u.s. navy music course - harmony

7/30/2019 U.S. Navy Music Course - Harmony

http://slidepdf.com/reader/full/us-navy-music-course-harmony 1/108

Training C ircularNo. 12-42

*TC12-42HEADQUARTERS

DEPARTMENT OF THE ARMYWashington, DC, 5 November 1984

HARMONY

Table of Contents

CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . .P rinciples of Writ ing . . . . . . . . . . . . . . . . . . . . . . . . . .Sca le Degree Funct ion . . . . . . . . . . . . . . . . . . . . . . . . . .P rima ry a nd Seconda ry Tria ds . . . . . . . . . . . . . . . .Voices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C HAP TER 2 MELODY WRITING . . . . . . . . . . . . . . . . . . . . . .Melody . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Types of Mot ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Melody G uidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Rhythm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CHAP TER 3 VERTICAL STRUCTURES . . . . . . . . . . . . . .P osit ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11111

333388

99

Adja cent Voice Spa cing . . . . . . . . . . . . . . . . . . . . . . . .10Low Interva l Limit s . . . . . . . . . . . . . . . . . . . . . . . . . .10

CHAP TER 4 VOICE MOTION . . . . . . . . . . . . . . . . . . . . . . . . .11Voicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11Indirect Mot ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11Direct Mot ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11Object ionable Mot ion . . . . . . . . . . . . . . . . . . . . . . . . .12

*This TC supersedes D A P am 350-42, 1 April 1969.

i



CHAPTER 5 ROOT POSITION PRIMARYTRIADS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

Connect ing P r ima ry Tr ia ds . . . . . . . .. . . . . . . .15Doubling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ..15Key Esta blishment . . . . . . . . . . . . . . . . . . . . . . . . . . . ..16Ana lysis a nd Figured B a ss . . . . . . . . . . . . . . . . . . .16Ca dences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18Chord Succession. . .. . . . . .. . . . . . . . . . . . . . . . .....22

CHAP TER 6 INVERSIONS OF PRIMARYTRIADS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23

First Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23Chord Succession . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24Second Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25Types of S econd Inversions . . . . . . . . . . . . . . . . . . .25

CHAPTER 7 DOMINANT SEVENTH CHORDS. . .. . . . . . 29Trit one Resolut ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29

Approa ching the Seventh . . . . . . . . . . . . . . . . . . . . . .30Figured B a ss a nd Doubling . . . . . . . . . . . . . . . . .. .30Chord Succession . . . . . . . . . . . . . . . . . . .. . . . . . . .. . .33

CHAP TER 8 NON-HARMONIC TONES . . . . . . . . . . . . . . .35Figured B a ss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35Dia tonic P a ssing Tone . . . . . . . . . . . . . . . . . . . . . . . . .36Accented P a ssing Tone . . . . . . . . . . . . . . . . . . . . . . . .36Chroma t ic P a ssing Tone . . . . . . . . . . . . . . . . . . . . ..36Double P a ssing Tone (melodic). . . . . . . . . . . . . . .37Chroma t ica lly Alt ered P a ssing Tone. . . . . . . .38Upper Auxilia ry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..38

Lower Auxilia ry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ..39Changing Tones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39Cambia ta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .....41Échappée . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41Suspension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41Appoggia tura . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42Ant icipa t ion . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . .43P eda l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43S imult a neous Non-H a rmonic Tones. . . . . . . . . . .44Chorda l Sevenths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46Voicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47

CHAP TER 9 SECONDARY TRIADS . . . . . . . . . . . . . . . .. . . ..49Chord P rogression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49G roup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49G roup 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49G roup 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49G roup 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49Figured B a ss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52Lea ding Tone Tr ia d . . . . . . . . . . . . . . . . . . . . . . . . . . ..52Common Funct ion Succession . . . . . . . . . . . . . . .53

ii



Supersonic Tria d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54Submedia nt Tr ia d . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .55Mediant Tr ia d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58Subtonic Tr ia d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59Subtonic Sca le Degree . . . . . . . . . . . . . . . . . . . . . . . . ..60

CHAPTER 10 DIATONIC SEVENTH . . . . . . . . . . . . . . . . . .61Lea ding Tone Seventh . . . . . . . . . . . . . . . . . . . . . . .. . ..61Supersonic Seventh . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62Subdominant Seventh . . . . . . . . . . . . . . . . . . . . . . . . ..63Submedia nt Seventh . . . . . . . . . . . . . . . . . . . . . . . . . . .64Mediant Seventh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..64Tonic Seventh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...66Subtonic Seventh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66Dia tonic Seventh Sequence . . . . . . . . . . . . . . . . . . .67

CHAPTER 11 EXTENSIONS ON DIATONICCHORDS. . . . . . . . . . . . . . . . . . . . . . . . . . .. . ...69

Ma jor Ninth . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . .69Minor Ninth, . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .72E leventh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72Thirteenth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73

CHAPTER 12 SIMP LE MODULATION . . . . . . . . . . . . .. . . .75Keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75P ivot Chord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76Esta blishing Keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77

CHAPTER 13 SECONDARY CHORDS, . . . . . . . . . . . . .. . ..79Ana lysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ..79Seconda ry Dominants . . . . . . . . . . . . . . . . . . . . . . . . .79V/V-V7/V .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . ...80V7/V-V/v-V7/v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80V/i-V7/i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..81V/vi-V7/vi-V7/VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82V/ii-V7/ii-V/ I I -V7/ II . . . . . . . . . . . . . . . . . . . . . . .82V/VII-V7/VII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 83Seconda ry Lea ding Tone Chords . . . . . . . . . . . .. 84

CHAPTER 14 BORROWED CHORDS . . . . . . . . . . . . . . . . .85B orrow ed Chords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .85B orrow ed from Minor . . . . . . . . . . . . . . . . . . . . . . . .. .85B orrow ed from Ma jor . . . . . . . . . . . . . . . . . . . . . . . .. .87

CHAPTER 15 CHROMATIC ALTERATIONS. .. .. . .. . .. . . . . .. . . . . .89Ra ised Fifth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Lowered Fifth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90Ra ised Root . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ..91

iii



CHAPTER 16 AUGMENTED SIXTH CHORDSIta l ianFrenchGerman

93939394

CHAPTER 17 NEAPOLITAN SIXTH CHORD . . . . . .. . . . . .7

CHAP TER 18 ADVANCED MODULATION . . . . . . . . .99Dia tonic to Dia tonic . . . . . . . . . . . . . . . . . . . . . . . . . . . .99Dia tonic to Chroma t ic . . . . . . . . . . . . . . . . . . . . . . . . .100Chroma t ic to Dia tonic . . . . . . . . . . . . . . . . . . . . . . . . .100Chroma t ic to Chroma t ic . . . . . . . . . . . . . . . . . . . . . .101Enha rmonic Modula t ion . . . . . . . . . . . . . . . . . . . . . .101Change of Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102

PURPOSE AND SCOPE

This t ra ining circula rs the principa l ha rmony reference for a ll Army bandsmen. I t maybe used, in conjunct ion w ith a cademic ma teria ls, a s a t ext for courses of inst ruct ion a t theUS Army E lement School of Music. I t encompa sses the ba sic a spect s of ha rmony,pr ogr ession a nd mod ula t ion.

INTRODUCTION

U sers of this publica tion a re encoura ged to recommend cha nges a nd submit comment sfor it s improvement . Comment s should be keyed to the specific pa ge, pa ra gra ph a nd line ofthe t ext in which the change is recommended. Rea sons w ill be provided for ea ch commentto ensure underst a nding and complete eva lua tion. Comments should be prepa red usingDA Form 2028 (Recommended Cha nges to P ublica tions a nd Forms) a nd forw arded direct lyto the Commandant , U S Army E lement School of Music, ATTN: ATTG -SM-DT, U S Nava lAm phibious B a se (L it tle C reek), Norfolk, Virginia 23521.

iv



CHAPTER1

Introduction

PRINCIPL ES OF WRITING

The study of Ha rmony examines the st ructure and rela t ionship between vertical

combina tions of musica l t ones a nd their succession, C ount erpoint exa mines t he st ructurea nd rela tionship bet ween horizontal combina tions of musica l tones a nd t heir succession.When these successions center on a key t hey become progressions t ha t est ablish a t ona lit y.

Th er efor e:

ha rmonic progression est ablishes t ona lit y vert ica lly; m elod ic pr og ression es ta blish estona lity horizont ally. In pra ct ice t hey a re direct ly rela ted.

SCALE DEGREE FUNCTION

In the ma jor a nd minor key syst ems, the tonic, subdominant , a nd dominant sca ledegrees a re prima ry t ones or tonal not es beca use the ea r perceives them a s most effect ive inest a blishing a tona l cent er. The leading tone/subtonic, media nt a nd submedia nt a reseconda ry tones and a re a lso cla ssed a smodal notes because the ea r perceives them a sest a blishing the mode. The supersonic t ends to be a seconda ry tone but ca n ha ve the effectof a prima ry tone.

PRIMARY AND SECONDARY TRIADS

P rima ry t ria ds occur on the t onic, subdomina nt , a nd domina nt sca le degrees. S econda ryt ria ds occur on t he supersonic, media nt , submedia nt , a nd lea ding t one/subt onic.

VOICES

Th er e a r e fou r t ra d it ion a l voi ces (pa rt s) used in t he study of H armony. They a re S opra no,Alto, Tenor, a nd B ass, using the gra nd sta ff for not a t ing pa r t s.

1



The Sopra no pa rt is w rit t en on the t rebleclef of the gra nd st a ff, st ems up. I t s ra nge is

to

The Alto pa r t is w rit t en on the t reble clef ofthe gra nd st a ff, st ems down. I t s ra nge is g to

The Tenor pa rt is w r it t en on the ba ss clef ofthe gra nd sta ff, st ems up. I t s ra nge is c to

The B a ss pa rt is w rit t en on the ba ss clef ofthe gra nd st a ff, st ems down. I t s ra nge is F to

Although the full ra nge of ea ch voice maybe used, it is a dvisa ble to confine the voices tothe middle of their respect ive ra nges. Range ext remes should occur only for rea sons ofmelodic line. P a rt s should not rema in in t hose registers.

FI GU RE 1.1: E xa mple of Four Voice Not at ion

2



CHAPTER2

MELODY WRITING

MELODY

Th e t erm melody is a pplied to a ll four voices. Ea ch voice should st a nd a lone a s a melody

ra ther than a s a succession of chord tones. The B ass voice does not a lways follow melodyguidelines a s

TYPES OF

closely a s t he other voices beca use it supplies

MOTION

t he ha rm on ic foun da tion.

Con ju nct m ot ion occurs w hen one pitch of a melody moves step-w ise t o a nother. Disjunctmotion occurs when one pit ch of a melody leaps to another. Conjunct mot ion occurs moreoft en t ha n disjunct mot ion.

F I GU RE 2.1: Exa mples of Conjunct a nd Disjunct Mot ion

MELODY GUIDEL INES

Disjunct mot ion grea ter than a fifth may be followed by any of the following, listed inor der of f requency :

(1) C onjunct mot ion in t he opposit e direct ion.

F I GU RE 2.2: Disjunct mot ion follow ed by conjunct mot ion in t he opposite direct ion

3



(2) D isjunct m ot ion in t he opposit e direct ion.

FI GURE 2.3: Disjunct mot ion follow ed by disjunct mot ion in t he opposit e direct ion

(3) C onjunct mot ion in the sa me direct ion.

F I GU RE 2.4: Disjunct mot ion follow ed by conjunct mot ion in the sa me direct ion

(4) D isjunct mot ion in t he sa me direct ion.

FI GU RE 2.5: Disjunct mot ion follow ed by disjunct mot ion in the sa me direct ion

Two consecut ive moves in the same direct ion which form a compound interva l a reforbidden. G enera lly, tw o or three consecut ive moves in the sa me direct ion w hich form a nocta ve or grea ter a re ra re. Melodies usua lly have a maximum range of an oct a ve. Thisra nge may occa siona lly ext end a st ep above or below . Some int erva ls in melodies requirespecia l considera tions. They a re a s follow s:

(1) Au gmen ted in ter va ls a r e forb idden .

F I GU RE 2.6: E xa mples of Augmented Interva ls

4



(2) C ompound int erva ls a re forbidden.

F I GU RE 2.7: E xa mples of C ompound Interva ls

(3) Ma jor sevent hs a re forbidden.

FI GURE 2.8: E xa mples of Ma jor S evenths

(4) Minor sevenths must be follow ed by conjunct mot ion in the opposit e direct ion.

FI GU RE 2.9: U se of Minor Seventh

(5) Diminished interva ls should be

direction.

followed by conjunct mot ion in the opposit e

F I GU RE 2.10: U se of Diminished Interva ls

5



S ca le degree a ct ivit y is discussed in B a sic Music (TC 12-41/NAVEDTRA 10244). F urt herexpla na tion of t hose concept s is necessa ry for t he proper const ruct ion of melodies.

Any number of st a ble tones ma y follow one a nother, but their overuse will empha sizet he t onic t ria d.

FIGURE 2.11: S uccession of S ta ble Tones

No more than two tendency tones may occur in succession.

F I GU RE 2.12: S uccession of Tendency Tones

When one a ct ive tone is followed by another which is more than a third away, the firsta ct ive t one is disr ega rd ed .

FI GU RE 2.13: Two act ive tones sepa ra t ed by more than a third

6



When tw o act ive tones surround a st a ble tone:

tha t st a ble tone ma y then follow ,

F IGU RE 2.14.a: Tw o Act ive Tones Surrounding a S ta ble Tone

OR

the la tter a ct ive tone ma y be considered for movement ,

F IGU RE 2.14.b: Tw o Act ive Tones Surrounding a S ta ble Tone

OR

a nother a ct ive t one ma y follow .

When

FIGURE

employing

2.14.c: Two

broken

Act iv e Tones Surrounding a Sta ble Tone

chords, sca le degree a ct ivity ma y not a pply.

FI GU RE 2.15: B roken C hord

7



FORM

A phrase in music is defined in B a sic Music (TC 12-41/NAVEDTRA 10244).Addit iona lly, a phra se should convey a defin it e feeling of beginning a nd ending (repose).Repose is a ccomplished by melodic a nd/or ha rmonic cessa tion (ca esura ), ca lled acadence.Two phra ses form a period; the first ca lled a n a nt eced en t p hr a se, t he second ca lled acon seq uen t p h r ase. When there is simila rity between the two phra ses, t hey a repara l le l .

F I GU RE 2.16: P a ra llel P h ra ses

When there is no simila rity between the two phra ses, t hey a recontrast ing.

F I GU RE 2.17: C ont ra st ing P hra ses

RHYTHM

Rhythms employed in the study of H armony a ppea r in the follow ing order of frequency:

(1) Regula r r hy thm.

(2) I rr egula r r hyt hm .

(3) U niform rh yt hm .

(4) S yn copa tion (used prim arily w it h specia l m elodic/h arm onic devices).

8



ADJ ACENT VOICE SPACING

H armonic interva ls w hich occur betw een the Sopra no a nd Alto or Alto a nd Tenor voicesmust be simple in terva ls. Compound int erva ls may occur between the Tenor a nd B a ssvoices.

F I GU RE 3.3: Adja cen t Voice S pa cin g

LOW INTERVAL LIMITS

When simple ha rmonic in terva ls occur betw een the B ass a nd Tenor voices, limita tionsmust be pla ced on how low they ma y occur. The lowest not e the B a ss voice may ha ve for a :

minor sixth is G .

t r itone is B .

third is c.

second is e.

There a re no other rest r ict ions for t he B ass voice of a ny other int erva ls. When tw o voicesform a perfect prime the voicing is ca lled unison.

10



CHAPTER4

Voice Motion

VOICING

Voice mot ion is genera lly descr ibed in t erms of simple int erva ls.

INDIRECT MOTION

I n di r ect m ot ion occurs when two pa r t s move in di

Con tr ar y M ot i on

s sim ila r d ir ect ion s.

Con tr ar y m ot i on is indirect mot ion tha t occurs when two pa rt s move in opposit edirections:

F I GU RE 4.1: C ont ra ry Mot ion

Obl i que M ot i on

Obl i qu e m ot i on is indirect mot ion tha t occurs w hen one pa rt moves a nd a nother sust a insor r epea t s .

F I GU RE 4.2: Obliq ue Mot ion

DIRECT MOTION

D ir ect m ot ion occurs w hen tw o pa rt s move in the sa me direct ion.

11



Sim i l a r M ot i on

Si mi lar m ot i on is direct mot ion tha t occurs when two pa rts move in the sa me direct ionproducing different ha rm on ic int erva ls.

F I GU RE 4.3: S im ila r Mot ion

Parallel Mot ion

Par al lel m ot ion is direct mot ion tha t occurs whenwo pa rt s move in the sa me direct ionproducing the sa me ha rmonic int erva l, w ithout rega rd for qua lity; a ma jor third to a minort hird is pa ra llel mot ion.

Indirect mot ion is

F I GU RE 4.4: Parallel Motion

g en er a lly pr ef er red

OBJ E CTIONABLE MOTION

Some kindscircumstances

t o dir ect m ot ion .

of pa ra llel mot ion must not occur except under a ppropria te ha rmonicbeca use t hey dest roy the four pa rt text ure: oct aves, unisons, perfect

a nd pa ra llel dissona nt interva ls. P ara llel perfect fourths a re a ccepta ble, but onlyu pper t hr ee v oices .

fifths,in the

F I GU RE 4.5: Object ion able P a ra llel Mot ion

12



When two pa rt s move in simila r mot ion to a unison, perfect fift h, or perfect octa ve, tha tmovement is ca lled Hidden or Covered. Hidden unisons a re forbidden . H idden perfectfifths a nd perfect octa ves may occur a t a ny t ime except between the Sopra no a nd B a ssvoices a t a cha nge of chord w ith the Sopra no moving by disjunct mot ion.

F I GU RE 4.6: Object ion a ble H id den

Par al lel s by con tr ar y m ot i on occur w hen tw o voices moveha rmonic interva l to the sa me ha rmonic int erva l.perfect fift hs by cont ra ry mot ion must not occur. An

Parallel

Motion

by cont ra ry mot ion from oneperfect octa ves a nd pa ra llel

octa ve to a unison ha s the sa me effect .

F IGU RE 4.7: P ara llels by Contra ry Mot ion

C r ossed v oi ces occur between a ny two a dja cent voices where the lower voice ha s a pit chhigher tha n the upper voice. Crossed voices a re not norma lly permit ted.

F I GU RE 4.8: Crossed

13

Voices



O ver l ap pi n g voi ces occur in the movement of a ny two voices when: a lower voice movesto a pitch higher tha n the previous pitch in a n upper voice, or a n upper voice moves to apitch low er tha n the previous pitch in a low er voice. Overla pping voices a re not norma llypermitted.

FI GU RE 4.9: Over la ppin g Voices

14



CHAPTER5

Root Position Primary Triads

CONNECTING PRIMARY TRIADS

P rima ry t ria ds in root posit ion ca n be connected with few errors using the followingguidelines:

P la ce roots of t r ia ds in the B ass voice.

Keep t he com mon tone in the same voice, t hen move the rema ining two voices to thenea rest chord t ones by st ep (con junct mot ion).

When there isca se, move a ll

conjunct root posit ion movement , t here is no common tone. In tha tupper voices cont ra ry to the B ass to the nea rest chord tones.

F IGU RE 5.1: Connect ing P rima ry Tria ds

DOUBLING

When writ ing t ria ds in four pa rt s, it is necessa ry to double one of the notes of the t ria d.G enera lly, double tona l not es. Moda l not es may occa siona lly be doubled a s a result ofmelodic line. In some insta nces it is necessa ry or desira ble to t riple the root a nd omit t hefifth.

FI GU RE 5.2: Doubling in P rima ry Tria ds

15



KEY ESTABLISHMENT

The prima ry means of est a blishing a key is to move from the ma jor domina nt t r ia d to thetonic t r ia d. The domina nt t r ia d in na tura l minor is minor. Therefore, the ma jor form of thet r ia d is borrowed from its pa ra llel ma jor key by ra ising the third w ith a n a ccidenta l tocrea t e a lea ding tone and st ronger resolut ion. This process crea t es the har mon i c m inor

scale.

F I GU RE 5.3: Ma jor Domina nt Tria d in Minor

U se of the ascen di ng m el od ic m in or sca le result s in a ma jor qua lity subdomina nt chordtha t may crea t e a cha nge of moda lity to ma jor.

ANALYSIS AND FIGURED BASS

Roman and Arabic numera ls a re used to indica te chords a nd doublings. Roma nnumera ls a re used for a na lysis a nd to indica te chord root s. The Roman numera l w illcorrespond to the sca le degree on w hich the t ria d is built . An upper case Rom an n um er alindica tes a ma jor t r ia d (unless qua lified). Alower case Roma n numera l indica tes a minort r ia d (unless qua lified). A plus sign (+ ) qua lifies a n upper ca se Roma n numera l to indica te

a n augmented t ria d. A circle (o) qua lifies a lower ca se Roman numera l to indica t e adiminished t ria d. All ot her a ltera tions or a ddit ions a re indica ted w ith chroma tic signs a ndAr abic numer a ls .

F I GU RE 5.4: Analysis

16



Ara bic numera ls a re used for f i gu red bass or f i gu r i ng a nd indica te notes a bove theBassvoice, prima rily a s simple interva ls. The complete figuring for a root posit ion t ria d withthe:

8When no Arabic numera ls a ppea r, aoot doubled is 5. This is often a bbrevia ted

3

root posit ion t ria d is int ended.

5fifth doubled is 5.

3

third doubled is

F IGU RE 5.5: Dou bled Root F igur in g

FI GU RE 5.6: Double F ift h F igur in g

FI GU RE 5.7: Doubled Th ir d Figuring

17



root t ripled a nd fift h om it ted8

is 83

F IGU RE 5.8: Tripled Root F igur in g

The Ara bic numera ls of figured ba ss refer to dia tonic int erva ls by na me. A 5 indica tes adia tonic fifth rega rdless of qua lity. When a ccidenta ls a re used, such a s w ith the domina ntchord in minor, t he same a ccident a l must a ppea r in the figured ba ss. This is done byw rit ing the a ccidenta l to the left of the Ara bic numera l. An a ccidenta l ma y be used w ithouta n Ara bic numera l t o indica t e a n a ltera t ion of the not e a th ird a bove the B ass note. Thisa pplies r eg a rd les scorrespondin g n ot ein dica t ed in figur ed

of chord posit ion . A sla sh throughis ra ised a ha lf step. An a ccident a l inbass.

a number indica t es tha t thethe B ass voice is not norma lly

F I GU RES 5.9: Accidentals a nd Figured B ass

CADENCES

P rima ry t ria ds in root posit ion may be used to form three types of ha rmonic ca dences:

AUTHENT IC .

PLAGAL.

HALF.

18



Au then t i c Cad ence

An a ut h en ti c ca den ce occurs when the dominant chord progresses to the tonic chord a t acadence point . In a Per fect A ut hen ti c cadence, both chords a re in root posit ion and thet onic sca le degree a ppea rs in t he S opra no voice over t he t onic chord. The P erfect Authent icoccurs most often a s a fina l ca dence.

F IGU RE 5.10: P er fect Aut hen tic C a dences

In an I m per fect A ut hen ti c ca dence, eit her chord is invert ed, a nd/or the root is not in theS opra no on the tonic chord. The Imperfect Authent ic ca dence occurs most often a t ca dencepoints other t ha n fina l.

F I GU RE 5.11: Imper fect Au th en t ic Cadences

Occa siona lly, in a P erfect Authent ic cadence, the leading tone may DROP to the fift h ofthe tonic chord w hen it is in the Alto or Tenor voices. This is usua lly a result of supersonic to

19



t onic voice lea ding in the Sopra no voice. I t is w rit ten this w ay to a llow a ll not es of the chordt o appea r.

F I GU RE 5.12: Lea ding Tone Dropping in a P erfect Authentic Cadence

Pl agal Cad en ce

A P l aga l ca d en ce occurs when the subdomina nt chord progresses to the tonic chord a t acadence point . In a Per fect P la ga l ca dence, both chords a re in root posit ion a nd the tonicsca le degree a ppea rs in the Sopra no voice over both chords.

F I GU RE 5.13: P erfect P la ga l C adence

In an I m per fect Pl aga l ca dence, eit her chord is inverted, a nd/or the root is not in theSoprano on the tonic chord. P laga l ca dences often follow fina l a uthent ic ca dences toempha siz e fin a lit y.

20



FI GU RE 5.14: I mperfect P la ga l C adences

H al f Cadence

A H a lf cad en ce (Sem i -cad en ce) occurs when any chord, rega rdless of inversion,progresses to the dominant a t a cadence point . G enera lly, t he dominant chord w ill be inroot posit ion. A Pl agal H al f ca dence occurs w hen any chord, rega rdless of inversion,progresses to the subdomina nt a t a ca dence point . G enera lly, t he subdomina nt chord w illbe in root posit ion. Ha lf cadences a re not used a s fina l ca dences.

F I GU RE 5.15: Ha lf C a den ces

Pi car dy Th i r d (T i er ce de Pi car d i e)

Occa siona lly, the tonic t r ia d in minor w ill be borrow ed from its pa ra llel ma jor a t a nauthent ic ca dence. This is known a s aPi car dy T hi r d (T i er ce d e Pi car di e) a nd occurs a t fina l

21



ca dences. When figured ba ss is used, it must reflect the a lt era tion tha t occurs.

FI GU RE 5.16: P ica rdy Th ir d

CHORD SUCCESSION

Chorda l movement s used w ith prima ry t ria ds in root posit ion a re:

I may progress to IV or V

IV may progress to V or I

V may progress to I

V may go to IV if IV immedia t ely progresses to V

Any chord may follow it self. Chords genera lly progress a cross a ba r line.

22



CHAPTER6

Inversions of Primary Triads

Tria d inversion is discussed in B a sic Music (TC 12-41/NAVEDTRA 10244). Inversionsa re used to give the B ass voice smoothness and va riety. Voice lea ding may differ from tha tdescribed for root posit ion prima ry t ria ds; how ever, object ionable mot ion must st ill beavoided.

FIRST INVERSION

Fir st i nver s ion primaryfirst inversion w ith the:

t r ia ds require no new doubling rules. Figured ba ss for t r ia ds in

6root doubled is This is oft en abbrevia t ed or more commonly 6.

3

F I GU RE 6.1: D oubled Root Figuring for First Inversion

6

fifth doubled is 3.

3

F I GU RE 6.2: D oubled Fift h Figuring for First Inversion

23



8

third doubled is 6.

3

FI GU RE 6.3: D oubled Third Figuring for First Inversion

6

root t r ipled and fift h omit ted is 6 This voicing is ra rely used and should be avoided

6

FI GURE 6.4 Tripled Root Figuring for First Inversion

CHORD SUCCESSION

Chord succession involving first inversion t r ia ds rema ins the same a s tha t for rootposit ion. Although IV6 to V6 is now ava ila ble in ma jor key, it is not w rit t en in minor (iv6 toV6) a s this result s in an augmented second in the B ass voice.

A Ph r ygi an cad en ce is crea t ed w ith the use of inversions in a minor key. I t is a form ofHa lf cadence crea t ed by the progression iv6 to V# w ith subdomina nt to domina nt voicelea ding in the Sopra no. The semitone in the B ass voice resembles the low ered supersonic totonic movement a nd the S opra no resembles the subtonic to tonic movement of a P hrygia nmode.

24



FI GU RE 6.5: P hrygia n C adence

SECOND INVERSION

Second inversion chords genera lly do not t a ke pa rt in a progression but ra ther a ppea r ina pa ttern in conjunct ion w ith other chords. Double the fifth of a ll second

8This result s in a figured ba ss of 6, being the a ccept ed abbrevia t ion.

6

4chords a re commonly ca lled Si x-F ou r Ch or d s.

4

F I GU RE 6.6: S econd I nversion Figuring

TYPES OF SECOND INVERSIONS

Cadential

in ver sion chor ds .

S econd inver sion

The most w idely used of a ll second inversions is the Ca den ti al si x-f ou r , a secondinversion tonic chord w hich moves to the domina nt chord a t a ca dence. Norma lly, t he sixthand fourth a bove the B a ss note resolve down by st ep to a fift h a nd third respect ively. Acadent ia l six-four a nd it s resolut ion to the dominant usua lly a ppea r in a st rong-w eakrhythmic rela t ionship. A weak-st rong rela t ionship may occur a t a Ha lf ca dence. In t r iplemeter it is often found on the second bea t w ith the fina l tonic t r ia d occurring on the first

25



bea t of t he follow ing mea sure.

F I GU RE 6.7: Caden tia l S ix-F ou r

Passing

A p assi n g si x-f ou r occurs w hen a second inversion chord a ppea rs betw een root posit ion

a nd first inversion of another chord. Therefore, a V ~ may appea r between a I a nd I6 or a I6

and I . A I may a ppea r betw een a IV and IV6 or a IV6 and IV. P a ssing six-fours must

a ppea r in a w ea k rhythmic posit ion.

FI GU RE 6.8: P a s sin g S ix-F ou r

26



Aux i l i a r y

An au xi l i ar y si x-f ou r (a lso ca lled a p ed al si x-f ou r ) occurs betw een tw o root posit ions ofthe same chord where the fift h of the auxilia ry six-four is the same note a s the root of theroot posit ion chord. E xpressed in t erms of voice mot ion, a n a uxilia ry six-four occurs w hen

the third and fifth of a root posit ion t r ia d, w ith root doubled,Auxilia ry six-fours must occur in a w ea k rhythmic posit ion.

ascend by st ep a nd return.

F I GU RE 6.9: Auxilia r y S ix-Fou r

Arpeggiated

An ar peggi at ed si x-f ou r occurs w hen the second inversion of a chord is immedia telypreceded or follow ed by the same chord in root posit ion a nd /or fir st inver sion .

F I GU RE 6.10: Arpeg gia t ed S ix-F ou r

27



28



CHAPTER7

Dominant Seventh Chord

B asic Music (TC 12-41/NAVE DTRA 01244) descr ibes the const ruct ion a nd interva lrela t ionships of a dominant seventh chord. In Ha rmony, thedom inan t seven th chor d

refers specifica lly to the dia tonic chord which a ppea rs on the dominant sca le degree. In

minor the chord is borrowed from it s pa ra llel ma jor just a s is the dominant t r ia d.

TRITONE RESOLUTION

An interva l of a t rit one appea rs between the third and seventh (lea ding tone andsubdomina nt sca le degrees) of t he domina nt seventh chord. D issona nt ha rmonic interva lssuch a s the t rit one of the dominant seventh chord require specific resolution. A r eg ula rresolut ion occurs w hen t he t hird (lea ding t one) resolves up t o the root of t he tonic chord a ndthe seventh (subdomina nt ) resolves down to the third of the tonic chord. This is the mostcommon resolut ion a nd sa tisfies the melody pull of the t endency tones.

FI GU RE 7.1: Regula r Resolut i on

When the seventh of a dominant seventh chord appea rs in a n upper voice and the chordprogresses to a first inversion tonic chord, a n I r r egu l ar R esol u ti on must occur. The B assvoice ha s taken t he not e of resolut ion (t hird of t he t onic chord) a nd the seventh in t he uppervoice w ill r ise to the fifth of the tonic chord. This w ill oft en produce ha rmonic int erva ls of adiminished fift h follow ed by a perfect fifth. This is ca lledU nequ al F if th s a n d is a ccept a bleunder s uch cir cums ta n ces .

FI GU RE 7.2: I r regula r Resolu tion

29



APPROACHING THE SEVENTH

No new guidelines a re required for a pproa ching a domina nt seventh chord except for themelodic a pproa ch to the seventh. The seventh of t he domina nt seventh chord is considereda dissonance and should not be a pproa ched by disjunct mot ion from above. This is aca rry-over from 16th century cont ra punta l technique, which required tha t no a ccent eddissona nce be a pproa ched in such a ma nner.

FI GURE 7.3: Approa ching t he S event h

FIGURED BASS AND DOUBLING

Figured ba ss for a dominant seventh chord is 5,5 , or 5 w ith the a ccept ed abbrevia t ion

8of 7 or 7. In root posit ion, t he root of the dominant seventh may be doubled and the fifth

#

om it ted w it h

888 7 8

a figured ba ss of 7, 7, or 7 . The 5 voicing is ca lled complete; the 7 voicing is

3 #3 $ 3 3

called incomplete. When a complete root posit ion dominant seventh resolves to a rootposit ion t onic chord, t he t onic chord w ill be incomplet e (fift h omit ted). When a n incomplet eroot posit ion domina nt seventh resolves to a tonic chord in root posit ion, the tonic chord

w ill b e complet e.

30



F I GURE 7.4: C omplete a nd I ncomplet e Domina nt S event h Resolut ion

a complet e spelling w ill be used.hen the domina nt seventh chord a ppea rs in inversion

The figured ba ss for a first inversion domina nt seventh is6

5, a bbrevia ted . I t resolves to a5

t on ic ch or d.oot pos it ion

S even th a nd R esolut ionI GURE 7.5: F ir st I n ver sion Dominant

31



When the dominant seventh chord a ppea rs in second inversion, it must pa ss between Iand I6. This requires a n irregula r resolut ion. When it occurs betw een 16 and I , regula r

resolut ion is required. Figured ba ss for a second inversion domina nt seventh is 4 , 4

6 4or4, a bbrevia t ed in ma jor keys.

33

F I GURE 7.6: Second Inversion Dominant Seventh a nd Resolution

With the a ddit ion of a four th note to a chord, a th ir d i nver si on is pos sib le. When t h eseventh of the dominant seventh is the lowest sounding note (B a ss voice) the third

inversion is crea t ed. Figured ba ss for a third inversion dominant seventh is 4 ,#4, or

4 #4 Kabbrevia ted , ,or (somet imes 2). This inversion w ill a lw ays

22 2

a r egu l a r r esol u t i on because the seventh in the B asst on ic chor d.

voice does

F I GU RE 7.7: Third Inve rs ion Dominant

32

resolve to a I6 but is still

resolve to the third of the

Seventh and Resolut ion



CHORD SUCCESSION

As indica t ed, the dominant seventh chord prima rily progresses to the tonic chord.Occa siona lly, t he dominant seventh chord may occur in a dominant seventh tosubdomina nt to domina nt sevent h chord succession. When this occurs, t he subdomina ntsca le degree must be ma int a ined a s a common tone from chord to chord. This dela ys theresolut ion of t he first seventh. The sevent h ult ima tely resolves to the media nt sca le degree.

F I GURE 7.8: Domina nt Seventh to Subdomina nt to Domina nt Seventh Chord Succession

33



34



CHAPTER8

Non-Harmonic Tones

N on -H ar mon ic t on es (non-chord tones) occur w ith chords but a re not chord members.

FIGURED BASS

Non-H armonic tones a re figured like chord t ones. Non-H armonic tones occurring after

the init ia l a tt a ck of the chord a re indica t ed w ith a change of numera l. When the B ass voicemoves w ithout movement in any upper voice, no addit iona l figured ba ss is necessa ry.When one or more voices rema in st a ble, a da sh(-) is used to indica te the cont inua tion of thesa me pitch. In root posit ion t ria ds w ith doubled root , only the voice tha t moves is figured.Figuring w ill be a rra nged from highest t o low est numera l.

F I GURE 8.1: F iguring Non-H arm onic Tones

Figuring for non-ha rmonic t ones occurring a t t he init ia l a tta ck of a chord (suspensions,a ppoggia tura s, a nd a ccented pa ssing tones), result s in figured ba ss w hich does notrepresent t he t rue posit ion of t he chor d. U sua lly, a chord's posit ion is represent ed w it h t heresolut ion of t he non-ha rmonic t one.

F I GU RE 8.2: Figuring Non-H armonic Tones a t Init ia l At ta ck

35



DIATONIC PASSING TONE

A d i at on i c passi ng tone fills the int erva l betw een two chord tones a third a pa r t a ndoccurs in a w ea k rhythmic posit ion.

F IGU RE 8.3: Dia tonic P a ssing Tone

ACCENTED PASSING TONE

Occa siona lly the int erva l of a third is filled w ith a non-ha rmonic tone w hichst rong rhythmic posit ion. This is ca lled a n accen ted passi ng t on e.

occurs in a

FI GU RE 8.4: Accented P a ssing Tone

CHROMATIC PASSING TONE

A ch rom at ic passi ng t on e fills t he interva l between two chord tones a ma jor second a pa rta nd occurs in a w ea k rhythmic posit ion.

36



F I GU RE 8.5: Chroma tic P assing Tone

Cr oss Rel at i on

C r oss R el a t i on occurs when a chroma tica lly a ltered not e in one voice is next t o the sa media tonic sca le degree in a different voice. I t should be a voided except when using the uppertet ra chord of the melodic minor sca le.

F I GU RE 8.6: Cros s Rela t ion

DOUBLE PASSING TONE (melodic)

D oubl e passi ng ton es fill t he int erva l of a perfect fourth between two chord tones a ndoccur in a weak rhythmic posit ion . In a minor key, t he melodic minor sca le is used fordouble pa ssing tones over the tonic chord.

F I GU RE 8.7: Double P a ssing Tone

37



CHROMATICALLY ALTERED PASSING TONE

A ch r om at i cal ly al ter ed passi ng ton e fills the interva l of a third between tw o chord tonesa nd uses a n a ccidenta l. I t a ppea rs in either a wea k or st rong rhythmic posit ion.Chroma tica lly a ltered pa ssing tones occur most often in the a scending melodic minor overthe domina nt chord.

F IGU RE 8.8: Chroma t ica lly Altered P assing Tone Over the Domina nt Chord

In ma jor keys, the subtonic sca le degree, borrow ed from the pa ra llel minor, pa sses to thesubm edia nt sca le degr ee.

F I GU RE 8.9: Subtonic a s Chroma tica lly Alt ered P assing Tone

UPPER AUXILIARY

An u pp er a ux il i ar y is a non-ha rmonic tone a st ep a bove two chord tones of the sa me pitcha nd a ppea rs in a w ea k rhythmic posit ion.

38



LOWER

F I GU RE 8.10: Upper Auxil ia ry

AUXILIARY

A l ow er a uxi l i ar y is a non-ha rmonic tone a st ep below two chord tones of the same pitcha nd a ppea rs in a w ea k rhythmic posit ion. Low er a uxilia ries ma y be chroma tica lly a lteredto crea te a semitone w hen one does not a ppea r dia tonica lly.

F IGU RE 8.11: Lower Auxi lia r ies

CHANGING TONES

Ch angi ng t on es a re two non-ha rmonic tones approa ching a chord tone, one above andone below . The first must occur in a weak rhythmic posit ion. The second may be in a weak

or st rong rhyt hmic posit ion.

F I GU RE 8.12: Rhythmic P osit ion of Cha nging Tones

39



Changing tones may be preceded by the same pitch a s the note of resolut ion,

FI GU RE 8.13: C ha nging TonesNote a s the Note

P receded by theof Resolut ion

Same

or by a chord tone a third removed from the follow ing chord tone. The la t ter is frequent lycalled N ot a Cam bi at a. Simila r melodic direct ion is used from the first chord t one t hrought he cha nging tones.

FI GU RE 8.14: Nota Cambia ta

The changing tone below the next chord tone may be chroma t ica lly a lt ered to crea t es em it on e movemen t .

F IGU RE 8.15: C ha nging Tones w it h Chroma tic Alt era tion

40



CAMBIATA

A cambia ta is a non-ha rmonic toneresolved by conjunct mot ion in theposit ion. When a ca mbia ta resolvess em it on e movemen t .

a pproa ched by dioppos it e d ir ect ion .

a ndjunct mot ion in one direct ionI t occurs in a weak rhythmic

upwa rd, it may be chroma t ica lly a lt ered to crea t e

F I GU RE 8.16: Cambiata

h IAPP~E

An ~ cha pp6e (esca pe t one) is non-ha rmonic tone a pproa ched by conjunct mot ion a nd leftby disjunct mot ion in the opposit e direct ion. I t occurs in a w ea k rhythmic posit ion.

F I GU RE 8.17: fichapp~e

SUSPENSION

A suspension is a non-ha rmonic tone occurring when a note’s na tura l melodicprogression is dela yed. This requires tw o different chords. A suspension is a chord tone inthe first chord susta ined or repea ted in the sa me voice a s a non-ha rmonic tone of the secondchor d. Ther e a re t hr ee pa rt s of a suspen sion : pr epar at i on (P), su spen si on (S), a nd resolution

(R). The prepa ra tion is a chord tone of the first chord. The suspension is non-ha rmonic a ndis the same pit ch a s the prepa ra t ion cont inued to the second chord.

41



The resolut ion occurs w hen the suspension resolves by conjunct mot ion to a chord tone ofthe second chord. An upwa rd resolut ion of a suspension is ca lled are ta rda t ion . The not e ofresolut ion ma y be present if it is a compound interva l below the suspension . Suspensionsma y be t ied or dot t ed note va lues; however, when repea t ed, they a re ca lled struck

suspensions. The suspension a nd resolut ion must be in a st rong-wea k rhythmicrela tionship. The prepa ra tion must be a s long or longer tha n the suspension . Resolut ionsof suspensions ma y be decora ted w ith other non-ha rmonic tones. Common suspensions a re9-8, 7-6, 6-5, a n d 4-3.

F I GU RE 8.18: Suspension

APPOGGIATURA

An appoggiatura is a non-ha rmonic tone a st ep a bove or below a chord tone of a singlechord. I t resolves to the chord tone. An a ppoggia tura funct ions a s a suspension without aprepa ra tion . Norma lly, a ppoggia tura s a re a pproa ched by disjunct mot ion in the oppositedirect ion of the resolut ion , or by conjunct mot ion from either direct ion . When a na ppoggia tura is a pproa ched by conjunct mot ion in the sa me direct ion a s it s resolut ion, it isa lso ca lled a n a ccented pa ssing tone.

F I GU RE 8.19: Appoggiatura

42



ANTICIPATION

An anticipation is a non-ha rmonic tone which becomes a chord tone in the followingchord. Ant icipa tions occur in a w ea k rhythmic posit ion, frequent ly a t t he subdivided bea tlevel. G enera lly, a nt icipa tions occur in the S opra no voice a t ca dence point s.

PEDAL

A pedal

F I GU RE 8.20: Anticipation

is a non-ha rmonic tone of long dura tionchords. A peda l begins a nd ends a s a chord tone of a

normallyharmony

occurring in three or morea nd must be n on -h armon ic

in a t lea st one chord between the first a nd la st chords. P eda ls occur prima rily in the B assvoice w ith the Tenor voice used for a na lysis a nd figured ba ss. A peda l in the Sopra no voiceis ca lled an i n ver t ed p ed al . A peda l in the Tenor or Alto voices is ca lled an i n ter n al ped al .

P eda ls occurring in tw o voices a re ca lled doubl e p ed a l s. The low est moving voice is used fora na lysis a nd figured ba ss. The tonic a nd dominant sca le degrees a re the commonly usedped a l n ot es.

FI GU RE 8.21: Pedal

43



SIMULTANEOUS NON-HARMONIC TONES

More than one non-ha rmonic tone may occur a t a given point . S imulta neousnon-ha rmonic tones norma lly form ha rmonic int erva ls of thirds, sixths, or oct a ves. Theocta ve occurs when two pa ssing tones move in cont ra ry mot ion. This is ca lledpassingt hr ou gh t he oct ave.

F I GU RE 8.22: P assing Through the Octa ve

S imult a neous non-ha rmonic tones ma y be figured tw o w ays. Vert ica l combina t ions a refigured w ith the numera ls a r ra nged from highest t o lowest , rega rdless of the voices inw hich t he non-ha rmonic t ones occur.

F I GU RE 8.23: Vert ica l Figuring for S imult aneous Non-H armonic Tones

44



Linea r movement of individua l voices is figured sta rt ing from the figuring of the chord’sposition.

F I GU RE 8.24: Linea r Figuring for S imult a neous Non-Ha rmonic Tones

Non-ha rmonic tones of the sa me kind can occur simulta neously. The most common a repa ssing tones or a uxilia ries. Some have become so w idely used tha t a cha nge of chord

6 ).na lysis may occur (a uxilia ry .+

F I GU RE 8.25: P a ssing Tones a nd Auxilia ries used S imult aneously

Another kind of simulta neous use is the ap poggi at ur a si x-f ou r . I t is simila r t o a ca dent ia lsix-four. I t uses the 6 to 5 a nd 4 to 3 voice lea ding and a ppea rs in a st rong-w eak rhythmic

45



rela tionship, but not a t a ca dence. The two uses of the a ppoggia tura six-four a re the I . to V

or IV to I .

F I GU RE 8.26: Appogg ia t ur a S ix-F ou r

Non-ha rmonic tones of different kinds a lso occur simulta neously. A pa ssing six-four isa n exa mple of the use of pa ssing tones, pa ssing through the octa ve, combined w ith a lowerauxiliary.

F IGURE 8.27: Compa rison of P a ssing S ix-Four a nd S imult a neous U se of DifferentNon -H a rm on ic Ton es

CHORDAL SEVENTHS

C ha pt er 15, B asic Music (TC 12-41/NAVEDTRA 10244) defines chorda l sevenths. C areshould be ta ken w hen using a non-ha rmonic tone w hich w ould be a chorda l seventh . U ndermost circumst a nces, the t rea tment of the seventh of the Domina nt Seventh chorddiscussed in Cha pt er VII is a n excellent guide.

46



F I GU RE 8.28: Chordal Sevenths

VOICING

Non-ha rmonic tones ma y occur in a ny voice. They occur less frequent ly in the B ass voicea nd a re genera lly limited to una ccented pa ssing tones, a uxilia ries, a nd peda ls.

F I GU RE 8.29: Voicing Non-H arm on ic Tones

47



CHAPTER9

Secondary Triads

Seconda ry t ria ds reinforce moda lity. They do not occur a s frequent ly a s prima ry t ria ds,which reinforce tona lity. Seconda ry t ria ds a re used in ha rmonic progressions to crea te

variety.

CHORD PROGRESSION

P r in ciples of chord progression ma y be discussed w ith the a ddit ion of seconda ry t ria ds toprima ry t ria ds. The tonic chord is considered sepa ra tely when describing chordprogression beca use a ll chord progressions move tow ard the tonic. The rema ining chordsa re a ssigned to Group s (C l assi f i ca t i on s) which rela t e genera lly to the funct ion of thechords.

GROUP 1

Gr ou p 1 (F ir st Cl assi fi ca ti on ) chords a re the ma jor domina nt a nd diminished lea dingtone chords a nd ha ve a d om i nan t fu nct ion . The first inversion a ugmented media nt t r ia dfound in ha rmonic a nd a scending melodic minor is in th is group beca use of it s simila rity tothe domina nt chord.

GROUP 2

G rou p 2 (secon d C la ssi fi ca ti on ) chords a re the subdomina nt a nd supersonic chords a ndha ve a su bd om i na nt fu nct ion .

GROUP 3

T he Gr ou p 3 (T hi rd Cl assi fi cat i on ) chord is t he submedia nt a nd ma y have a ton ic

function.

GROUP 4

T he Gr oup 4 (F ou r th Cl assi fi cat i on ) chord is t he media nt a nd may have a ton ic ord om i na nt fu nct ion .

F I GURE 9.1: C hord C ha rt

49



FI GU RE 9.4: Norma l C hor d P r ogr ession

Elision in a chord progression occurs when one chord group is skipped in left t o rightmovement . E lision must be followed by norma l chord progression. iii(I II ) t o IV(iv) a ndvi(VI) t o V(V#) a re common exa mples of elision.

F IGURE 9.5: Elision

A n eu tr al ton ic chord occurs when a tonic chord a ppea rs between any two chords in aprogression or betw een tw o posit ions of t he sa me chord. Neutra l t onic chords usua lly occurw it h n orma l pr og ress ion .

FI GU RE 9.6: Neut ra l Tonic C hord

Retrogr ession occurs when chords move from right to left on the chord cha rt .Ret rogression is usua lly follow ed by norma l movement .

F IGURE 9.7: Retrogression

51



+ 6The II I chord in minor oft en ha s a dominant funct ion beca use it is simila r to the

$dominant chord. The chord may be described a s a dominant chord w ith an unresolvedn on -h armonic t one.

FI GU RE 9.8: I I I in Minor

FIGURED BASS

The principles of figured ba ss rema in the same w ith the addit ion of seconda ry t r ia ds.

LEADING TONE TRIAD

B asic Music (TC 12-41/NAVEDTRA 10244) describes the spelling a nd qua lity of thelea ding tone t ria d. This chord is oft en ca lled a dominant seventh w ith root omit ted. Thethird is norma lly doubled to avoid doubling a note of the t rit one. The root a nd fifth of thechord a scend to the root a nd fift h of the tonic chord often producing unequa l fift hs. I t isused exclusively in fir st in ver sion.

FI GU RE 9.9: L ea ding Tone Tria d

52



The fifth of the chord is doubled when it a ppea rs in the Soprano voice.

FI GU RE 9.10: Doubled Fifth on Lea ding Tone Tria d

An I n t erm ed i at e

may appea r a t a nyCadence occurs w ith a vii 06 to I (i)ca dence but fina l.

progression a t a cadence point . I t

FI GU RE 9.11: I nt ermedia t e C a den ce

COMMON FUNCTION SUCCESSION

The vii”t j chord may follow a dominant t r ia d w ithin a progression. A vii06 can befollow ed only by the domina nt seventh (V7).

53



SUPERTONIC TRIAD

B asic Music (TC 12-41/NAVE I)TRA 10244) descr ibes the spelling a nd qua lity of thesupersonic t ria d. I t occurs prima rily in first inversion w ith doubled third (tona l note). Thechord ma y a ppea r in root posit ion w ith doubled root (moda l note) or doubled third (tona lnote).

FI GU RE 9.12: Super tonic Tr iad

In ma jor keys, the supersonic chord ma y be used in second inversion a s a pa ssingsix-four.

F I GU RE 9.13: S econd In version S upersonic Tria d

54



The supersonic chord may be used to ha rmonize the ra ised sixth sca le degree ina scending melodic minor. The leading tone may be ha rmonized w ith the V# or itmay a lso be a non-ha rmonic tone.

F I GU RE 9.14: Ha rmonizing the Ra ised S ixth in Minor w ith Supersonic Chord

SUBMEDIANT TRIAD

B asic Music (TC 12-41/NAVEDTRA 10244) describes the spelling and qua lity of the

submedia nt t r ia d. I t a ppea rs primarily in root posit ion. In ma jor keys the root (moda l note)or third (tona l not e) may be doubled. In minor keys the root is usua lly doubled because ofthe ma jor qua lit y of the t ria d.

F IGU RE 9.15: S ubmedia nt Tria d

55



In minor, the t hird must be doubled w hen t here is elision (VI to V#) or ret rogression (V# toVI). Augmented melodic interva ls, pa ra llels, or la rge lea ps occur if a ny other not e isdoubled.

F IGU RE 9.16: Submedia nt with Doubled Third in Minor

The D ecept i ve Cad en ce i s a V to vi or V# to VI progression a t a cadence point . I t mayoccur a t a ny cadence but fina l. The submedia nt t r ia d repla ces the tonic. The third of thesubmedia nt (tonic sca le degree) is doubled. This ca dence is follow ed by a chord t ha t w ouldnorma lly follow t he subm edia nt ,

F I GU RE 9.17: Decept iv e Cadence

56



First inversion of the submedia nt t r ia d occurs prima rily a s a tonic chord w ith resolved orunr es olv ed appoggia t u ra .

I

F I GU RE 9.18: F irst I nversion S ubm edia nt a s Appoggia tura

The chord ma y progress to a G roup 2 chord from first inversion. I t ma y a lso be used tocrea te st epw ise mot ion in the B ass Voice to a G roup 1 chord (elision). The third is doubled inf ir s t i nver s ion .

F I GU RE 9.19: F ir st I nver sion S ubm ed ia nt

57



MEDIANT TRIAD

B asic Music (TC 12-41/NAVEDTRA 10244) describes the spelling and qua lity of themedia nt t r ia d. In ma jor keys, it ma y a ppea r in root posit ion w ith doubled root (moda l note)or occa siona l doubled third (tona l note). In first inversion the third is norma lly doubled.

FI GU RE 9.20: Media nt Tr ia d

In minor keys, t he ma jor qua lity media nt t r ia d may appea r in root posit ion or firstinversion w ith doubled root . The fifth of the chord (subtonic sca le degree) must descend tot he submedia nt sca le degree.

FI GU RE 9.21: Media nt Chord in Minor

58



The Augmented qua lit y media nt t r ia d may a ppea r in root posit ion w ith doubled root , orin first inversion w ith doubled third.

FI GU RE 9.22: Augment ed Media nt Tria d

SUBTONIC TRIAD

B asic Music (TC 12-41/NAVEDTRA 10244) descr ibes the spelling and qua lit y of thesubtonic t ria d. This chord is not considered in the chord cha rt because it only occurs inminor and ha s an unusua l cha ra cter. I t occurs in root posit ion or first inversion w ith

doubled root progressing to the ma jor qua lit y media nt chord. The subtonic chord ma ybepreceded by either i or iv.

FI GU RE 9.23: S ubt onic Tr ia d

59



SUBTONIC SCALE DEGREE

The subtonic sca le degree may be ha rmonized w ith the subtonic or the minor qua lit ydomina nt chords. The follow ing chord w ill be the subdomina nt or submedia nt . The effectof such movement is tha t of pa ssing chords w ithout progression.

F I GU RE 9.24: S ubt on ic S ca le

60

Degree



CHAPTER 1O

Diatonic Sevenths

D i at on i c sev en t hs a re crea ted by a dding a seventh above the root of ea ch dia tonic t r ia d.The a pproa ch to the seventh a nd it s resolut ion is t he sa me a s tha t for the domina nt seventhchord (Cha pter 7). Accept able chord progression m ust be ma int ained. The chord follow ingthe dia tonic seventh chord norma lly conta ins the not e of resolut ion. Ad el a yed r esol u t i on

of the seventh occurs when the seventh is susta ined or repea t ed in the following chord.U lt ima tely it must resolve. Figured ba ss for dia tonic sevenths is the same a s tha t for thedom in an t seven th .

LEADING TONE SEVENTH

(bh)The lea ding tone seventh is a min7

occur in root posit ion resolving to a rootn ma jor keys a nd a dim7 in minor keys. I t mayposit ion tonic chord; in first inversion it may

resolve either t o a root posit ion or first nversion tonic chord. In ma jor, the vii to I w ill

.6

result in pa ra llel fifths. To a void the pa ra llel fifths, viit )h should be borrowed from thepa r a llel m in or .

F I GU RE 10.1. Lea ding Tone Sevent h C hords

When chord roots a re chroma tica lly a ltered a nd the chord a ppea rs in root posit ion, thea na lysis (Roma n numera l) must reflect t he a lt era tion.

F I GU RE 10.2. Ana lysis of Chroma tica lly Alt ered Roots

61



SUPERTONIC SEVENTH

The supertonic seventh is a min 7 in ma jor keys a nd a min 7 in minor keys. In ma jor ita ppea rs in root posit ion a nd a ll inversions; in minor it a ppea rs in root posit ion, first , a ndth ird inversions. F irst inversion is used most frequent ly to a pproa ch a ca dence.

F igu r e 10.3 . Supe rton ic Seven th Chords

Chords following the supersonic seventh a re the domina nt t r ia d or domina nt seventh,

the lea ding tone t ria d or lea ding tone seventh, or the

resolut ion of t he seven th .

The I ~ (i ~ ) dela ys the

F IGURE 1 0.4. Super ton ic Seven th Chordo

62



SUBDOMINANT SEVENTH

The subdominant seventh is a Ma j7 in ma jor keys a nd a min7 in minor keys. Ma jorsevent hs a re dissona nt a nd occur infrequent ly. I nversions produce minor seconds or minorninths; t herefore, t he IV7 in ma jor occurs pr ima r ily in root posit ion a nd occa siona lly infirst inversion. I n minor, t he iv7 occur s only in root posit ion. The I V7 (iv7) pr ogresses eit hert o a domina nt t r ia d (seventh) or lea ding tone t r ia d (seventh). In minor it ma y a lso progresst o t he subt onic chord.

F I GU RE 10.5. S ubdomina nt S event hs

The IV7 (iv7) freq uent ly occurs before t he supersonic sevent hseventh occurs while t he rema ining voices sust a in. I t ca n beseven th w it h a ppoggia t ur a.

F I GU RE 10.6. Progression

chord. Resolut ion of t hefigured a s a supersonic

of t he Subdomina nt Seventh to Supersonic Seventh

63



SUBMEDIANT SEVENTH

The submedia nt seventh is a min7 in ma jor keys a nd a Ma j7 in minor keys. In ma jor itoccurs in root posit ion, first inversion, or t hird inversion. In m inor it occurs in root posit ionor first inversion. I t is used prima rily a s a n a pproa ch to G roup 2 chords. Regula r resolut ionof the submedia nt seventh chord occurs w hen the subdomina nt sca le degree is doubled ont he s uper son ic ch or d.

FI GU RE 10.7. The S ubmedia nt S event h

MEDIANT SEVENTH

The media nt seventh is a min7 in ma jor keys a nd a Ma j7 in minor keys. In ma jor, itoccurs in root posit ion or first or third inversions. In minor, it occurs in root posit ion or firstinversion. I t progresses to the submedia nt or subdomina nt chord. Descending root

movement should be a voided. The II I+ 7 in minor ra rely occurs.

64



F I GU RE 10.8. The Med ia n t Seventh

Occa siona lly the media nt seventh in minor w ill ha ve al ow er ed sev en t h . This II I isnorma lly followed by iv. I t ma y a lso be followed by VI .

F I GU RE 10.9. The Media nt Seventh w ith Low ered Seventh

65



TONIC SEVENTH

The tonic seventh is a Ma j7 in ma jor keys a nd a min7 in minor keys. A min\Ma j7(lea ding t one) in minor is never used. The t onic seventh ra rely follow s a domina nt funct ionchord. I t usua lly follows a n esta blished tonic t r ia d or occurs a s a neut ra l I (i). In ma jor, itoccurs in root posit ion or first inversion . In minor, it occurs in a ll posit ions. When required,a n irregula r resolut ion w ill be used. This w ill ca use the subtonic in minor to a scend.

F IGU RE 10.10. Th e Ton ic S even th

SUBTONIC SEVENTH

The subtonic seventh is a dom7 chord. I t occurs in root posit ion, first or third inversion. I tmust progress to the I I I chord.

F IGU RE 10.11. Th e S ubt on ic S even th

66



DIATONIC SEVENTH SEQUENCE

When the seventh of a dia tonic seventh chord resolves regula rly with the rema inder ofthe chord sust a ining, a new dia tonic seventh chord is crea ted, forming a SEQU ENCE .

F IGU RE 10.12. Th e D ia tonic S even th S eq uence

67



68



CHAPTER 11

Extensions

Extended Chords a re discussed in

on Diatonic Chords

B asic Music (TC 12-41\ NAVEDTRA 10244). Thesechords conta in five or more pitches, which requires a select ion of notes for four pa rt s.Chords w ith ext ensions a ppea r prima rily in root posit ion. An extension ma y be a na lyzed

a s a n essent ia l ha rmonic tone or a s a n unessent ia l non-ha rmonic tone (a ppoggia tura ora ccented pa ssing tone). Ext ensions a ppea r prima rily in the sopra no voice.

MAJ OR NINTH

Ma jor ninths a ppea r in ma jor keys on the domina nt seventh or supersonic seventh chord.Norma lly, the fifth of the chord is omit ted.

The ma jor ninth on a domina nt seventh resolves dow n by step to the root of t he domina ntseventh (a ppoggia tura ) or to the fift h of the tonic a t the cha nge of chord. The third of thedomina nt seventh is occa siona lly omit ted a nd the ninth funct ions a s a n upw ard resolvinga ppoggia tura to the third. F iguring for chords in root posit ion with a ninth is the single

numera l 9.

F I GU RE 11.1. The Ma jor Ninth in Root P osit ion

The domina nt ninth may a ppea r in inversion. Figuring for inversion is:76 for fir st in ver sion .E l

FI GU RE 11.2. First Inversion of the Ma jor Ninth

69



65 for second inversion. The second inversion of the domina nt ninth chord is bet ter a na lyzed

(4 omit ted)0(. j

a s vii s.

F I GU R E 11.3. Second I nver sion of the Ma jor Ninth

for t hir d in ver sion .

F I GU R E 11.4. Third Inversion of the Ma jor Ninth

70



6for fourth inversion (ra re) resolving to a I d .

F I GU RE 11.5. Fourth Inversion of the Ma jor Ninth

The ma jor ninth on a supersonic seventh resolves down by st ep: to the root of thesupersonic chord (a ppoggia tura ), to the fifth of the domina nt chord (supersonic), or to thethird of the lea ding t one chord (supersonic). An interva l of a ma jor seventh exist s bet weenthe third and ninth ofvoices w hen they form

t his chord. Thea m inor secon d.

third and ninth should not be voiced in adja centThe supersonic ninth may occa siona lly a ppea r in

t he fir st in ver sion

F I GU RE 11.6. The Ma jor Ninth on the Supersonic Seventh

71



MINOR NINTH

The minor ninth a ppea rs in minor keys on the domina nt seventh chord. The minor ninthmust resolve dow n by st ep. The minor ninth should never be reduced to a minor second.I nversions a re ra re. The fourt h inversion is forbidden.

F I GU RE 11.7. The Minor Nint h a nd Inversions

ELEVENTH

Major chords w ith an eleventh a re referred to a s sus4 chords in B a sic Music(TC 12-41/NAVEDTRA 10244). The eleventh a ppea rs prima rily over the dominantseventh chord. The seventh a nd ninth usua lly a ppea r w ith a n eleventh, omit t ing the thirdand fift h. Chords w ith elevenths a re used exclusively in root posit ion. The dominanteleventh chord ma y resolve in three w ays:

(1) Direct ly to the tonic chord w ith the eleventh repea ting to become the root of thet onic, the ninth a nd seventh resolving norma lly.

(2) The eleventh resolves down by st ep to the lea ding tone, forming a dominantninth.

(3) The eleventh a nd ninth resolve simulta neously, forming a domina nt seventh.

72



F I GU RE 11.8. The D omina nt E levent h

THIRTEENTH

The thirteenth appea rs on the domina nt seventh chord only. I t a ppea rs exclusively inroot posit ion with the fifth, ninth, a nd eleventh omit t ed. The thirteenth may resolve dow nby st ep to the fifth of the domina nt seventh (a ppoggia tura ) or by lea p to the root of the tonicchord. When t he la tt er occurs, t he B a ss voice must a scend to a void a n object iona ble hiddenoctave.

F I GU RE 11.9. Th e D om in ant Th irt eent h

73



74



CHAPTER 12

Simple Modulation

Modula t ion is t he process of moving from one tona lit y to a nother. S imp l e m od u l at i on ismovement to a closely rela ted key. C losel y r el at ed keys a re those adja cent to a key on the

circle of fift hs a nd their rela tive keys. Therefore, a ny one key ha s five closely rela ted keys.

FI GU RE 12.1. Closely Rela ted K eys

KEYS

Terms a pplied to keys in modula tion a re origina l key, old key, a nd new key. Theoriginalkey is t he beginning key. Usua lly, music begins a nd ends in the origina l key. In amodula tion, the music moves from the ol d k ey t o t he n ew k ey ret aining the key signa ture ofthe origina l key. When a series of modula tions ha s t a ken the music fa r from the origina lkey, sufficient phra ses must rema in to work ba ck to the origina l key.

FI GU RE 12.2. Modula tion S eries in a C om posit ion

75



PIVOT CHORD

A pi vot chor d is used to effect a modula t ion. In simple modula t ion acom mon chor d

(dia tonic in the old and new keys) is used a s a pivot chord. For example, the tonic chord in C

ma jor could be used a s the pivot chord to modula te to G ma jor a s the subdominant chord.P ivot chords a re ana lyzed in both the old and new keys. The pivot chord should not be thedominant chord of the new key.

F I GU RE 12.3. P ivot C hor d Modula t ion

Accidenta ls used to crea t e notes in a new key need not be indica t ed in figured ba ss whena ccompa nied w it h a na lysis.

F I GU RE 12.4. Figuring of Accidenta ls in a Modula tion

76



ESTABLISHING KEYS

Chords on ea ch side of a pivot chord must esta blish the tona lit y a nd moda lity of ea chkey. The new key must be est a blished by the end of the phra se in which the pivot chordappears.

F I GU RE 12.5. Est a blishment of Old a nd New Key in a Modula t ion

77



78



CHAPTER 13

Secondary Chords

Seconda ry chords rela te t o the key of t he chord which follows (key of t he moment ) but donot effect a modula t ion. For example, t he seconda ry chords to the supersonic chord in Cma jor come from the key of d minor. A seconda ry chord cont a ins a t lea st one chroma tica llya lt ered not e; t he chroma tica lly a lt ered not e is never doubled. Seconda ry chords usua lly

ha ve dominant funct ion, Chords must be ma jor or minor in qua lit y t o be preceded bysecon da ry ch or ds.

ANALYSIS

Two Roma n numera ls sepa ra t ed by a sla sh a re used to a na lyze seconda ry chords. Thefir st numera l shows the funct ion a nd qua lit y of t he seconda ry chord in rela t ion to t hefollow ing chord; t he second numera l show s the follow ing chord.

FI GU RE 13.1. Ana lysis of Seconda ry Chords

SECONDARY DOMINANTS

Seconda ry domina nt s may be t r ia ds, domina nt sevenths, or dominant sevenths w ithext ensions (elevenths a re ra re). When a seconda ry dominant progresses t o a dia t onicseventh chord, t he momenta ry lea ding tone (t hird of t he chord) may descend by a ha lf st ept o become t he sevent h.

79



The V/V or occurs in ma jor or minor a s a chroma t ica lly a lt ered supersonic chord.I t is used in any posit ion in ma jor. In minor it is used in any posit ion except secondinversion.

F I GU RE 13.2. Seconda ry Domina nts of the Domina nt

B ecause the is the tonic chord, t he must be used in ma jor to have achroma t ic a ltera t ion in the tonic chord. In minor, the seconda ry dominant t r ia d ordominant seventh may be used because both a re a lt ered tonic chords. These seconda rydomina nt s ma y be used in a ll posit ions.

80



F I GU RE 13.3. Seconda ry D omina nts of t he S ubdomina nt

occurs in ma jor a s a chroma tica lly a lt ered submedia nt chord. I t is usedhe or Vin a ll pos it ion s second inver s ion .xcept

F I GU RE 13.4. S econda ry Domina nts of the Supersonic

81



The or occurs in ma jor a s a chroma tica lly a lt ered media nt chord. I t is usedin a ll posit ions except second inversion. In minor, t he seconda ry domina nt seventh must

be used so tha t a chroma t ic a ltera t ion occurs on the media nt chord isusa ble in a ll posit ions; second inversion occurs only in a descending line beca use itin volves t he subt onic sca le degree.

F I GU RE 13.5. Seconda ry Domina nt s of t he Submedia nt

The V/ iii occurs in ma jor a s a chroma tica lly a ltered lea ding tone chord a nd is used in a ll

posit ions except second inversion. In a minor key the a nd a re thet r ia d a nd subtonic seventh chord. Although no a ltera t ion occurs, t hese chords could bea na lyzed a s seconda ry domina nts.

82



F I GU RE 13.6. Seconda ry Domina nt s of the Media nt

occurs in minor a s a chroma t ica lly a lt ered subdominant chord. I tis used in a ll posit ions except second inversion.

F I GU RE 13.7. Seconda ry Domina nts of the Subtonic

83



SECONDARY LEADING TONE CHORDS

S econda ry Lea ding Tone chords const ruct ed using the key of the moment .

FI GU RE 13.8. S econda ry Lea ding Tone C hords

84



CHAPTER 14

Borrowed Chords

BORROWED CHORDS

Chords in a ma jor key may be borrow ed from the pa ra llel minor a nd chords in a minorkey may be borrowed from the pa ra llel ma jor. Cont inuous use of borrow ed chords mayeffect a modula tion to the pa ra llel key.

BORROWED FROM MINOR

When writ ing in a ma jor key, the follow ing chords may be borrow ed from the pa ra llelminor:

F I GU RE 14.1. The B orrow ed S upersonic from Minor

FI GU RE 14.2. The Bor r owed

85

Leading Tone Seventh



Subdom inant (m in ) in a P l a ga l cad en ce

F I GU RE 14.3. The B orrowed Subdominant in a P laga l Cadence

E xtensions on the domina nt chord

F I GU RE 14.4.

S ubmedia nt (Ma j)

B orrow ed E xt ensions on t he Domina nt

F I GU RE 14.5. The B or row ed S ubm ed ia nt

86



Non-ha rmonic tones occurring w ith borrow ed chords must be borrow ed from t he pa ra llelminor.

F I GU RE 14.6. Non-ha rmonic Tones U sed w ith B orrow ed Chords

Overuse of borrowed chords a nd a ccompa nying non-ha rmonics should be a voided amodula tion ma y occur.

BORROWED FROM MAJ OR

When w rit ing in a minor key, t he following chords ma y be borrow ed from the pa ra llelmajor:

Domina nt (ma j.) a nd Domina nt Seventh

Lea ding tone t ria d (dim.)

P ica rdy third on tonic chord (ma j.)

Supersonic chord (min.) when ha rmonizing the ra ised sixth sca le degree ina scending form of melodic minor sca le.

Non-ha rmonic tones occurring w it h borrow ed chords must be borrow ed from t he pa ra llelmajor.

87



88



CHAPTER 15

Chromatic Alterations

Chords ma y be chroma tica lly a ltered. The fifth of a chord is the most frequent ly a lteredchord tone. Chroma tica lly a ltered notes a re never doubled.

RAISED FIFTH

The ra ised fifth ma y a ppea r on domina nt , tonic, a nd subdomina nt chord in ma jor keys.The ra ised fift h (ra ised supersonic sca le degree) of the domina nt chord must a scend to thethird of the tonic chord. This w ill result in a n a ccept a ble doubled third of the tonic chord infirst inversion. The a ugmented domina nt chord ma y be used in root posit ion or firstinversion.

F I GU RE 15.1. The Augmented Domina nt Chord

The ra ised fifth (ra ised domina nt sca le degree) of the tonic chord must a scend to thesubmedia nt sca le degree (subdomina nt or submedia nt chord). This w ill result in a na ccepta ble doubled third of the subdomina nt chord in first inversion . The a ugmented tonicchord ma y be used in root posit ion or first inversion w hen a pproa ching the subdomina ntchord. I t is used only in root posit ion when a pproa ching the submedia nt chord.

F I GU RE 15.2. The Augmented

89

Ton ic Chor d



A ra ised fifth (ra ised tonic sca le degree) of the subdomina nt chord must a scend to thesupersonic sca le degree (supersonic or domina nt chord). The a ugmented subdomina ntchord may be used in root posit ion or first inversion when a pproa ching the domina nt

chord. I t is used only in root posit ion when a pproa ching the supersonic chord.

F I GU RE 15.3. The Augmented Subdomina nt Chord

LOWERED FIFTH

The lowered fifth ma y a ppea r on the domina nt chord; it must descend to the tonic sca ledegree. The domina nt chord w ith lowered fifth ma y be used in root posit ion or firstinversion.

90



92



CHAPTER 16

Augmented Sixth Chords

The augmented sixth chords a re named It a lia n, French, a nd G erman. Augmented sixthchords a re oft en ident ified using a n a bbrevia t ion of their respect ive na mes. Augmentedsixth chords progress to a domina nt chord or to a tonic six-four follow ed by the domina nt

chord.

The dissona nt a ugmented sixth int erva l norma lly occurs in outer voices a nd resolves tothe d om i nan t oct ave. Tendencies of the chroma t ica lly a lt ered notes must be followed.Commonly used a pproa ch chords a re supersonic, subdomina nt , or submedia nt chords.

ITALIAN

The I tal ian si xth is const ruct ed on the ra ised subdominant sca le degree and is used in

first inversion with doubled fift h. I t is a na lyzed and figured a s

F I GU RE 16.1. The I ta lia n Augmented S ixth

FRENCH

The F ren ch si xt h is const ruct ed on the supersonic sca le degree and is used in second6

inversion. I t is a na lyzed a nd figured a s I I4.3

93



FI GU RE 16.2. The French Augmented S ixth

GERMAN

There a re two forms of the Ger man si xth . The first is const ructed on the ra isedsubdomina nt sca le degree a ndchord in ma jor or minor. I t ma y

is used in first inversion. I t w ill progress to the domina nta lso progr ess t o t he t onic six-four follow ed by t he domina nt

$chord in minor. I t is a na lyzed a nd figured a s IVb5. The pa ra llel fift hs tha t occur in

3resolving this chord to the domina nt a re a ccept a ble, but they should not a ppea r in the outervoices.

F I GU RE 16.3 The G erma n Augmented S ixth on the Ra ised Subdomina nt

94



he second form of the Ger m an si xt h is const ruct ed on t he ra ised supersonic sca le degreea nd is used in second inversion. I t w ill progress to the tonic six-four followed by the

6dominant chord in ma jor. I t is a na lyzed and figured a s I I ~ .

3

F I GU RE 16.4. The G erma n Augmented S ixth on the Ra ised Supersonic

Occa siona lly, other forms of a ugmented sixth a re used in different inversions or a re

const ruct ed on other sca le degrees lea ding to other than dominant chords. The interva lrela tionships must rema in int a ct a nd chroma tic t endencies must be follow ed.

95



96



CHAPTER 17

Neapolitan Sixth Chord

A N eapol it an si xth chord is a ma jor t r ia d const ructed on the low ered supersonic sca le

degree a nd is used in first inversion . I t is a na lyzed a nd figured a s The chord ha sa subdominant funct ion. The third is a lwa ys doubled.

FI GU RE 17.1. The Nea polita n S ixth Chord

The N6 chord progresses to domina nt ha rmony or domina nt ha rmony decora ted by tonicsix-four. When resolving to the domina nt chord the low ered supersonic (root of N6) movesto the lea ding tone (t hird of V). This produces a cross rela tion w hich is not object iona ble.

F I GU RE 17.2. P rogressions of the Nea polita n Sixth

97



Thechord.

Nea polita n chord may occur in root posit ion progressing to a root posit ion tonicThe fifth w ill a scend to the tonic to avoid pa ra llel fift hs.

F I GU R E 17.3. Voice Leading of the Neapolit a n Chord in Root P osit ion

The Neapol it and om in ant seven th

sixth chord may bechord.

preceded by it s seconda ry domina nt or seconda ry

F I GU R E 17.4. The Neapolit a n S ixth P receded by Secondary Dominant

C hords simila r t o t he Nea polit an chord ma ybe found on ot her sca le degrees progressingto other tha n domina nt chords.

98



CHAPTER 18

Advanced Modulation

A dva nced m od ul at ion is the process of moving to a dista nt ly rela ted key or to a closelyrela ted key using a dva nced modula tion techniques. All pivot chords ma y be described a s:

P iv ot ch or ds

oldkey . . . . . . . . . . . . . . new key

Dia tonic . . . . . . . . . . . . . . . D ia tonic

Dia tonic. . . . . . . . . . . . . . Chroma t ic

Chroma t ic. . . . . . . . . . . . . . D ia tonic

Chroma t ic. . . . . . . . . . . . Chroma t ic

ma y be enha rmonica lly spelled.

DIATONIC TO DIATONIC

The pivot chord will be dia tonic in both the old a nd new keys using dia tonic to dia tonicmodulations.

F I GU RE 18.1. Modula t ion U sing the Dia tonic to Dia tonic P ivot Chord

99



DIATONIC TO CHROMATIC

The pivot chord will be dia tonic in the old key a nd chroma t ic in the new key usingdia t on ic t o ch rom a tic m odu la t ion s.

F I GU RE 18.2. Modula tion U sing the Dia tonic to Chroma tic P ivot Chord

CHROMATIC TO DIATONIC

The pivot chord will be chroma t ic in the old key a nd dia tonicch rom at ic t o dia t on ic m odu la t ion s.

in the new key using

F I GU RE 18.3. Modula tion U sing the Chroma tic to Dia tonic P ivot Chord

100



CHROMATIC TO CHROMATIC

The pivot chord w ill be chroma t ic in both the old a nd new keys using chroma t ic toch roma t ic modula t ion s.

F I GU RE 18.4. Modula tion U sing the Chroma t ic to Chroma t ic P ivot Chord

ENHARMONIC MODULATION

An en har m on ic m od ul at ion occurs when the pivot chord sounds the same in both keysa nd is enha rmonica lly spelled in the new key.

F I GU RE 18.5. Modula tion U sing the Enha rmonica lly Spelled P ivot Chord

101



CHANGE OF MODE

A ch an ge of m od e is a modula t ion tha t occurs w hen a ma jor or minor key modula tes to it spa ra llel key.

F I GU RE 18.6. Change of Mode

102

u.s. navy music course - harmony

Documents