us navy course navedtra 12012 - harmony

8/14/2019 US Navy Course NAVEDTRA 12012 - Harmony

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DISTRIBUTION STATEMENT A: Approved for public release; distribution is unlimited.

SPECIAL PUBLICATION

March 1990

Harmony

NAVEDTRA 12012


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DISTRIBUTION STATEMENT A: Approved for public release; distribution is unlimited.

ACKNOWLEDGEMENT

The contents of this SpecialPublication were furnished by the courtesy ofthe United States Army.


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PREFACE

Special Publications (SPs) are manuals or catalogs that provide information of general benefit and career

development. SPs have no associated assignments or tests.

Harmony provides an overview of the basic principles of harmony, progression, and modulation. This SP

is available ONLY in electronic Portable Document Format from the following web site:

http://www.advancement.cnet.navy.mil

Refer questions about this SP to:

COMMANDING OFFICERSCHOOL OF MUSIC

ATTN TRAINING OFFICER

1420 GATOR BLVD

NORFOLK VA 23521-2617

DSN: 253-7509COMM: (757) 462-7509

FAX: DSN 253-4836/COMM (757) 462-4836

Provided by

NAVAL EDUCATION AND TRAINING

PROFESSIONAL DEVELOPMENT

AND TECHNOLOGY CENTER


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Sailors Creed

I am a United States Sailor.

I will support and defend theConstitution of the United States of

America and I will obey the ordersof those appointed over me.

I represent the fighting spirit of theNavy and those who have gonebefore me to defend freedom anddemocracy around the world.

I proudly serve my countrys Navycombat team with honor, courageand commitment.

I am committed to excellence andthe fair treatment of all.


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Tr ain in g Cir cu la rNo. 12-42

*TC12-42HEADQUARTERS

DEP ARTMENT OF THE ARMYWa sh in gt on , DC, 5 Novem b e r 1984

HARMONYTa b le of Con t e n t s

CH AP TE R 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . .P r inciples of Writ ing . . . . . . . . . . . . . . . . . . . . . . . . . .Scale Degree Funct ion . . . . . . . . . . . . . . . . . . . . . . . . . .P r imary and Secondary Triads . . . . . . . . . . . . . . . .Voices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CH AP TE R 2 MELODY WRITING . . . . . . . . . . . . . . . . . . . . . .Melody . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Types of Mot ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Melody Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Rhythm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CHAPTER 3 VERTICAL STRUCTURES . . . . . . . . . . . . . .Posit ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1111133338899

Adjacent Voice Spacing . . . . . . . . . . . . . . . . . . . . . . . . 10Low Interval Limit s . . . . . . . . . . . . . . . . . . . . . . . . . .10CH AP TE R 4 VOICE MOTION . . . . . . . . . . . . . . . . . . . . . . . . . 11

Voicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Indir ect Mot ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...11Direct Mot ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...11Object ionable Mot ion . . . . . . . . . . . . . . . . . . . . . . . ..12

*Th is TC supersedes DA Pam 350-42, 1 April 1969.

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CHAPTER 5 ROOT POSITION PRIMARYTRIADS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Connect ing Pr imary Tr iads . . . . . . . .. . . . . . ..15

Doubling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....15Key Establishment . . . . . . . . . . . . . . . . . . . . . . . . . . . ..16Ana lysis and Figured Bass . . . . . . . . . . . . . . . . . ..16Cadences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..18Chord Succession . ......... . . . . . . . . . . . .........22

CHAPTER 6 INVERSIONS OF PRIMARYTRIADS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23

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

CHAPTER 7 DOMINANT SEVENTH CHORDS. ........ 29Tritone Resolu t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....29Approaching the Seventh . . . . . . . . . . . . . . . . . . . . . . 30Figured Bass and Doubling . . . . . . . . . . . . . . . . ...30Chord Succession . . . . . . . . . . . . . . . . . . .. . . . . . . ....33

CHAPTER 8 NON-HARMONIC TONES . . . . . . . . . . . ....35Figured Bass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...35Diatonic Passing Tone . . . . . . . . . . . . . . . . . . . . . . ...36Accented Passing Tone . . . . . . . . . . . . . . . . . . . . . ...36Chromat ic Passing Tone . . . . . . . . . . . . . . . . . . . . ..36Double Passing Tone (melodic). . . . . . . . . . . . . ..37Chromatica lly Altered Passing Tone. . . . . . ..38Upper Auxiliary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .....38Lower Auxiliary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....39Changing Tones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..39Cambia ta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........41chappe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...41Suspension . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . ..41Appoggia tura . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..42Ant icipat ion . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . ..43Pedal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Simultaneous Non-Harmonic Tones. . . . . . . ....44Chordal Sevenths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Voicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...47

CH AP TE R 9 SECONDARY TRIADS . . . . . . . . . . . . . . . ......49Chord Progression . . . . . . . . . . . . . . . . . . . . . . . . . . . ....49Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Group 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Group 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Group 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Figured Bass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....52Leading Tone Tr iad . . . . . . . . . . . . . . . . . . . . . . . . . . ..52Common Funct ion Succession . . . . . . . . . . . . . ..53

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Super sonic Triad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Submediant Tr iad . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .55Mediant Tr iad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Subtonic Tr iad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Subtonic Scale Degree . . . . . . . . . . . . . . . . . . . . . . . ...60

CHAPTER 10 DIATONIC SEVENTH . . . . . . . . . . . . . . ....61Leading Tone Seventh . . . . . . . . . . . . . . . . . . . . . . .....61Supersonic Seventh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Subdominant Seventh . . . . . . . . . . . . . . . . . . . . . . . . ..63Submediant Seventh . . . . . . . . . . . . . . . . . . . . . . . . ...64Mediant Seventh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....64Tonic Seventh . . . . . . . . . . . . . . . . . . . . . . . . . . . . .....66Subtonic Seventh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66Diatonic Seventh Sequence . . . . . . . . . . . . . . . . . ..67

CHAPTER 11 EXTENSIONS ON DIATONICCHORDS. . . . . . . . . . . . . . . . . . . . . . . . . . ......69Major Ninth . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . ....69Minor Ninth , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....72Eleventh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....72

Thir teenth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

CHAPTER 12 SIMPLE MODULATION . . . . . . . . . . . . .....75Keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..75Pivot Chord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76Establish ing Keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77

CHAPTER 13 SECONDARY CHORDS, . . . . . . . . . . . . .....79Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....79Secondary Dominants . . . . . . . . . . . . . . . . . . . . . . . ..79V/V-V7/V .. ...... . . . . . . . . . . . . . . . . . . . . . . ...80V7/IV-V/iv-V7/iv . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..80V/ii-V7/ii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...81V/vi-V7/vi-V7/VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82V/iii-V7/iii-V/III-V7/III . . . . . . . . . . . . . . . . . . . . . . .82V/VII-V7/VII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Secondary Leading Tone Chords . . . . . . . . . . . . . 84

CHAPTER 14 BORROWED CHORDS . . . . . . . . . . . . . . . . . 85Borrowed Chords . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...85Borrowed from Minor . . . . . . . . . . . . . . . . . . . . . . . ...85Borrowed from Major . . . . . . . . . . . . . . . . . . . . . . . ...87

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

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CHAPTER 16 AUGMENTED SIXTH CHORDSItalianFrenchGerman

93939394

CHAPTER 17 NEAPOLITAN SIXTH CHORD . . . . . . ......7CHAPTER 18 ADVANCED MODULATION . . . . . . ...99Diatonic to Diatonic . . . . . . . . . . . . . . . . . . . . . . . . . . ..99

Diatonic to Chromat ic . . . . . . . . . . . . . . . . . . . . . . ...100Chromat ic to Diatonic . . . . . . . . . . . . . . . . . . . . . . ...100Chromatic to Chromatic . . . . . . . . . . . . . . . . . . . ...101Enharmonic Modulat ion . . . . . . . . . . . . . . . . . . . ...101Change of Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...102

P URPOSE AND SCOP EThis t ra in ing circula rs the pr incipa l ha rmony reference for all Army bandsmen. It maybe used, in conjunct ion with academic mater ia ls, a s a text for cour ses of instruct ion at the

US Army Element School of Music. It encompasses the basic aspects of harmony,pr ogr es sion a nd mod ula tion .

INTRODUCTIONUsers of th is publicat ion are encouraged to recommend changes and submit commentsfor it s improvement. Comments should be keyed to the specific page, pa ragraph and line ofthe text in which the change is r ecommended. Reasons will be provided for each commentto ensure understanding and complete evalua t ion . Comments should be prepa red using

DA Form 2028 (Recommended Cha nges to Publica tions and Forms) and for wa rded direct lyto the Commandant , US Army Element School of Music, ATTN: ATTG-SM-DT, US NavalAm phibiou s Ba se (Lit t le Cr eek), Nor folk, Vir gin ia 23521.

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CHAPTER 1I n t r oduc t i on

PR INCIP LES OF WRITINGThe study of Harmony examines the structure and rela t ionship between vertical

combinat ions of musical tones a nd their succession , Counter point examines the st ructurea nd r ela tion sh ip bet ween horizontal combina tion s of mu sica l ton es a nd t heir su ccession.When these successions center on a key they become progressions t ha t est ablish a t on alit y.

Therefore:h ar mon ic pr ogr ession est ablish es t on alit y ver tica lly; m elodic p rogr ession es ta blish es

tona lity hor izont ally. In pr act ice t hey a re dir ect ly r ela ted.

SCALE DEGREE FUNCTIONIn the major and minor key systems, the tonic, subdominant , and dominant scale

degrees a re pr imary tones or tonal notes because the ear perceives them as most effect ive inestablish ing a tonal center . The leading tone/subtonic, mediant and submediant aresecondary tones and are also classed as modal notes because the ear perceives them asestablish ing the mode. The supersonic tends to be a secondary tone but can have the effectof a pr imary tone.

P RIMARY AND SECONDARY TRIADSPrimary t r iads occur on the tonic, subdominant , a nd dominant scale degrees. Secondary

tr ia ds occu r on t he su per sonic, media nt , su bmedia nt , a nd lea din g t on e/subt onic.

VOICESTh er e a r e fou r t ra dit ion al voices (par t s) used in the study of Harmony. They a re Sopra no,

Alto, Tenor , and Bass, using the grand sta ff for notat ing par t s.

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The Soprano par t is writ t en on the t rebleclef of the grand staff, stems up. It s range is

to

The Alto par t is writ t en on the treble clef ofthe grand staff, stems down. It s range is g to

The Tenor par t is wr it t en on the bass clef ofthe grand sta ff, stems up. It s range is c to

The Bass par t is writ t en on the bass clef ofthe grand staff, stems down. It s range is F to

Although the fu ll range of each voice maybe used, it is advisable to confine the voices tothe middle of their respect ive ranges. Range ext remes should occur only for reasons ofmelodic line. Pa rt s should not rema in in those r egisters.

FIGURE 1.1: Exa mple of Fou r Voice Not at ion2


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CHAPTER2MELODY WRITING

MELODYTh e ter m melody is applied to a ll four voices. Each voice shou ld stand alone a s a melody

ra ther than as a succession of chord tones. The Bass voice does not a lways follow melodyguidelin es a sTYP ES OF

closely a s the other voices because it suppliesMOTION

t he h armon ic fou nda tion .

Con ju n ct mot ion occurs when one pitch of a melody moves step-wise to another . Disjunctmotion occurs when one pit ch of a melody leaps to another . Conjunct motion occurs moreoften t ha n disjun ct m ot ion.

FIGUR E 2.1: Examples of Conjunct and Disjunct Motion

ME LODY GUIDELINE SDisjunct motion grea ter than a fifth may be followed by any of the following, listed in

or der of fr equ en cy:(1) Conju nct m otion in t he opposite dir ect ion.

FIGUR E 2.2: Disjunct mot ion followed by conjunct mot ion in the opposite direct ion

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(2) Disju nct m ot ion in t he opposit e dir ect ion.

FIGUR E 2.3: Disjunct mot ion followed by disjunct mot ion in the opposite direct ion

(3) Conjunct motion in the same dir ect ion .

FIGUR E 2.4: Disjunct mot ion followed by conjunct mot ion in the sa me direct ion(4) Disju nct motion in th e sa me dir ect ion .

FIGUR E 2.5: Disjunct mot ion followed by disjunct motion in the sa me direct ion

Two consecutive moves in the same direct ion which form a compound in terval areforbidden. Generally, two or three consecut ive moves in the same direct ion which form anoctave or grea ter are rare. Melodies usually have a maximum range of an octave. Thisrange may occasionally extend a step above or below. Some intervals in melodies requirespecia l con sider at ion s. Th ey a re a s follows:

(1) Au gmen ted in ter va ls are forb idden.

FIGUR E 2.6: E xa mples of Au gmen ted In ter va ls4


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(2) Compou nd int er va ls a re for bidden .

FIGUR E 2.7: Examples of Compound Intervals

(3) Ma jor seven th s a re for bidden .

FIGUR E 2.8: Examples of Ma jor Sevenths

(4) Minor sevenths must be followed by conjunct mot ion in the opposite direct ion.

FIGUR E 2.9: Use of Minor Seventh

(5) Diminished in tervals should bedirection.

followed by conjunct mot ion in the opposite

FIGUR E 2.10: Use of Dim in ish ed In ter va ls5


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Sca le degr ee a ct ivity is discu ssed in Ba sic Mu sic (TC 12-41/NAVEDTRA 10244). F ur th erexplanat ion of those concepts is necessar y for the proper const ruct ion of melodies.

Any number of stable tones may follow one another , but their overuse will emphasizeth e tonic t ria d.

FIGURE 2.11: Su ccession of St able Ton es

No more than two tendency tones may occur in succession .

FIGUR E 2.12: Su ccession of Ten den cy Ton es

When one act ive tone is followed by another which is more than a third away, the firsta ct ive t on e is disr ega r ded .

FIGUR E 2.13: Two act ive tones sepa ra ted by more than a th ird

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When two active tones sur round a stable tone:that stable tone may then follow,

FIGURE 2.14.a: Two Active Tones Surrounding a Stable ToneOR

the lat ter act ive tone may be considered for movement,

FIGURE 2.14.b: Two Act ive Tones Surrounding a Stable ToneOR

a noth er a ct ive t on e ma y follow.

When

FIGURE

employing

2.14.c: Two

broken

Act ive Tones Surrounding a Stable Tone

chords, scale degree act ivity may not apply.

FIGUR E 2.15: Br ok en Ch or d7


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FORMA phrase in music is defined in Basic Music (TC 12-41/NAVEDTRA 10244).Addit iona lly, a phrase shou ld convey a defin it e feeling of beginning and ending (repose).

Repose is accomplished by melodic and/or harmonic cessa t ion (caesura), ca lled a cadence.Two phrases form a period; the fir st ca lled an a nt eced en t ph ra se, t he second ca lled acon sequ en t p hra se. When there is simila rity between the two phrases, they are parallel.

FIGUR E 2.16: P ar allel P hr a ses

When there is n o simila r ity between the two phrases, they are contrasting.

FIGUR E 2.17: Con tr ast in g P hr ases

RHYTHMRhythms employed in the study of Harmony appear in the following order of frequency:

(1) Regu la r r hyt hm .(2) Ir regu la r r hyt hm .(3) Un ifor m r hyt hm .(4) Syn copa tion (used pr im ar ily with specia l m elodic/h ar monic devices).

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CHAPTER3Ver t ica l S t r u ct u r es

POSITIONH ar mon ic in terva l r ela tion sh ips between t he fou r voices occu r in specific a rr an gem en ts.

When the harmonic interval between the Soprano and Tenor voices is a simple in terval,close posi tion occurs.

FIGUR E 3.1: Close Pos it ion

When the harmonic in terval between the Soprano and Tenor voices is a compoundinterval, open pos it ion occurs. The Bass voice is not considered in determining close oropen pos it ion .

FIGURE 3.2: Open Pos it ion

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ADJ ACENT VOICE SPACINGHarmonic interva ls which occur between the Soprano and Alto or Alto and Tenor voices

must be simple in terva ls. Compound interva ls may occur between the Tenor and Bassvoices.

FIGURE 3.3: Adja cen t Voice Spa cin g

LOW INTERVAL LIMITSWhen simple harmonic in terva ls occur between the Bass a nd Tenor voices, limita t ions

must be placed on how low they may occur . The lowest note the Bass voice may have for a :minor sixth is G.

t r itone is B.third is c.second is e.

There are no other rest r ict ions for the Bass voice of any other intervals. When two voicesform a per fect pr ime the voicing is ca lled unison.

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CHAPTER4Voice Mot ion

VOICINGVoice mot ion is generally descr ibed in terms of simple in ter vals.

INDIRECT MOTIONI nd irect mot ion occurs when two par t s move in diContrary Motion

s sim ila r d ir ect ions .

Con trary m otion is indirect mot ion that occurs when two par t s move in oppositedirections:

FIGURE 4.1: Con tr a ry Mot ion

Oblique Motion

Ob lique mot ion is indir ect mot ion that occur s when one par t moves and another susta insor r ep ea t s.

FIGURE 4.2: Obliq ue Mot ion

DIRECT MOTIONDi rect mot ion occu rs when two par t s move in the same direct ion .

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S im ilar MotionS im ilar motion is direct mot ion tha t occurs when two par ts move in the same direct ion

pr odu cin g differ en t h ar mon ic in ter va ls.

FIGUR E 4.3: S im ila r Mot ionParallel MotionParal lel mot ion is direct motion tha t occurs whenwo par t s move in the same direct ionproducing the same harmonic interva l, withou t regard for quality; a major third to a minor

t hir d is pa ra llel m ot ion .

Indirect motion isFIGUR E 4.4: Parallel Motion

gen er a lly p re fe rr ed

OBJ ECTIONABLE MOTION

Some kindscircumstances

t o dir ect mot ion .

of para llel mot ion must not occur except under appropr ia te harmonicbecause they dest roy the four par t texture: octaves, unisons, per fectand para llel dissonant interva ls. Para llel per fect four ths are acceptable, bu t onlyu pp er t hr ee voices.

fifths,in the

FIGUR E 4.5: Object ion able P ar allel Mot ion

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When two par t s move in simila r motion to a unison, per fect fifth , or per fect octave, tha tmovement is ca lled Hidden or Covered. Hidden un isons are forbidden . Hidden per fectfifths and per fect octaves may occur at any t ime except between the Soprano and Bassvoices a t a change of chord with the Soprano moving by disjunct motion.

FIGUR E 4.6: Obje ct ion able H id den

Parallels by con trary m otion occur when two voices moveharmonic interva l to the same harmonic interva l.per fect fifths by con tra ry mot ion must not occur . An Parallel

Motion

by cont ra ry motion from oneper fect octa ves a nd pa ra lleloctave to a un ison has the sa me effect .

FIGURE 4.7: Pa ra llels by Con tr ary Motion

Cros sed voi ces occur between any two adjacent voices where the lower voice has a pit chh igher than the upper voice. Cr ossed voices are not normally permit ted.

FIGUR E 4.8: Crossed13

Voices


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Over la pp ing v oi ces occur in the movement of any two voices when : a lower voice movesto a pitch higher than the previous pitch in an upper voice, or an upper voice moves to apitch lower than the previous pitch in a lower voice. Over lapping voices are not normallypermitted.

FIGUR E 4.9: Over la ppin g Voices

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CHAPTER5Root P osit ion P r im a r y Tr ia d s

CONNECTING P RIMARY TRIADSPr imary t r iads in root posit ion can be connected with few errors using the followingguidelines:

Place roots of t r iads in the Bass voice.Keep t he com m on tone in the same voice, then move the remaining two voices to thenea rest chor d t ones by step (con junct mot ion).When there isca se, move all conjunct root posit ion movement , there is no common tone. In tha tupper voices contra ry to the Bass to the nearest chord tones.

FIGUR E 5.1: Connect ing P rima ry Tr iads

DOUBLINGWhen writ ing tr iads in four par t s, it is necessary to double one of the notes of the t r iad.Generally, double tonal notes. Modal notes may occasiona lly be doubled as a result ofmelodic line. In some instances it is necessary or desirable to tr iple the root and omit thefifth.

FIGUR E 5.2: Doubling in P rimar y Tria ds

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KEY ESTABLI SHMENTThe primary means of est ablish ing a key is to move from the major dominant t r iad to the

tonic t r iad. The dominant t r iad in na tura l minor is minor . Therefore, the major form of thet r iad is bor rowed from its parallel ma jor key by raising the th ird with an accidenta l tocreat e a leading tone and st ronger resolu t ion . This process creat es the h arm on ic m in orscale.

FIGUR E 5.3: Major Dominant Tr iad in MinorUse of the ascen din g m elod ic m in or sca le resu lt s in a major quality subdominant chordthat may creat e a change of modality to major .

ANALYSIS AND FIGURED BASSRoman and Arabic numera ls a re used to indicate chords and doublings. Roman

numera ls a re u sed for ana lysis and to indicate chord root s. The Roman numeral willcor respond to the scale degree on which the t r iad is built . An u pp er ca se Rom an n um er alin dicat es a m ajor t riad (u nless qu alified). A lo w er c a se Rom an numera l indicates a m inort r iad (unless qualified). A plus sign (+) qua lifies an upper case Rom an numeral to indica tean augmented t r iad. A circle (o) qualifies a lower case Roman numeral to indicat e adiminished t r iad. All ot her altera t ions or addit ions are indica ted with chrom at ic signs an dAr a bic nume ra ls .

FIGUR E 5.4: Analysis16


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Arabic numerals are used for figu red bass or figuring and indica te notes above the Bassvoice , primarily as simple intervals. The complete figur ing for a root posit ion tr iad withthe:

8 When no Arabic numera ls appear , aoot doubled is 5. This is often abbrevia ted3

r oot posit ion t ria d is in ten ded.

5fifth doubled is 5.3

third doubled is

FIGUR E 5.5: Dou bled Root F igu rin g

FIGURE 5.6: Dou ble F ift h F igu rin g

FIGURE 5.7: Dou bled Th ir d Figuring17


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root t ripled a nd fift h om it ted 8is 83

FIGUR E 5.8: Tripled Root F igu r ing

The Arabic numera ls of figured bass refer to dia tonic interva ls by name. A 5 indica tes adia tonic fifth regardless of quality. When acciden ta ls are used, such as with the dominan tchord in minor , the s ame accidenta l must appear in the figured bass. Th is is done bywrit ing the acciden ta l to the left of the Arabic numera l. An accidenta l may be used withoutan Arabic numera l to indicate an a lterat ion of the note a th ird above the Bass note. Th isa pplies r ega rdlesscor respon din g n ot ein dica ted in figu red

of chord posit ion . A slash throughis ra ised a half step. An accidenta l inbass.

a number indica tes tha t thethe Bass voice is not normally

FIGURES 5.9: Accidentals and Figured Bass

CADENCESPr imary t r iads in root posit ion may be used to form three types of harmonic cadences:

AUTHENTIC.PLAGAL.HALF.

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Authen tic CadenceAn aut hen tic ca den ce occurs when the dominant chord progresses to the ton ic chord a t acadence point . In a Perfect Aut hen tic cadence, both chords are in root posit ion and thetonic sca le degree a ppea rs in the Soprano voice over the tonic chord. The Per fect Authen t ic

occurs m ost often a s a fina l cadence.

FIGUR E 5.10: P er fect Au th en tic Ca den ces

In an Imperfect Aut hen tic cadence, either chord is inver t ed, and/or the root is not in theSopra no on the tonic chord. The Im perfect Authen t ic cadence occurs most often a t cadencepoin ts other than fina l.

FIGUR E 5.11: Imp er fe ct Au t hen t ic Cadences

Occasiona lly, in a Per fect Authen t ic cadence, the leading tone may DROP to the fifth ofthe tonic chord when it is in the Alto or Tenor voices. This is usua lly a resu lt of super son ic to

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t onic voice leading in the Soprano voice. It is wr it ten this way to a llow all notes of the chordt o a pp ea r .

FIGUR E 5.12: Leading Tone Dropping in a Per fect Authentic Cadence

Plagal CadenceA Plaga l cadence occurs when the subdominant chord progresses to the ton ic chord a t acadence poin t . In a Perfect P la ga l cadence, both chords are in root posit ion and the tonic

sca le degree appea rs in the Soprano voice over both chords.

FIGUR E 5.13: P er fect P la ga l Ca den ce

In an Im p erfect Plaga l cadence, either chord is inver ted, and/or the root is not in theSoprano on the tonic chord. Plaga l cadences often follow final authent ic cadences toempha size fin a lit y.

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FIGUR E 5.14: Im per fect P la ga l Ca den ces

Half CadenceA Half cad en ce (S em i-cad en ce) occurs when any chord, regardless of inversion ,

progresses to the dominant at a cadence poin t . Generally, the dominant chord will be inroot posit ion. A Plagal H alf cadence occur s when any chord, rega rdless of inver sion ,progresses to the subdominant at a cadence poin t . Generally, the subdominant chord willbe in root posit ion . Half cadences are not used as final cadences.

FIGUR E 5.15: Ha lf Cadence s

Picardy Third (T ierce de Picard ie)Occasiona lly, the tonic tr iad in minor will be borrowed from its parallel major at anauthent ic cadence. This is known as a Pica rd y T h ird (T ierce d e Picard ie) a nd occu rs a t fin al

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cadences. When figured bass is used, it must reflect the a lt era t ion tha t occurs.

FIGUR E 5.16: P ica rdy Th ir d

CHORD SUCCESSIONChorda l movements used with primary t r iads in root posit ion are:

I may progress to IV or VIV may progress to V or IV may progress to IV may go to IV if IV immedia tely progresses to V

Any chord may follow it self. Chords genera lly progress across a bar line.

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CHAPTER6In ve r s ion s of P r im a r y Tr ia d s

Triad inversion is discu ssed in Ba sic Music (TC 12-41/NAVEDTRA 10244). Inversionsare used to give the Bass voice smoothness and var iety. Voice leading may differ from tha tdescr ibed for root posit ion pr imary t r iads; however , object ionable motion must st ill beavoided.F IR ST INVE RSION

F ir s t inve rs ion primaryfir st in ver sion with th e:

t r iads require no new doubling rules. F igured bass for t r iads in

6root doubled is This is often abbreviated or more commonly 6.3

FIGUR E 6.1: Dou bled Root Figu ring for F ir st In ver sion

6fifth doubled is 3.

3

FIGUR E 6.2: Dou bled Fift h Figu rin g for F ir st In ver sion

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8th ird doubled is 6.

3

FIGUR E 6.3: Doubled Third Figur ing for F irst In version

6root t r ipled and fifth omit ted is 6 This voicing is rarely used and should be avoided

6

FIGURE 6.4 Tr ipled Root Figur in g for F ir st In ver sion

CHORD SUCCE SSION

Chord succession involving first inver sion t r iads remains the same as that for rootposit ion . Although IV6 to V6 is now available in major key, it is not writ t en in minor (iv6 toV6) as th is resu lt s in an augmented second in the Bass voice.

A Ph rygia n ca den ce is created with the use of inversions in a minor key. It is a form ofHalf cadence crea ted by the progression iv6 to V# with subdominant to dominant voiceleading in the Soprano. The semitone in the Bass voice resembles the lowered super sonic totonic movement and the Soprano resembles the subtonic to tonic movement of a Phrygianmode.

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FIGUR E 6.5: P hr ygia n Ca den ce

SECOND INVERSIONSecond inversion chords genera lly do not take par t in a progression but ra ther appea r in

a pa tter n in conjunct ion with other chor ds. Double the fifth of all second8

This result s in a figured bass of 6, being the accepted abbreviat ion .64chor ds are commonly ca lled S i x-Fou r Chord s.

4

FIGURE 6.6: Secon d In ver sion F igu rin g

TYP ES OF SECOND INVERSIONSCadential

in ve rs ion chords .Second inver sion

The most widely used of all second inversions is the Caden tia l s ix -fou r, a secon dinversion tonic chord which moves to the dominant chord at a cadence. Normally, the sixthand four th above the Bass note resolve down by step to a fifth and th ird respect ively. Acadent ia l six-four and it s resolu t ion to the dominant usually appea r in a strong-weakrhythmic rela t ionship. A weak-strong rela t ionship may occur a t a Half cadence. In tr iplemeter it is often found on the second beat with the fina l tonic tr iad occurr ing on the first

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bea t of t he following m ea su re.

FIGURE 6.7: Cadent ia l S ix-F ou rPassingA pas si ng si x-fou r occurs when a second inversion chord appea rs between root posit ion

and first inversion of another chord. Therefore, a V ~ may appear between a I and I6 or a I6and I. A I may appear between a IV and IV6 or a IV6 and IV. Passing six-four s mustappea r in a weak rhythmic posit ion .

FIGURE 6.8: Pa ss in g S ix-F ou r26


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AuxiliaryAn aux il ia ry si x-fou r (a lso called a peda l s ix -f ou r) occurs between two root posit ions of

the same chord where the fifth of the auxiliary six-four is the same note as the root of theroot posit ion chord. Expressed in terms of voice motion , an auxiliary six-four occurs whenthe th ird and fifth of a root posit ion tr iad, with root doubled,Auxiliary six-fours must occur in a wea k rhythmic posit ion . ascend by step and return .

FIGUR E 6.9: Auxilia r y S ix-F ou r

ArpeggiatedAn a rp eggia ted si x-fou r occurs when the second inver sion of a chord is immediatelypreceded or followed by the same chord in root posit ion a nd/or fir st in ver sion .

FIGUR E 6.10: Arpeggia t ed S ix-F ou r

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CHAPTER7Dom in a n t Seven t h Ch or d

Basic Music (TC 12-41/NAVEDTRA 01244) descr ibes the const ruct ion and in terva lrela t ionships of a dominan t seven th chord. In Harmony, the dom inant seven th chordrefers specifica lly to the dia ton ic chord which appea rs on the dominant sca le degree. Inminor the chord is bor rowed from it s para llel major just as is the dominan t t r iad.TRITONE R ESOLUTION

An interva l of a t r itone appears between the third and seventh (leading tone andsubdominant sca le degrees) of the dominant seven th chord. Dissonan t harmonic in terva lssuch as the t r itone of the dominan t seven th chord requ ire specific resolution. A regu la rresolu t ion occurs when the th ird (leading tone) resolves up to the root of the tonic chord andthe seventh (subdominant ) resolves down to the th ir d of the ton ic chord. This is the mostcommon resolu t ion and sa t isfies the melody pu ll of the tendency tones.

FIGURE 7.1: Regu la r Resolu t ionWhen the seven th of a dominan t seven th chord appears in an upper voice and the chordprogresses to a fir st inversion ton ic chord, an I rr egu la r Resolut ion must occur . The Bassvoice h as taken t he note of resolu t ion (third of the ton ic chord) a nd the seven th in the upper

voice will r ise to the fifth of the ton ic chord. Th is will oft en produce harmonic interva ls of adim in ish ed fift h followed by a per fect fifth . Th is is ca lled Unequal Fif th s a n d is a cce pt a bleu n de r s uch cir cumst a nce s.

FIGURE 7.2: I r r egu la r Resolu t ion29


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FIGURE 7.4: Complete and Incomplete Dominant Seventh Resolu t ion

a com plet e spellin g will be u sed.hen the dominant seventh chord appea r s in inversionThe figured bass for a first inver sion dominant seventh is 65, abbrevia ted . I t resolves to a5

t on ic chord .oot pos it ion

Seven th a nd Resolu tionIGURE 7.5: F ir s t Inve r sion Dominant31


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When the dominant seventh chord appea rs in second inversion, it must pass between Iand I6. This requires an ir regular resolu t ion . When it occurs between 16 and I, regula rresolu t ion is required. F igured bass for a second inversion dominant seventh is 4 , 4

6 4or 4, abbreviated in major keys.33

FIGURE 7.6: Second Inversion Dominant Seventh and Resolution

With the addit ion of a four th note to a chord, a th ird in version is p os sible. Wh en t heseventh of the dominant seventh is the lowest sounding note (Bass voice) the th ird

inversion is created. Figured bass for a th ird inversion dominant seventh is 4 ,#4, or4 #4 Kabbreviated ,,or (somet imes 2). This inversion will a lways22 2

a regular resolu tion because the seventh in the Basst on ic chord. voice doe s

FIGURE 7.7: Th ir d I nve rs ion Dominant32

resolve to a I6 but is st i l lresolve to the th ird of the

Seventh and Resolu t ion


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CHORD SUCCESSIONAs indicated, the dominant seventh chord pr imar ily progresses to the tonic chord.

Occasionally, the dominant seventh chord may occur in a dominant seventh tosubdominant to dominant seventh chord succession . When th is occurs, the subdominantscale degree must be mainta ined as a common tone from chord to chord. This delays theresolu t ion of the first seventh . The seventh ult imately resolves to the mediant scale degree.

FIGURE 7.8: Dominant Seventh to Subdominant to Dominant Seventh Chord Succession

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CHAPTER8Non -Ha r mon ic Ton es

Non -H arm on ic ton es (non-chord tones) occur with chords but a re not chord members.F IGURED BASS

Non-Harmonic tones are figured like ch or d tones. Non-Harmonic tones occurr ing afterthe in it ia l a t tack of the chord are indicated with a change of numeral. When the Bass voicemoves without movement in any upper voice, no addit iona l figured bass is necessa ry.When one or more voices remain stable, a dash(-) is used to indicate the continuat ion of thesame pitch . In root posit ion t r iads with doubled root , only the voice that moves is figured.Figur ing will be a rranged from highest to lowest numeral.

FIGUR E 8.1: Figur ing Non-Harmonic Tones

Figur ing for non-harmonic tones occurr ing at the in it ia l a t ta ck of a chor d (suspensions,appoggiaturas, and accented passing tones), resu lt s in figured bass which does notr epr esen t t he t ru e posit ion of t he ch or d. Usu ally, a ch or d's posit ion is r epr esen ted wit h t heresolu t ion of the non-ha rmonic tone.

FIGURE 8.2: Figur ing Non-Harmonic Tones at In it ia l At tack35


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DIATONIC P ASSING TONEA diaton ic passing tone fills the interval between two chord tones a th ird apar t and

occur s in a weak rhythmic posit ion .

FIGUR E 8.3: Diatonic Passing Tone

ACCENTED PASSING TONEOccasionally the interval of a third is filled with a non-ha rmonic tone which

st rong rhythmic posit ion . This is called an accented passin g ton e.occurs in a

FIGUR E 8.4: Accented Passing Tone

CHROMATIC P ASSING TONEA ch rom atic passing ton e fills the in terval between two chord tones a major second apar t

and occur s in a weak rhythmic posit ion.36


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CHROMATICALLY ALTERED PASSING TONEA ch rom atically altered passin g ton e fills the inter va l of a t hird bet ween two chor d tones

and uses an accidenta l. It appears in either a weak or st rong rhythmic posit ion.Chromatica lly a ltered passing tones occur most often in the ascending melodic minor overthe domina nt chor d.

FIGUR E 8.8: Chromat ically Altered Passing Tone Over the Dominant Chord

In major keys, the subton ic scale degree, bor rowed from the parallel minor, passes to thesu bm edia nt sca le degr ee.

FIGUR E 8.9: Subton ic as Chromatica lly Altered Passing Tone

UP P ER AUXILIAR YAn upper auxi li ary is a non-harmonic tone a step above two chord tones of the same pitchand appears in a weak rhythmic posit ion.

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LOWER

FIGUR E 8.10: Upper Auxilia ry

AUXILIARY

A lower auxi liary is a non-harmonic tone a step below two chord tones of the same pitchand appears in a weak rhythmic posit ion . Lower auxiliar ies may be chromatica lly a lteredto crea te a semitone when one does not appear dia ton ica lly.

FIGUR E 8.11: Lower Auxi lia r i es

CHANGING TONESCh an gin g ton es are two non-harmonic tones approaching a chord tone, one above andone below. The fir st must occur in a weak rhythmic posit ion . The second may be in a weak

or st ron g r hyt hm ic posit ion .

FIGUR E 8.12: Rhythmic Posit ion of Changing Tones39


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

FIGUR E 8.13: Cha ngin g Ton esNote as the NotePreceded by theof Resolut ion Same

or by a chord tone a third removed from the following chord tone. The lat ter is frequentlycalled Nota Cambiat a. Similar melodic direct ion is used from the first chor d tone throughthe changing tones.

FIGUR E 8.14: Nota CambiataThe changing tone below the next chord tone may be chromatically altered to create

s em it on e movemen t .

FIGUR E 8.15: Changing Tones with Chromat ic Altera t ion40


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CAMBIATAA cambiata is a non-harmonic toneresolved by con junct mot ion in theposit ion . When a cambia ta resolves

s em it on e movemen t .

approached by diop pos it e d ir ect ion .

andju nct m ot ion in on e dir ect ionIt occurs in a weak rhythmicupward, it may be chromatica lly a lt ered to crea te

FIGUR E 8.16: CambiatahIAPP~E

An ~chapp6e (esca pe tone) is non-harmonic tone approa ched by con junct mot ion and leftby disjunct motion in the opposit e direct ion . It occurs in a weak rhythmic posit ion .

FIGUR E 8.17: fichapp~eSUSPENSION

A suspension is a non-harmonic tone occurr ing when a notes na tu ra l melodicprogression is delayed. This requires two differen t chords. A suspension is a chord tone inthe fir st chord susta ined or r epea ted in the same voice a s a non-harmonic tone of the secondchor d. Ther e a re th ree pa rt s of a su spen sion : preparation (P), su spen sion (S ), and resolution(R). The prepara t ion is a chord tone of the fir st chord. The suspension is non-harmonic andis the same pit ch as the prepara t ion cont inued to the second chord.

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The resolut ion occurs when the suspension resolves by con junct mot ion to a chord tone ofthe second chord. An upward resolut ion of a suspension is ca lled a retardation. The note ofresolut ion may be present if it is a compound interva l below the suspension . Suspensionsmay be t ied or dot t ed note va lues; however , when repea ted, they are ca lled strucksuspensions. The suspension and resolut ion must be in a st rong-weak rhythmicrelat ionsh ip. The preparat ion must be as long or longer than the suspension . Resolut ionsof suspensions may be decora ted with other non-harmonic tones. Common suspensions are9-8, 7-6, 6-5, a nd 4-3.

FIGUR E 8.18: Suspension

APPOGGIATURAAn appoggiatura is a non-harmonic tone a step above or below a chord tone of a singlechord. It resolves to the chord tone. An appoggia tura funct ions as a suspension without a

prepara t ion . Normally, appoggia tu ras are approached by disjunct mot ion in the oppositedirect ion of the resolu t ion , or by con junct motion from either direct ion . When anappoggia tura is approached by con junct motion in the same direct ion a s its resolut ion, it isa lso ca lled an accen ted passing tone.

FIGUR E 8.19: Appoggiatura42


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ANTICIPATIONAn anticipation is a non-harmonic tone which becomes a chord tone in the following

chord. Ant icipat ions occur in a weak rhythmic posit ion , frequent ly at the subdivided beatlevel. Generally, an t icipat ions occur in the Sopra no voice at cadence poin ts.

PEDALA pedal

FIGUR E 8.20: Anticipation

is a non-harmonic tone of long dura t ionchords. A pedal begins and ends as a chord tone of a

normallyharmony

occurring in three or morea nd m ust be n on -h ar mon ic

in at least one chord between the first and last chords. Pedals occur pr imar ily in the Bassvoice with the Tenor voice used for analysis and figured bass. A peda l in the Soprano voiceis called an i nv ert ed p edal. A pedal in the Tenor or Alto voices is called an in tern al p edal.Peda ls occur rin g in two voices a re ca lled doubl e peda ls . The lowest moving voice is used forana lysis and figured bass. The tonic and dominant scale degrees are the commonly usedpeda l n ot es.

FIGUR E 8.21: Pedal

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SIMULTANEOUS NON-HARMONIC TONESMore than one non-harmonic tone may occur at a given poin t . Simultaneous

non-ha rmonic tones normally form harmonic intervals of th irds, sixths, or octaves. Theoctave occur s when two passing tones move in cont rary mot ion. This is called passingth rou gh th e octave.

FIGUR E 8.22: Passing Through the Octave

Simultaneous non-harmonic tones may be figured two ways. Ver t ical combinat ions a refigured with the numera ls ar ranged from highest to lowest , regardless of the voices inwhich the non-ha rmonic tones occur .

FIGUR E 8.23: Vert ical F igur ing for Simulta neous Non-Harmonic Ton es

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Linear movement of individual voices is figured sta rt ing from the figur ing of the chor dsposition.

FIGUR E 8.24: Linear Figur ing for Simultaneous Non-Ha rmonic Tones

Non-ha rmonic tones of the same kind can occur simultaneously. The most common arepassing tones or auxiliar ies. Some have become so widely used tha t a change of chord

6 ).nalysis may occur (auxiliary .+

FIGUR E 8.25: P assin g Ton es a nd Au xilia ries u sed Simu lt an eou sly

Another kind of simultaneous use is the appoggia tu ra si x-fou r. It is simila r t o a ca den tia lsix-four . It uses the 6 to 5 and 4 to 3 voice leading and appear s in a strong-weak rhythmic

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rela t ionship, but not a t a cadence. The two uses of the appoggia tura six-four are the I . to Vor IV to I .

FIGUR E 8.26: Appoggia tu ra Six-F ou r

Non-harmonic tones of different kinds a lso occur simultaneously. A passing six-four isan example of the use of passing tones, passing through the octave, combined with a lowerauxiliary.

FIGURE 8.27: Compar ison of Passing Six-Four and Simultaneous Use of DifferentNon -H ar mon ic Ton es

CHORDAL SEVENTHSChapter 15, Basic Music (TC 12-41/NAVEDTRA 10244) defines chorda l seven ths. Careshould be taken when using a non-harmonic tone which would be a chorda l seven th . Undermost circumstances, the trea tment of the seventh of the Dominant Seventh chorddiscussed in Chapter VII is an excellent guide.

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FIGUR E 8.28: Chordal Sevenths

VOICINGNon-harmonic tones may occur in any voice. They occur less frequent ly in the Bass voiceand are genera lly limited to unaccen ted passing tones, auxiliar ies, and pedals.

FIGUR E 8.29: Voicing Non-Ha rm on ic Tones

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CHAPTER9Secon d a r y Tr ia d s

Secondary t r iads reinforce modality. They do not occur a s frequen t ly as primary t r iads,which reinforce tona lity. Secondary t r iads are used in harmonic progressions to crea tevariety.CHORD P ROGRESSION

P rin ciples of chord progression may be discussed with the addit ion of secondary t r iads topr imary tr iads. The tonic chord is considered separa tely when descr ibing chordprogression because all chord progressions move toward the ton ic. The remaining chordsare assigned to Groups (Classi ficat ions) which rela t e genera lly to the funct ion of thechords.GROUP 1

Group 1 (First C la ssifica tion ) chords are the major dominant and dimin ished leadingtone chords and have a dom i nant fu n ct ion . The fir st inversion augmented median t t r iadfound in harmonic and ascending melodic minor is in th is group because of its simila rity toth e dom ina nt ch or d.GROUP 2

Group 2 (s econd Cla ss if ica ti on ) chords are the subdominant and supersonic chords andhave a su bd om in an t fu nction .GROUP 3

T he Grou p 3 (T hird Classification ) chord is the submediant and may have a tonicfunction.GROUP 4

T he Grou p 4 (Fou rth Classification ) chord is the mediant and may have a tonic ordom i nant fu n ct ion .

FIGURE 9.1: Chor d Cha rt49


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Dom i nant rela tion sh ip is the associa t ion of two chords whose roots area per fect fifthapar t . Dominant rela t ionsh ip preva ils when the chord Groups are assembled from Group 4through Group 1 and then the tonic.

FIGUR E 9.2: Domin ant Re la t ion sh ip

An est ablish ed t on ic ch ord occurs whenever a dominant funct ion chord progresses to thetonic chord. Any chord may follow an established ton ic chord. Any chord may follow itself.Chords genera lly change from weak to st rong rhythmic posit ion unless they are of longduration.

FIGUR E 9.3: Chord Progres sion

Normal chor d pr ogr ession occu rs a fter an est ablish ed t onic ch or d, wh en ch or ds pr ogr essfrom left to r ight through each successive group.

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FIGUR E 9.4: Nor ma l Ch or d P rogr ession

Elision in a chord progression occurs when one chord group is skipped in left to r ightmovement. Elision must be followed by normal chord progression. iii(III) to IV(iv) andvi(VI) to V(V#) are common examples of elision .

FIGUR E 9.5: Elision

A n eu tral ton ic chord occurs when a tonic chord appear s between any two chords in aprogression or between two posit ions of the same chord. Neutra l tonic chords usually occurwit h n orma l pr ogr ess ion .

FIGUR E 9.6: Neu tr al Ton ic Ch or d

Retrogression occurs when chords move from right to left on the chord char t .Ret rogr ession is usu ally followed by n or ma l m ovemen t.

FIGUR E 9.7: Retrogression51


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+6The III chord in minor often has a dominant funct ion because it is similar to the$dominant chord. The chord may be descr ibed as a dominant chord with an unresolvedn on -h ar mon ic t on e.

FIGUR E 9.8: III in Minor

F IGURED BASSThe pr inciples of figured bass remain the same with the addit ion of secondary tr iads.

LEADING TONE TRIADBasic Music (TC 12-41/NAVEDTRA 10244) descr ibes the spelling and quality of theleading tone t r iad. This chord is often called a dominant seventh with root omit ted. The

third is normally doubled to avoid doubling a note of the tr itone. The root and fifth of thechord ascend to the root and fifth of the tonic chord often producing unequal fifths. It isu sed exclu sively in fir st in ver sion .

FIGUR E 9.9: Leading Tone Triad52


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SUP ERTONIC TRIADBasic Music (TC 12-41/NAVEI)TRA 10244) descr ibes the spelling and quality of thesupersonic t r iad. It occurs pr imarily in fir st inversion with doubled third (tona l note). The

chord may appear in root posit ion with doubled root (modal note) or doubled third (tona lnote).

FIGUR E 9.12: Super ton ic Tr iad

In major keys, the supersonic chord may be used in second inversion as a passingsix-four.

FIGUR E 9.13: Second In version Su per sonic Tr ia d

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The supersonic chord may be used to harmonize the r a ised sixth sca le degree inascending melodic minor . The leading tone may be harmonized with the V# or itmay also be a non-harmonic tone.

FIGUR E 9.14: Harmonizing the Raised Sixth in Minor with Superson ic Chord

SUBMEDIANT TRIADBasic Music (TC 12-41/NAVEDTRA 10244) descr ibes the spelling and quality of the

submedian t t r iad. It appears pr imar ily in root posit ion. In m ajor keys the root (modal note)or th ird (tona l note) may be doubled. In minor keys the root is usua lly doubled because ofthe major quality of the t r iad.

FIGUR E 9.15: Subm edia nt Tr ia d

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In minor , the third must be doubled when there is elision (VI to V#) or ret rogression (V# toVI). Augmented melodic in terva ls, para llels, or la rge leaps occur if any other note isdoubled.

FIGUR E 9.16: Submediant with Doubled Third in Minor

Th e Deceptive Cadence is a V to vi or V# to VI progression a t a cadence point . It mayoccur a t any cadence but fina l. The submediant t r iad replaces the tonic. The th ird of thesubmedian t (tonic sca le degree) is doubled. Th is cadence is followed by a chord tha t wouldn or ma lly follow t he su bm edia nt ,

FIGUR E 9.17: Decept ive Cad en ce

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First inversion of the submedian t t r iad occurs pr imar ily as a ton ic chord with resolved orun resolved appoggia t u ra .

I

FIGUR E 9.18: F ir st In ver sion Subm edia nt a s Appoggia tur a

The chord may progress to a Group 2 chord from first inversion. It may also be used tocrea te st epwise mot ion in the Bass Voice to a Group 1 chord (elision). The third is doubled infi r st invers ion .

FIGUR E 9.19: F ir st In ver sion Su bm edia nt

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MEDIANT TRIADBasic Music (TC 12-41/NAVEDTRA 10244) descr ibes the spelling and quality of the

median t t r iad. In ma jor keys, it may appea r in root posit ion with doubled root (modal note)or occasiona l doubled th ird (tona l note). In fir st inversion the third is normally doubled.

FIGUR E 9.20: Media nt Tr ia d

In minor keys, the major quality median t t r iad may appear in root posit ion or fir stinversion with doubled root . The fifth of the chord (subton ic sca le degree) must descend tot he subm edia nt sca le degr ee.

FIGUR E 9.21: Median t Chord in Minor

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SUBTONIC SCALE DEGREEThe subton ic sca le degree may be harmonized with the subtonic or the minor qualitydominant chords. The following chord will be the subdominan t or submedian t . The effect

of such movement is tha t of passing chor ds withou t progression.

FIGUR E 9.24: Su bt on ic Sca le

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CHAP TE R 1ODia ton ic Seven th s

Dia ton ic sev en th s are crea ted by adding a seventh above the root of each dia tonic t r iad.The approach to the seventh and its resolut ion is the same as tha t for the dominant seventhchord (Chapter 7). Accepta ble chor d progr ession m ust be ma inta ined. The chor d followingthe dia tonic seven th chord normally conta ins the note of resolut ion. A delayed resolu tionof the seventh occurs when the seventh is susta ined or repea ted in the following chord.Ult imately it must resolve. Figured bass for dia tonic sevenths is the same as tha t for thedom in an t seven th .LEADING TONE SEVENTH

(bh)The leading tone seventh is a min7occur in root posit ion resolving to a root n major keys and a dim7 in minor keys. It mayposit ion tonic chord; in fir st inversion it mayresolve either to a root posit ion or first nversion tonic chord. In major , the vii to I will

.6result in parallel fifths. To avoid the para llel fifths, vii t )h should be borrowed from thepa r allel m in or .

FIGUR E 10.1. Leading Tone Sevent h Chor dsWhen chord roots are chromatica lly a ltered and the chord appears in root posit ion, the

ana lysis (Roma n numer al) must r eflect t he a lt era tion.

FIGUR E 10.2. Analysis of Chroma tically Alt er ed Roots61


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SUP ERTONIC SEVENTHThe supertonic seventh is a min 7 in major keys and a min 7 in minor keys. In major itappears in root posit ion and all inversions; in minor it appears in root posit ion, fir st , and

th ird inversions. F irst inversion is used most frequent ly to approach a cadence.

Figure 10.3. Supe rt on ic Sevent h Chords

Chords following the supersonic seven th are the dominant t r iad or dominant seventh,the leading tone t r iad or leading tone seven th, or ther esolu tion of t he seven th .

The I ~ (i ~) delays the

FIGURE 10.4 . Super t on ic Sevent h Chordo

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SUBDOMINANT SEVENTHThe subdominant seventh is a Maj7 in major keys and a min7 in minor keys. Majorsevenths are dissonant and occur infrequent ly. Inversions produce minor seconds or minor

n in ths; therefore, the IV7 in major occurs pr imar ily in root posit ion and occasiona lly infirst in version . In m in or , t he iv7 occu rs only in root posit ion. Th e IV7 (iv7) pr ogresses eit herto a dominant t r iad (seventh) or leading tone t r iad (seventh). In minor it may also progresst o t he subt on ic ch or d.

FIGUR E 10.5. Su bdom in an t Seven th sThe IV7 (iv7) frequent ly occurs before the supersonic seventh

seventh occurs while the remain ing voices sust a in . It can bes even th wit h a ppoggia tu ra .

FIGUR E 10.6. Progression

chord. Resolut ion of thefigured as a supersonic

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SUBMEDIANT SEVENTHThe submediant seventh is a min7 in major keys and a Maj7 in minor keys. In major it

occu rs in r oot posit ion , fir st in ver sion , or t hird in version . In m in or it occu rs in root posit ionor first inversion . It is u sed primar ily as an approach to Group 2 chords. Regula r resolu t ionof the submediant seventh chord occurs when the subdominant sca le degree is doubled ont he su per son ic ch or d.

FIGUR E 10.7. Th e Su bm edia nt Seven th

MEDIANT SEVENTHThe mediant seventh is a min7 in major keys and a Maj7 in minor keys. In major , it

occurs in root posit ion or fir st or th ird inver sions. In minor , it occurs in root posit ion or firstinversion . It progresses to the submedian t or subdominant chord. Descending rootmovement should be avoided. The III+7 in minor rarely occurs.

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FIGUR E 10.8. Th e Media nt Seventh

Occasionally the mediant seventh in minor will have a l owered seven th. This III isnormally followed by iv. It may also be followed by VI.

FIGUR E 10.9. The Mediant Seventh with Lowered Seventh

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DIATONIC SEVENTH SEQUENCEWhen the seven th of a dia tonic seven th chord resolves regular ly with the remainder of

the chord sustaining, a new dia ton ic seven th chord is crea ted, forming a SEQUENCE.

FIGURE 10.12. Th e Dia tonic Seven th Sequence

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65 for secon d inversion. The secon d inver sion of th e domina nt ninth chor d is bet ter a nalyzed

(4 omit ted)0(.jas vii s.

FIGURE 11.3. Second Inve rs ion of the Major Ninth

for t hir d in ver sion .

FIGURE 11.4. Third Inversion of the Major Ninth

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6for four th inversion (rare) resolving to a I d .

FIGUR E 11.5. Fourth Inversion of the Major Nin th

The major n in th on a superson ic seventh resolves down by step: to the root of thesuper sonic chord (appoggia tu ra), to the fifth of the dominant chord (supersonic), or to theth ird of the leading tone chord (supersonic). An interva l of a m ajor seven th exist s betweenthe th ird and n in th ofvoices when they form

this chord. Thea m in or secon d.

th ird and n in th shou ld not be voiced in adjacen tThe superson ic n inth may occasiona lly appear in

t h e fir st in ver sion

FIGUR E 11.6. The Major Ninth on the Supersonic Seventh

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MINOR NINTHThe minor ninth appears in minor keys on the dominant seventh chord. The minor ninth

must resolve down by step. The minor nin th should never be reduced to a minor second.In ver sions a re ra re. Th e four th inver sion is for bidden .

FIGUR E 11.7. The Minor Ninth and Inversions

ELEVENTHMajor chords with an eleven th are refer red to a s sus4 chords in Basic Music

(TC 12-41/NAVEDTRA 10244). The eleven th appea rs pr imar ily over the dominan tseventh chord. The seventh and ninth usua lly appear with an eleventh, omit t ing the thirdand fifth . Chords with elevenths are used exclusively in root posit ion . The dominan televen th chord may resolve in th ree ways:

(1) Direct ly to the tonic chord with the eleven th repea t ing to become the root of theton ic, the nin th and seven th resolving normally.(2) The eleventh resolves down by step to the leading tone, forming a dominan tninth .(3) The eleventh and n inth resolve simultaneously, forming a dominant seven th .

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FIGUR E 11.8. The Dom in ant Eleven th

THIRTEENTHThe thir teen th appears on the dominant seventh chord on ly. It appear s exclusively in

root posit ion with the fifth , n in th , and eleventh omit t ed. The thir teen th may resolve downby step to the fifth of the dominant seven th (appoggia tura) or by leap to the root of the tonicchord. When the la t t er occur s, the Ba ss voice must ascend to avoid an object ionable h iddenoctave.

FIGUR E 11.9. Th e Dom in ant Th irt eent h

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CHAP TER 12

Sim p le Mod u la t ionModulation is the process of moving from one tonality to another . S impl e modu la ti on ismovement to a closely rela ted key. Closel y r el at ed keys are those adjacent to a key on the

circle of fifths and their rela t ive keys. Therefore, any one key has five closely rela ted keys.

FIGUR E 12.1. Closely Rela ted Keys

KEYSTerms applied to keys in modulat ion are or iginal key, old key, and new key. The original

key is the beginning key. Usually, music begins and ends in the or iginal key. In amodulat ion , the music moves from the old k ey t o t he new key reta ining the key signature ofthe original key. When a ser ies of modula t ions has taken the music fa r from the or iginalkey, sufficien t phrases must remain to work back to the or iginal key.

FIGUR E 12.2. Modu la tion Ser ies in a Com posit ion

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ESTABLISHING KEYSChords on each side of a pivot chord must establish the tona lity and modality of eachkey. The new key must be established by the end of the phrase in which the pivot chord

appears .

FIGUR E 12.5. Establishment of Old and New Key in a Modula t ion

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CHAPTER 13

Secon d a r y Ch or d sSecondary chords rela te to the key of the chord which follows (key of the moment) but donot effect a modula t ion . For example, t he secondary chords to the supersonic chord in C

major come from the key of d minor . A secondary chord conta ins a t least one chromat icallyaltered note; the chromatica lly altered note is never doubled. Secondary chords usuallyhave dominant funct ion, Chords must be major or minor in quality to be preceded bys econ da ry ch or ds .ANALYSIS

Two Roman numerals sepa ra ted by a sla sh are used to analyze secondary chords. Thefir st numera l shows the funct ion and quality of the secondary chord in rela t ion to thefollowing chord; t he second numera l shows the following chord.

FIGUR E 13.1. Analysis of Secondary Chords

SECONDARY DOMINANTSSecondary dominants may be t r iads, dominant sevenths, or dominant sevenths with

extensions (elevenths a re ra re). When a secondary dominant progresses to a diatonicseventh chord, the momentary leading tone (th ird of the chord) may descend by a half stept o becom e t he sevent h.

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The V/V or occurs in major or minor as a chromatica lly a lt ered supersonic chord.It is used in any posit ion in major . In minor it is used in any posit ion except secondinversion.

FIGUR E 13.2. Secondary Dominan ts of the Dominan t

Because the is the tonic chord, the must be used in major to have achromatic a ltera t ion in the ton ic chord. In minor , the secondary dominant t r iad ordominan t seventh may be used because both are a lt ered tonic chords. These secondarydominant s may be used in all posit ions.

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FIGUR E 13.3. Seconda ry Dom ina nts of t he Subdom ina nt

occurs in major as a chromatica lly alt ered submedian t chord. It is usedhe or Vin a ll p os it ion s s econd inve rs ion .xcept

FIGUR E 13.4. Secon da ry Domina nts of the Su per sonic81


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The or occurs in major as a chromatica lly a lt ered mediant chord. It is usedin a ll posit ions except second inversion. In minor , the secondary dominan t seven th mustbe used so tha t a chromat ic altera t ion occurs on the mediant chord isusable in all posit ions; second inversion occurs only in a descending line because itin volves the su btonic sca le degr ee.

FIGUR E 13.5. Seconda ry Dom ina nt s of t he Subm edia nt

The V/ iii occurs in major as a chromatically a ltered leading tone chord and is used in a llposit ions except second inversion. In a minor key the and are thet r iad and subtonic seven th chord. Although no altera t ion occurs, these chords cou ld bea na lyzed a s seconda ry dom ina nts.

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FIGURE 13.6. Secondary Dom inant s of the Median t

occurs in minor a s a chromatically a lt ered subdominant chord. Itis u sed in all posit ions except second inver sion.

FIGUR E 13.7. Secondary Dominan ts of the Subton ic

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SECONDARY LEADING TONE CHORDSSeconda ry Leading Tone chords const ructed using the key of the moment .

FIGUR E 13.8. Seconda ry Lea ding Tone Chords

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Subdominan t (min ) in aP l aga l cadence

FIGUR E 14.3. The Borrowed Subdominant in a Plaga l Cadence

Extensions on the dominan t chord

FIGUR E 14.4.

Su bm edia nt (Ma j)

Borrowed Extensions on the Dominant

FIGUR E 14.5. Th e Bor rowed Su bm edia nt86


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Non-harmonic tones occur ring with bor rowed chords must be borrowed from the para llelminor.

FIGUR E 14.6. Non-harmonic Tones Used with Borrowed Chords

Overuse of bor rowed chords and accompanying non-harmonics shou ld be avoided asmodula tion ma y occur .

BORROWED FROM MAJ ORWhen writ ing in a minor key, the following chords may be borrowed from the p ara llel

major:Dominant (maj.) and Dominant SeventhLea ding ton e tr ia d (dim .)Picardy third on ton ic chord (maj.)Supersonic chord (min.) when harmonizing the ra ised sixth sca le degree inascending form of melodic minor sca le.

Non-harmonic tones occur r ing with bor rowed chords must be borrowed from the parallelmajor.

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CHAP TER 15

Ch r om a tic Alt er a t ion sChords may be chromatically a ltered. The fifth of a chord is the most frequent ly a ltered

chor d tone. Chr om atica lly altered notes ar e never doubled.RAISED F IFTH

The ra ised fifth may appear on dominant , tonic, and subdominant chord in major keys.The ra ised fifth (ra ised superson ic sca le degree) of the dominan t chord must ascend to thethird of the tonic chord. Th is will result in an acceptable doubled third of the tonic chord infir st inversion. The augmented dominant chord may be used in root posit ion or fir stinversion.

FIGUR E 15.1. The Augmented Dominan t Chord

The ra ised fifth (ra ised dominant sca le degree) of the tonic chord must ascend to thesubmedian t sca le degree (subdominant or submediant chord). Th is will resu lt in anacceptable doubled third of the subdominant chord in first inversion . The augmented tonicchord may be used in root posit ion or fir st inversion when approaching the subdominantchord. It is used only in root posit ion when approach ing the submedian t chord.

FIGUR E 15.2. The Augmen t ed89

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A raised fifth (ra ised tonic sca le degree) of the subdominant chord must ascend to thesuper son ic sca le degree (superson ic or dominant chord). The augmented subdominantchord may be used in root posit ion or fir st inversion when approaching the dominantchord. It is used only in root posit ion when approaching the supersonic chord.

FIGUR E 15.3. The Augmented Subdominant Chord

LOWERED F IFTHThe lowered fifth may appear on the dominant chord; it must descend to the ton ic sca ledegree. The dominant chord with lowered fifth may be used in root posit ion or fir stinversion.

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CHAPTER 16

Au gm en t ed Sixt h Ch or d s

The augmented sixth chords are named Ita lian , French , and German . Augmented sixthchords are oft en ident ified using an abbreviat ion of their respect ive names. Augmentedsixth chords progress to a dominan t chord or to a ton ic six-four followed by the dominan tchord.

The dissonan t augmented sixth interva l normally occur s in ou ter voices and resolves tothe d om in an t octave. Tendencies of the chromat ica lly a lt ered notes must be followed.Commonly used approach chords are supersonic, subdominant , or submedia nt chords.

ITALIANTh e I talian sixth is const ructed on the ra ised subdominan t sca le degree and is used in

fir st inversion with doubled fifth . It is ana lyzed and figured as

FIGUR E 16.1. The Ita lian Augmented Sixth

FRENCHTh e Fren ch sixth is constructed on the superson ic sca le degree and is used in second

6inversion. It is ana lyzed and figured a s II4.3

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FIGUR E 16.2. The French Augmented Sixth

GERMANThere are two forms of the Germ an sixth . The first is const ructed on the ra isedsubdominant scale degree andchord in major or minor . It may is used in first inversion. It will progress to the dominanta lso pr ogr ess t o t he ton ic six-fou r followed by t he domin an t

$chord in minor . It is analyzed and figured as IVb5. The parallel fifths that occur in3resolving th is chord to the dominant a re acceptable, but they should not appear in the outervoices.

FIGURE 16.3 The German Augmented Sixth on the Ra ised Subdominant

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he second form of the Germ an sixth is con st ru ct ed on th e r aised super son ic sca le degr eeand is used in second inversion . It will progress to the tonic six-four followed by the

6dominant chord in major . It is analyzed and figured as II ~.3

FIGUR E 16.4. The German Augmented Sixth on the Ra ised Supersonic

Occasionally, other forms of augmented sixth are used in different inversions or a reconst ructed on other sca le degrees leading to other than dominant chords. The intervalrela t ionships must remain intact a nd chromat ic tendencies must be followed.

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CHAP TER 17

Nea p oli t a n Six t h Ch or dA Neapolitan sixth chord is a major t r iad const ructed on the lowered superson ic sca le

degree and is used in fir st inversion . It is analyzed and figured as The chord hasa subdominan t funct ion. The third is a lways doubled.

FIGUR E 17.1. The Neapolitan Sixth Chord

The N6 chord progresses to dominant harmony or dominant harmony decora ted by tonicsix-four . When resolving to the dominan t chord the lowered supersonic (root of N6) movesto the leading tone (third of V). This produces a cross rela t ion which is not object ionable.

FIGUR E 17.2. Progressions of the Neapolitan Sixth

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Th echord.

Neapolitan chord may occur in root posit ion progressing to a root posit ion tonicThe fifth will ascend to the tonic to avoid parallel fifths.

FIGURE 17.3. Voice Leading of the Neapolitan Chord in Root Posit ion

The Neapolit a ndom in an t seven th sixth chord may bechord. preceded by it s secondary dominant or secondary

FIGURE 17.4. The Neapolitan Sixth Preceded by Secondary Dominant

Chor ds simila r to the Neapolitan chord maybe found on other scale degr ees pr ogressingto other than dominant chords.

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CHAP TER 18

Ad va nced Mod u la t ionAdva nced mod ula tion is the process of moving to a distant ly rela t ed key or to a closelyrela ted key using advanced modula t ion techniques. All pivot chords may be descr ibed as:

P ivot ch or ds

o ld k e y . . . . . . . . . . . . . . n ew k eyDiatonic . . . . . . . . . . . . . . . Dia tonicDia tonic. . . . . . . . . . . . . . ChromaticChromatic. . . . . . . . . . . . . . Dia tonicChromatic. . . . . . . . . . . . Chromatic

ma y be enh ar monically spelled.

DIATONIC TO DIATONICThe pivot chord will be dia tonic in both the old and new keys using dia tonic to dia ton ic

modulations.

FIGUR E 18.1. Modulat ion Using the Dia tonic to Dia ton ic Pivot Chord

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CHROMATIC TO CHROMATICThe pivot chord will be chromat ic in both the old and new keys using chromatic to

ch r oma tic modula t ion s.

FIGUR E 18.4. Modula t ion Using the Chromat ic to Chromat ic Pivot Chord

ENHARMONIC MODULATION

An en harmon ic mod ula tion occur s when the pivot chord sounds the same in both keysa nd is en ha rmonica lly spelled in the new key.

FIGUR E 18.5. Modulat ion Using the Enharmonica lly Spelled Pivot Chord

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CHANGE OF MODEA change of mod e is a modulat ion tha t occur s when a major or minor key modula tes to it s

pa r allel k ey.

FIGURE 18.6. Change of Mode

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us navy course navedtra 12012 - harmony

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