present such chords a re s imply ignored.

In pa s sa ges of a pure ly me lodic character . tha t is mel ody w ithout

harmony ( a s in mea sures 1 and 5 a f ter the rep et it ion S ign ) , f or the

pre sent , the tona l funct ions may be omit ted .

1 50

Although the style of music of Kuhl au’s S onatinas is a verysimple form, and therefore

,at the beginn ing

,especia lly suitable

for the instruc t ive study of“Harmon ic Ana lys is,” on the other

hand,as the student progresses in this branch of study , the more

compl icated works of the great Masters must also be interpretedand ana lyz ed .

In fact, in order to prove that a l l music , whether simple or

complex ,rests upon the three mighty pilla rs, Ton ic , Dominant , and

Subdominant,and the structural development of any and a l l com

position s take root in these Tona l function s,it will be interesting

to note that in Book II,for example, Wagne ’

r s P relude to Tr istanand Isolde will be harmon ical ly ana lyz ed .

As the well known musical critic, E rnest Newman,wr ites :

The music in Tristan and Isol de is in many respects the mos t

complex , the most subtle , the most modern ; three centuries Of development were necessary before music could attain to such depthOf imagination and such control of form —it undoubtedly willappea l as doub ly interesting to even the most Skeptica l that suchana lys is is certa in ly possible of the most difficult music involvingthe use of the boldest and f reest chord formations of modern music .

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