U.S. Navy Music Course - Harmony

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*TC12-42

Training Circular No. 12-42

HEADQUARTERS DEPARTMENT OF THE Washington,

DC,

HARMONY Table

of

Contents

CHAPTER 1

......................... 1 Principles of Writing .......... ................ 1 Scale Degree Function .......................... 1 Primary and Secondary Triads ................ 1 Voices ............................................. 1

CHAPTER 2

...................... 3 Melody ..... ........ ............................... 3 Types of Motion .................................. 3 Melody Guidelines ............................... 3 Form .............................................. 8 Rhythm ........................................... 8

CHAPTER

INTRODUCTION

MELODY

3

WRITING

STRUCTURES .............. 9 .......... .... .. ...... ..................... 9

VERTICAL

Position

Adjacent Voice Spacing . . . . . . . . . . . . . . . . . . . . . . . . 10 Low Interval Limits . . . . . . . . . . . . . . . . . . . . . . . . . .10 CHAPTER 4

VOICE

MOTION

. . . . . . . . . . . . . . . . . . . . . . . . . 11

Voicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Indirect Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....11 Direct Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...11 Objectionable

*This TC supersedes

Motion

DA Pam 350-42, 1 April

i

. . . . . . . . . . . . . . . . . . . . . . . ..12

1969.

ARMY

5 November

1984

CHAPTER

5

ROOT

POSITION

PRIMARY

TRIADS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Connecting Primary Triads . . . . . . . .. . . . . . ..15 Doubling

......... ....................

. . . . . . . . ....15

Key Establishment . . . . . . . . . . . . . . . . . . . . . . . . . . ...16 Analysis and Figured Bass . . . . . . . . . . . . . . . . . ..16 Cadences

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..18

Chord CHAPTER

Succession. .........

6

INVERSIONS TRIADS

First

CHAPTER

OF

PRIMARY

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..23

Inversion

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..23

Chord

Succession

. . . . . . . . . . . . . . . . . . . . . . . . . . . . ..24

Second Types

Inversion of Second

. . . . . . . . . . . . . . . . . . . . . . . . . . . . ..25 Inversions . . . . . . . . . . . . . . . . . ..25

7

DOMINANT

Tritone

SEVENTH

Resolution

Approaching Figured Bass Chord CHAPTER

. . . . . . . . . . . .........22

8

. . . . . . . . . . . . . . . . . . ..

NON-HARMONIC Bass

Diatonic Accented Double

Tone Tone

Passing Passing

. . . . . . . . . . . . . . . . . . . . ..36

(melodic).

Altered

Auxiliary Auxiliary

Changing Cambiata Échappée

. . . . . . . . . . . ....35

. . . . . . . . . . . . . . . . . . . . . . ...36 . . . . . . . . . . . . . . . . . . . . . ...36

Tone

Tone

Chromatically Upper Lower

TONES

. . . . . . ....33

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...35

Passing Passing

Chromatic

29

the Seventh . . . . . . . . . . . . . . . . . . . . . . 30 and Doubling . . . . . . . . . . . . . . . . ...30

Succession

Figured

CHORDS. ........

. . . . . . . . . . . . . . . . . . . . . . . . . . . .....29

Passing

. . . . . . . . . . . . ..37 Tone.

. . . . . ..38

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .....38 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....39

Tones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..39 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .........41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...41

Suspension Appoggiatura

. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . ..41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..42

Anticipation

. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . ..43

Pedal

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Simultaneous Non-Harmonic Tones. . . . . . . ....44 Chordal Sevenths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Voicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....47 CHAPTER 9

SECONDARY Chord

TRIADS

Progression

. . . . . . . . . . . . . . . ......49

. . . . . . . . . . . . . . . . . . . . . . . . . . . ....49

Group

.

Group

2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

.....................................

49

Group

3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Group 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Figured Bass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....52 Leading Common

Tone

Triad

Function

. . . . . . . . . . . . . . . . . . . . . . . . . . ..52 Succession

ii

. . . . . . . . . . . . . ..53

Supersonic

Triad

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Submediant Triad . . . .. . . . . . . . . . . . . . . . . . . .. . . . ..55 Mediant Triad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Subtonic Subtonic

CHAPTER

10

Triad Scale

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Degree . . . . . . . . . . . . . . . . . . . . . . . ...60

DIATONIC

Leading

Tone

Supersonic

SEVENTH Seventh

Seventh

. . . . . . . . . . . . . . ....61

. . . . . . . . . . . . . . . . . . . . . . .....61

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Subdominant Seventh . . . . . . . . . . . . . . . . . . . . . . . . ..63 Submediant Seventh . . . . . . . . . . . . . . . . . . . . . . . . ...64 Mediant Seventh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....64 Tonic

Seventh

Subtonic Diatonic

CHAPTER

11

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .....66

Seventh Seventh

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66 Sequence . . . . . . . . . . . . . . . . . ..67

EXTENSIONS

ON

DIATONIC

CHORDS. . . . . . . . . . . . . . . . . . . . . . . . . . ......69 Major Ninth . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . ....69 Minor Ninth, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....72 Eleventh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .....72 Thirteenth

CHAPTER

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

12 SIMPLE MODULATION Keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pivot Chord . . . . . . . . . . . . . . . . . . . . . . Establishing Keys . . . . . . . . . . . . . .

CHAPTER

SECONDARY

13 Analysis

CHORDS,

........... ............ ............ ............

. .....75 . ..75 . ..76 . ..77

. . . . . . . . . . . . .....79

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....79

Secondary Dominants . . . . . . . . . . . . . . . . . . . . . . . ..79 V/V-V7/V .. ...... . . . . . . . . . . . . . . . . . . . . . . ...80 V7/IV-V/iv-V7/iv . . . . . . . . . . . . . . . . . . . . . . . . . . . ...80 V/ii-V7/ii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....81 V/vi-V7/vi-V7/VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 V/iii-V7/iii-V/III-V7/III V/VII-V7/VII Secondary

CHAPTER 14

CHAPTER

. . . . . . . . . . . . . . . . . . . . . ..82

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Leading

Tone

BORROWED

Chords

CHORDS

. . . . . . . . . . . . . 84

. . . . . . . . . . . . . . . . . 85

Borrowed Borrowed

Chords . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...85 from Minor . . . . . . . . . . . . . . . . . . . . . . . ...85

Borrowed

from

15

Major

CHROMATIC

. . . . . . . . . . . . . . . . . . . . . . . ...87

ALTERATIONS.

....

. ................89

Raised Lowered

Fifth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Fifth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

Raised

Root. ..

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....91 iii

CHAPTER

CHAPTER CHAPTER

16 AUGMENTED Italian

93 93

German

94

17

NEAPOLITAN

SIXTH

18 ADVANCED Diatonic to Diatonic

Change

CHORD

. . . . . . ...... 97

MODULATION . . . . . . ...99 . . . . . . . . . . . . . . . . . . . . . . . . . ...99

to Chromatic

Chromatic Chromatic Enharmonic

AND

93

CHORDS

French

Diatonic

PURPOSE

SIXTH

. . . . . . . . . . . . . . . . . . . . . . ...100

to Diatonic . . . . . . . . . . . . . . . . . . . . . . ...100 to Chromatic . . . . . . . . . . . . . . . . . . . ...101 Modulation . . . . . . . . . . . . . . . . . . . ...101

of Mode

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...102

SCOPE

This training circulars the principal harmony be used, in conjunction with academic materials, US Army Element School progression and modulation.

of Music.

reference for all Army bandsmen. It may as a text for courses of instruction at the

It encompasses

the basic

aspects

of harmony,

INTRODUCTION Users of this publication are encouraged to recommend changes and submit comments for its improvement. Comments should be keyed to the specific page, paragraph and line of the text in which the change is recommended. Reasons will be provided for each comment to ensure understanding and complete evaluation. Comments should be prepared using DA Form 2028 (Recommended Changes to Publications and Forms) and forwarded directly to the Commandant, US Army Element School of Music, ATTN: ATTG-SM-DT, US Naval Amphibious

Base (Little Creek), Norfolk,

Virginia

iv

23521.

CHAPTER 1

Introduction

PRINCIPLES The

study

combinations

OF WRITING of Harmony of musical

examines

the structure

tones and their succession,

and

relationship

Counterpoint

between

examines

vertical

the structure

and relationship between horizontal combinations of musical tones and their succession. When these successions center on a key they become progressions that establish a tonality. Therefore: harmonic

progression

establishes

tonality

horizontally.

In practice

SCALE

DEGREE

FUNCTION

In the major

and minor

degrees are primary establishing secondary

a tonal

tonality

key systems,

center.

the tonic,

The leading

tones and are also classed the mode. The supersonic

subdominant,

of a primary

tone.

PRIMARY

AND

SECONDARY

tone/subtonic,

as modal

establishes

and dominant

notes because

scale

them as most effective

mediant

tends to be a secondary

and submediant

the ear perceives

in are

them as

tone but can have the effect

TRIADS

triads occur on the tonic, subdominant,

triads occur on the supersonic,

progression

related.

tones or tonal notes because the ear perceives

establishing

Primary

melodic

vertically;

they are directly

mediant,

and dominant

submediant,

and leading

scale degrees. Secondary tone/subtonic.

VOICES There are four traditional Alto, Tenor,

voices (parts) used in the study of Harmony.

and Bass, using the grand

staff for notating

1

parts.

They are Soprano,

The Soprano clef of the grand

part is written

on the treble

staff, stems up. Its range is

to

The Alto part is written on the treble clef of the grand

staff, stems down. Its range is g to

The Tenor part is written on the bass clef of the grand staff, stems up. Its range is c to

The Bass part is written on the bass clef of the grand staff, stems down. Its range is F to

Although the middle melodic

the full range of each voice maybe of their respective

line. Parts should

ranges.

not remain

FIGURE

Range

used, it is advisable extremes

should

in those registers.

1.1: Example

of Four Voice Notation 2

to confine

the voices to

occur only for reasons

of

CHAPTER2

MELODY

WRITING

MELODY The term melody

is applied

to all four voices.

Each voice should stand alone as a melody

rather than as a succession guidelines TYPES

as closely

of chord tones. The Bass voice does not always follow melody as the other voices because it supplies the harmonic foundation.

OF MOTION

Conjunct

motion occurs when one pitch of a melody

motion occurs when one pitch of a melody often than disjunct motion.

FIGURE

MELODY Disjunct

2.1: Examples

moves step-wise

leaps to another.

of Conjunct

Conjunct

and Disjunct

to another. motion

Disjunct

occurs more

Motion

GUIDELINES motion

greater

than a fifth may be followed

motion

in the opposite

by any of the following,

listed in

order of frequency: (1) Conjunct

FIGURE

2.2: Disjunct

motion

followed

direction.

by conjunct

3

motion

in the opposite

direction

(2) Disjunct

FIGURE

motion

2.3: Disjunct

(3) Conjunct

FIGURE

2.4: Disjunct

(4) Disjunct

FIGURE

Two

motion

2.5: Disjunct

consecutive

forbidden. octave

motion

moves

Generally,

or greater

in the opposite

motion

followed

by disjunct

motion

in the opposite

direction

in the same direction.

motion

followed

by conjunct

motion

in the same direction

in the same direction.

motion

followed

in the same

by disjunct

direction

two or three consecutive

are rare. Melodies

range may occasionally special considerations.

(1) Augmented

direction.

motion

which

form

in the same direction

a compound

moves in the same direction

usually

have a maximum

range of an octave.

extend a step above or below. Some intervals They are as follows:

intervals

FIGURE

are forbidden.

2.6: Examples

of Augmented 4

interval

Intervals

are

which form an

in melodies

This

require

(2) Compound

intervals

are forbidden.

FIGURE

(3) Major sevenths

2.8: Examples

must be followed

FIGURE

(5) Diminished direction.

of Compound

Intervals

are forbidden.

FIGURE

(4) Minor sevenths

2.7: Examples

intervals

FIGURE

of Major Sevenths

by conjunct

motion

in the opposite

direction.

2.9: Use of Minor Seventh

should

be followed

by conjunct

2.10: Use of Diminished 5

Intervals

motion

in the opposite

Scale degree activity explanation

is discussed

of those concepts

in Basic Music (TC 12-41/NAVEDTRA

is necessary

for the proper construction

Any number of stable tones may follow one another,

10244). Further of melodies.

but their overuse will emphasize

the tonic triad.

FIGURE

No more than two tendency

FIGURE

2.11: Succession

of Stable Tones

tones may occur in succession.

2.12: Succession

When one active tone is followed

by another

of Tendency

Tones

which is more than a third away, the first

active tone is disregarded.

FIGURE

2.13: Two active tones separated

6

by more than a third

When two active tones surround

a stable tone:

that stable tone may then follow,

FIGURE

2.14.a: Two Active

Tones

Surrounding

a Stable Tone

OR the latter active tone may be considered

FIGURE

2.14.b: Two

Active

Tones

for movement,

Surrounding

a Stable Tone

Surrounding

a Stable Tone

OR another

active tone may follow.

FIGURE

When employing

2.14.c: Two

Active

broken chords,

FIGURE

Tones

scale degree activity

2.15: Broken 7

Chord

may not apply.

FORM A phrase Additionally,

in music is defined in Basic Music (TC 12-41/NAVEDTRA a phrase should convey a definite feeling of beginning and ending

10244). (repose).

Repose is accomplished by melodic and/or harmonic cessation (caesura), called a cadence. Two phrases form a period; the first called an antecedent phrase, the second called a consequent

phrase.

When there is similarity

FIGURE

When there is no similarity

between

FIGURE

between

2.16: Parallel

the two phrases,

Phrases

the two phrases,

2.17: Contrasting

they are parallel.

they are contrasting.

Phrases

RHYTHM Rhythms

employed

(1) Regular

in the study of Harmony

appear in the following

order of frequency:

rhythm.

(2) Irregular

rhythm.

(3) Uniform

rhythm.

(4) Syncopation

(used primarily

with special 8

melodic/harmonic

devices).

CHAPTER3

Vertical Structures POSITION Harmonic interval relationships between the four voices occur in specific arrangements. When the harmonic interval between the Soprano and Tenor voices is a simple interval, close position occurs.

FIGURE

When the harmonic interval, open position

3.1: Close Position

interval between the Soprano and Tenor voices is a compound occurs. The Bass voice is not considered in determining close or

open position.

FIGURE

3.2: Open Position

9

ADJACENT Harmonic

VOICE intervals

must be simple

SPACING which occur between

intervals.

Compound

the Soprano

intervals

and Alto or Alto and Tenor voices

may occur between

the Tenor

and Bass

voices.

FIGURE

LOW

INTERVAL

3.3: Adjacent

Voice Spacing

LIMITS

When simple harmonic

intervals

occur between

the Bass and Tenor voices,

limitations

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

is e.

There are no other restrictions form a perfect prime the voicing

for the Bass voice of any other intervals. is called unison.

10

When two voices

CHAPTER4

Voice

Motion

VOICING Voice motion

INDIRECT Indirect

is generally

Contrary directions:

in terms of simple intervals.

MOTION occurs when two parts move in di ssimilar

motion

Contrary

described

Motion motion

is indirect

motion

FIGURE

Oblique

occurs

4.1: Contrary

when

two

parts

move

in opposite

Motion

motion that occurs when one part moves and another sustains

FIGURE

Direct

that

Motion

Oblique motion is indirect or repeats.

DIRECT

directions.

4.2: Oblique

Motion

MOTION motion

occurs when two parts move in the same direction.

11

Similar Similar

Motion motion

producing

is direct motion

different

harmonic

that occurs

FIGURE Parallel

motion

is direct motion

the same harmonic

third is parallel

that

interval,

motion

is generally

OBJECTIONABLE Some

kinds

circumstances and parallel

Motion

occurs when two parts move in the same direction without regard for quality; a major third to a minor

motion.

FIGURE Indirect

4.3: Similar

Motion

Parallel producing

when two parts move in the same direction

intervals.

4.4: Parallel

preferred

Motion

to direct motion.

MOTION

of parallel

motion

must

not occur

except

because they destroy the four part texture: dissonant

intervals.

Parallel

perfect

fourths

under octaves,

4.5: Objectionable

12

Parallel

unisons,

are acceptable,

upper three voices.

FIGURE

appropriate

Motion

harmonic

perfect fifths, but only in the

When two parts move in similar movement fifths

is called

and perfect

voices at a change

Hidden

octaves

harmonic

by contrary interval

to a unison, Hidden

perfect fifth, or perfect octave,

unisons

may occur at any time except

of chord with the Soprano

FIGURE

Parallels

motion

or Covered.

moving

4.6: Objectionable

are forbidden. between

by disjunct

Hidden

Hidden

the Soprano

that

perfect

and Bass

motion.

Motion

motion

occur when two voices move by contrary motion from one to the same harmonic interval. Parallel perfect octaves and parallel

perfect fifths by contrary

motion must not occur. An octave to a unison has the same effect.

FIGURE

4.7: Parallels

by Contrary

Motion

Crossed voices occur between any two adjacent voices where the lower voice has a pitch higher than the upper voice. Crossed voices are not normally permitted.

FIGURE

4.8: Crossed

13

Voices

Overlapping voices occur in the movement of any two voices when: a lower voice moves to a pitch higher than the previous pitch in an upper voice, or an upper voice moves to a pitch lower than the previous

pitch in a lower voice. Overlapping

permitted.

FIGURE

4.9: Overlapping

14

Voices

voices

are not normally

CHAPTER5

Root Position CONNECTING Primary guidelines:

PRIMARY

Primary Triads

TRIADS

triads in root position

can be connected

with few errors using the following

Place roots of triads in the Bass voice. Keep the common tone in the same voice, then move the remaining nearest chord tones by step (conjunct motion).

two voices to the

When there is conjunct root position movement, there is no common tone. In that case, move all upper voices contrary to the Bass to the nearest chord tones.

FIGURE

5.1: Connecting

Primary

Triads

DOUBLING When writing triads in four parts, it is necessary to double one of the notes of the triad. Generally, double tonal notes. Modal notes may occasionally be doubled as a result of melodic fifth.

line. In some instances

FIGURE

it is necessary

5.2: Doubling

15

or desirable

in Primary

to triple the root and omit the

Triads

KEY ESTABLISHMENT The primary means of establishing a key is to move from the major dominant triad to the tonic triad. The dominant triad in natural minor is minor. Therefore, the major form of the triad is borrowed

from its parallel

create a leading scale.

tone and stronger

FIGURE

major

key by raising

resolution.

the third with an accidental

This process

5.3: Major Dominant

creates

Roman numerals correspond indicates

AND and

FIGURED

Arabic

numerals

are used for analysis

minor

subdominant

chord

Triad in Minor

Use of the ascending melodic minor scale results in a major quality that may create a change of modality to major.

ANALYSIS

BASS are used

to indicate

and to indicate

chord

chords roots.

and

doublings.

The Roman

A lower case

A plus sign (+) qualifies

Roman

numeral indicates

an upper case Roman

Roman

numeral

to the scale degree on which the triad is built. An upper case Roman a major triad (unless qualified).

triad (unless qualified).

to

the harmonic

numeral

will

numeral a minor

to indicate

an augmented triad. A circle (o) qualifies a lower case Roman numeral to indicate a diminished triad. All other alterations or additions are indicated with chromatic signs and Arabic

numerals.

FIGURE

5.4: Analysis 16

Arabic numerals are used for figured bass or figuring and indicate notes above the Bass voice, primarily as simple intervals. The complete figuring for a root position triad with the: root doubled

8 is 5.

This is often abbreviated

When no Arabic

3 root position

fifth doubled

triad is intended.

FIGURE

5.5: Doubled

FIGURE

5.6: Double

Root Figuring

5 5.

is

3

third

doubled

Fifth Figuring

is

FIGURE

5.7: Doubled 17

Third Figuring

numerals

appear, a

8 is 8

root tripled and fifth omitted

3

FIGURE

The Arabic diatonic

numerals

fifth regardless

5.8: Tripled

Root Figuring

of figured bass refer to diatonic of quality.

When accidentals

intervals

by name. A 5 indicates

a

are used, such as with the dominant

chord in minor, the same accidental must appear in the figured bass. This is done by writing the accidental to the left of the Arabic numeral. An accidental may be used without an Arabic numeral applies regardless

to indicate

an alteration

of the note a third above the Bass note. This

of chord position. A slash through a number indicates that the corresponding note is raised a half step. An accidental in the Bass voice is not normally indicated in figured bass.

FIGURES

5.9: Accidentals

and Figured

Bass

CADENCES Primary

triads in root position

may be used to form three types of harmonic

AUTHENTIC. PLAGAL. HALF.

18

cadences:

Authentic

Cadence

An authentic cadence point.

cadence occurs when the dominant chord progresses to the tonic chord at a In a Perfect Authentic cadence, both chords are in root position and the

tonic scale degree appears

in the Soprano

voice over the tonic chord. The Perfect Authentic

occurs most often as a final cadence.

FIGURE

In an Imperfect

Authentic

5.10: Perfect

cadence,

Occasionally,

Authentic

5.11: Imperfect

in a Perfect Authentic

Cadences

either chord is inverted,

Soprano on the tonic chord. The Imperfect points other than final.

FIGURE

Authentic

cadence,

cadence

Authentic

the leading

and/or

the root is not in the

occurs most often at cadence

Cadences

tone may DROP to the fifth of

the tonic chord when it is in the Alto or Tenor voices. This is usually a result of supersonic

19

to

tonic voice leading

in the Soprano

voice. It is written this way to allow all notes of the chord

to appear.

FIGURE

Plagal

5.12: Leading

Tone Dropping

in a Perfect Authentic

Cadence

Cadence

A Plagal cadence occurs when the subdominant chord progresses to the tonic chord at a cadence point. In a Perfect Plagal cadence, both chords are in root position and the tonic scale degree appears

in the Soprano

FIGURE

voice over both chords.

5.13: Perfect

Plagal

Cadence

In an Imperfect Plagal cadence, either chord is inverted, and/or the root is not in the Soprano on the tonic chord. Plagal cadences often follow final authentic cadences to emphasize

finality.

20

FIGURE

Half

5.14: Imperfect

Plagal

Cadences

Cadence

A Half

cadence

(Semi-cadence)

occurs

when

any

chord,

regardless

of inversion,

progresses to the dominant at a cadence point. Generally, the dominant chord will be in root position. A Plagal Half cadence occurs when any chord, regardless of inversion, progresses to the subdominant at a cadence point. Generally, the subdominant be in root position. Half cadences are not used as final cadences.

FIGURE

Picardy

Third

(Tierce

chord will

5.15: Half Cadences

de Picardie)

Occasionally, the tonic triad in minor will be borrowed from its parallel major at an authentic cadence. This is known as a Picardy Third (Tierce de Picardie) and occurs at final

21

cadences.

When figured

bass is used, it must reflect the alteration

FIGURE

CHORD Chordal

5.16: Picardy

that occurs.

Third

SUCCESSION movements

I may progress IV may progress V may progress

used with primary

triads in root position

are:

to IV or V to V or I to I

V may go to IV if IV immediately Any chord may follow itself. Chords

progresses generally

22

to V

progress

across

a bar line.

CHAPTER6

Inversions Triad inversion

is discussed

of Primary Triads

in Basic Music (TC 12-41/NAVEDTRA

are used to give the Bass voice smoothness described

for root position

primary

and variety.

triads;

however,

Voice leading objectionable

10244). Inversions may differ from that motion

must still be

avoided. FIRST

INVERSION primary

First inversion first inversion

root doubled

triads require no new doubling

rules. Figured

bass for triads in

with the:

is

This is often abbreviated

6

or more commonly

6.

3

FIGURE

6.1: Doubled

Root Figuring

for First Inversion

6.2: Doubled

Fifth Figuring

for First Inversion

6 fifth doubled

is

3. 3

FIGURE

23

8 third doubled

is

6. 3

FIGURE

6.3: Doubled

Third Figuring

for First Inversion

6 root tripled and fifth omitted

is

6

This voicing

is rarely used and should

be avoided

6

FIGURE

CHORD Chord position.

6.4 Tripled

for First Inversion

SUCCESSION succession Although

involving

first inversion

IV6 to V6 is now available

V6) as this results in an augmented A Phrygian Half cadence leading

Root Figuring

cadence created

in the Soprano.

tonic movement

is created

second

remains

The semitone

the same as that for root

in the Bass voice.

with the use of inversions

by the progression

and the Soprano

triads

in major key, it is not written in minor (iv6 to

in a minor key. It is a form of

iv6 to V# with subdominant

in the Bass voice resembles

resembles

the subtonic

mode. 24

to dominant

voice

the lowered supersonic

to tonic movement

of a Phrygian

to

FIGURE

SECOND

chords generally

a pattern in conjunction

8 bass of 6,

4 called Six-Four

are commonly

FIGURE

OF SECOND

do not take part in a progression

with other chords.

This results in a figured

TYPES

Cadence

INVERSION

Second inversion

chords

6.5: Phrygian

but rather appear in Double the fifth of all second inversion chords.

6 being the accepted 4

abbreviation.

Second

inversion

six-four,

a second

Normally,

the sixth

Chords.

6.6: Second

Inversion

Figuring

INVERSIONS

Cadential The

most

inversion and fourth cadential rhythmic

widely

used of all second

inversions

tonic chord which moves to the dominant above the Bass note resolve six-four and its resolution relationship. A weak-strong

meter it is often found on the second

is the Cadential chord at a cadence.

down by step to a fifth and third respectively.

A

to the dominant usually appear in a strong-weak relationship may occur at a Half cadence. In triple beat with the final tonic triad occurring 25

on the first

beat of the following

measure.

FIGURE

6.7: Cadential

Six-Four

Passing A passing

six-four

and first inversion and I. A I

occurs

when a second

of another

may appear

appear in a weak rhythmic

inversion

chord. Therefore,

between

chord appears

between

a V ~ may appear between a I and I6 or a I6

a IV and IV6 or a IV6 and IV. Passing

position.

FIGURE

6.8: Passing 26

root position

Six-Four

six-fours

must

Auxiliary An auxiliary

six-four

(also called a pedal six-four)

the same chord where the fifth of the auxiliary root position

chord. Expressed

six-fours

between

two root positions

of

is the same note as the root of the

in terms of voice motion,

an auxiliary six-four occurs when ascend by step and return.

the third and fifth of a root position Auxiliary

occurs

six-four

triad, with root doubled,

must occur in a weak rhythmic

FIGURE

position.

6.9: Auxiliary

Six-Four

Arpeggiated An arpeggiated six-four occurs when the second inversion of a chord is immediately preceded or followed by the same chord in root position and/or first inversion.

FIGURE

6.10: Arpeggiated

27

Six-Four

28

CHAPTER7

Dominant Basic Music (TC 12-41/NAVEDTRA relationships of a dominant seventh refers specifically

to the diatonic

minor the chord is borrowed TRITONE

Chord

01244) describes the construction and interval chord. In Harmony, the dominant seventh chord

chord

which

from its parallel

appears

on the dominant

scale degree.

major just as is the dominant

In

triad.

RESOLUTION

An interval subdominant

Seventh

of a tritone

appears

between

scale degrees) of the dominant

the third seventh

and seventh

chord. Dissonant

(leading harmonic

tone

and

intervals

such as the tritone of the dominant seventh chord require specific resolution. A regular resolution occurs when the third (leading tone) resolves up to the root of the tonic chord and the seventh (subdominant) resolves down to the third of the tonic chord. This is the most common resolution and satisfies the melody pull of the tendency tones.

FIGURE

7.1: Regular

Resolution

When the seventh of a dominant seventh chord appears in an upper voice and the chord progresses to a first inversion tonic chord, an Irregular Resolution must occur. The Bass voice has taken the note of resolution (third of the tonic chord) and the seventh in the upper voice will rise to the fifth of the tonic chord. This will often produce harmonic diminished

fifth followed

by a perfect fifth. This is called

Unequal

under such circumstances.

FIGURE

7.2: Irregular 29

Resolution

intervals

of a

Fifths and is acceptable

APPROACHING

THE SEVENTH

No new guidelines are required for approaching a dominant melodic approach to the seventh. The seventh of the dominant a dissonance carry-over dissonance

and should from

not be approached

16th century

be approached

contrapuntal

Figured

BASS

AND

technique,

motion

which

from above.

required

This is a

that no accented

in such a manner.

FIGURE

FIGURED

by disjunct

seventh chord except for the seventh chord is considered

7.3: Approaching

the Seventh

DOUBLING

bass for a dominant

seventh

chord is 5,5

, or 5 with the accepted

abbreviation

8 of 7 or 7. In root position, #

the root of the dominant 888

seventh

$

3

and the fifth 8

7

omitted with a figured bass of 7, 7, or 7 . The 5 voicing 3 #3

may be doubled

is called complete;

the 7 voicing

is

3

called incomplete. When a complete root position dominant seventh resolves to a root position tonic chord, the tonic chord will be incomplete (fifth omitted). When an incomplete root position dominant seventh resolves to a tonic chord in root position, the tonic chord will be complete.

30

FIGURE

7.4: Complete

When the dominant

seventh

chord appears

The figured bass for a first inversion root position

and Incomplete

Dominant

in inversion

dominant

seventh

Seventh

a complete

Resolution

spelling

is 5, abbreviated

6

. It resolves

5

tonic chord.

FIGURE

7.5: First Inversion

Dominant 31

Seventh

will be used.

and Resolution

to a

When the dominant and I6. This requires

seventh chord appears in second inversion, it must pass between I an irregular resolution. When it occurs between 16 and I, regular

resolution

Figured

is required.

6 or 4,

4

abbreviated

bass for a second

inversion

dominant

seventh

is 4 , 4

in major keys.

3

3

FIGURE

7.6: Second

Inversion

Dominant

Seventh

and Resolution

With the addition of a fourth note to a chord, a third inversion is possible. When the seventh of the dominant seventh is the lowest sounding note (Bass voice) the third

inversion

is created. 4 #4

abbreviated

22

,,or 2

a regular resolution tonic chord.

FIGURE

Figured K

bass for a third inversion

(sometimes

because

2). This inversion

the seventh

7.7: Third Inversion

dominant

will always

seventh

is 4 ,#4, or

resolve to a I6 but is still

in the Bass voice does resolve to the third of the

Dominant 32

Seventh

and Resolution

CHORD

SUCCESSION

As indicated, Occasionally, subdominant

the dominant the

dominant

to dominant

seventh

chord

seventh

chord

seventh

scale degree must be maintained resolution

of the first seventh.

FIGURE

7.8: Dominant

may

chord succession. as a common

The seventh

Seventh

primarily

33

to the tonic

in a dominant

When this occurs,

chord.

seventh

resolves

to Dominant

to the mediant

Seventh

to

the subdominant

tone from chord to chord. This delays

ultimately

to Subdominant

progresses

occur

the

scale degree.

Chord Succession

34

CHAPTER8

Non-Harmonic Non-Harmonic FIGURED

tones (non-chord

Tones

tones) occur with chords

but are not chord members.

BASS

Non-Harmonic

tones are figured

like chord tones. Non-Harmonic

tones occurring

after

the initial attack of the chord are indicated with a change of numeral. When the Bass voice in any upper voice, no additional figured bass is necessary. moves without movement When one or more voices remain stable, a dash(-) is used to indicate the continuation of the same pitch. In root position triads with doubled root, only the voice that moves is figured. Figuring

will be arranged

from highest

FIGURE

Figuring

for non-harmonic

to lowest numeral.

8.1: Figuring

tones occurring

Non-Harmonic

Tones

at the initial attack of a chord (suspensions,

appoggiaturas, and accented passing tones), results in figured bass which does not represent the true position of the chord. Usually, achord's position is represented with the resolution of the non-harmonic tone.

FIGURE

8.2: Figuring

Non-Harmonic 35

Tones

at Initial Attack

DIATONIC A diatonic

PASSING passing

TONE

tone fills the interval

occurs in a weak rhythmic

PASSING

Occasionally

the interval

strong rhythmic

position.

A chromatic

8.3: Diatonic

Passing

and

Tone

tone which occurs in a

of a third is filled with a non-harmonic This is called an accented

PASSING passing

tones a third apart

TONE

FIGURE

CHROMATIC

two chord

position.

FIGURE

ACCENTED

between

8.4: Accented

Passing

tone.

Tone

TONE

tone fills the interval

and occurs in a weak rhythmic

passing

between

position.

36

two chord

tones a major second apart

FIGURE Cross

8.5: Chromatic

Passing

Tone

Relation

Cross Relation occurs when a chromatically altered note in one voice is next to the same diatonic scale degree in a different voice. It should be avoided except when using the upper tetrachord

of the melodic

minor scale.

FIGURE

DOUBLE Double

PASSING passing

TONE

8.6: Cross Relation

(melodic)

tones fill the interval

of a perfect

occur in a weak rhythmic position. In a minor double passing tones over the tonic chord.

FIGURE

fourth

key, the melodic

8.7: Double Passing 37

between

Tone

two chord tones and

minor

scale is used for

CHROMATICALLY A chromatically and

uses

an

ALTERED altered passing

accidental.

Chromatically the dominant

FIGURE

UPPER

in either

of a third between two chord tones

a weak

or strong

tones occur most often in the ascending

8.8: Chromatically

In major keys, the subtonic submediant scale degree.

TONE

tone fills the interval

It appears

altered passing chord.

FIGURE

PASSING

Altered

Passing

scale degree, borrowed

8.9: Subtonic

as Chromatically

rhythmic melodic

Tone Over the Dominant

from the parallel

Altered

Passing

position. minor over

Chord

minor, passes to the

Tone

AUXILIARY

An upper auxiliary is a non-harmonic tone a step above two chord tones of the same pitch and appears in a weak rhythmic position. 38

FIGURE

LOWER

8.10: Upper Auxiliary

AUXILIARY

A lower auxiliary

is a non-harmonic

tone a step below two chord tones of the same pitch

and appears in a weak rhythmic position. Lower auxiliaries to create a semitone when one does not appear diatonically.

FIGURE

CHANGING

altered

8.11: Lower Auxiliaries

TONES

Changing tones are two non-harmonic tones approaching one below. The first must occur in a weak rhythmic position. or strong

may be chromatically

rhythmic

a chord tone, one above and The second may be in a weak

position.

FIGURE

8.12: Rhythmic

Position

39

of Changing

Tones

Changing

tones may be preceded

FIGURE

8.13: Changing Tones Preceded by the Same Note as the Note of Resolution

or by a chord tone a third removed called Nota Cambiata. the changing tones.

by the same pitch as the note of resolution,

Similar

from the following

melodic

FIGURE

The changing semitone

direction

chord tone. The latter is frequently

is used from the first chord tone through

8.14: Nota Cambiata

tone below the next chord

tone may be chromatically

altered

movement.

FIGURE

8.15: Changing

Tones with Chromatic 40

Alteration

to create

CAMBIATA

resolved position.

by di sjunct motion in one direction and tone approached It occurs in a weak rhythmic opposite direction. by conjunct motion in the altered to create When a cambiata resolves upward, it may be chromatically

semitone

movement.

A cambiata

is a non-harmonic

FIGURE

8.16: Cambiata

hIAPP~E An ~chapp6e (escape tone) is non-harmonic by disjunct motion in the opposite direction.

FIGURE

tone approached by conjunct It occurs in a weak rhythmic

motion and left position.

8.17: fichapp~e

SUSPENSION A suspension progression

is a non-harmonic

is delayed.

the first chord sustained

This requires

tone

occurring

two different

when

chords.

a note’s

A suspension

or repeated in the same voice as a non-harmonic

natural

melodic

is a chord tone in tone of the second

chord. There are three parts of a suspension: preparation (P), suspension (S), and resolution (R). The preparation is a chord tone of the first chord. The suspension is non-harmonic and is the same pitch as the preparation continued to the second chord. 41

The resolution occurs when the suspension resolves by conjunct motion to a chord tone of the second chord. An upward resolution of a suspension is called a retardation. The note of resolution may be present if it is a compound interval below the suspension. Suspensions may be tied suspensions. relationship. of suspensions

or dotted note values; The suspension and The preparation

however, resolution

when repeated, they are called struck must be in a strong-weak rhythmic

must be as long or longer

may be decorated

than the suspension.

with other non-harmonic

tones. Common

Resolutions

suspensions

are

9-8, 7-6, 6-5, and 4-3.

FIGURE

8.18: Suspension

APPOGGIATURA An appoggiatura is a non-harmonic tone a step above or below a chord tone of a single chord. It resolves to the chord tone. An appoggiatura functions as a suspension without a preparation. direction

Normally,

appoggiaturas

of the resolution,

appoggiatura

is approached

also called an accented

are approached

or by conjunct by conjunct

passing

motion

by disjunct from

motion in the same direction

tone.

FIGURE

either

8.19: Appoggiatura 42

motion in the opposite direction.

When

as its resolution,

an it is

ANTICIPATION An anticipation

is a non-harmonic

tone which

becomes

a chord

tone in the following

chord. Anticipations occur in a weak rhythmic position, frequently at the subdivided level. Generally, anticipations occur in the Soprano voice at cadence points.

FIGURE

beat

8.20: Anticipation

PEDAL tone of long duration normally A pedal is a non-harmonic chords. A pedal begins and ends as a chord tone of a harmony in at least one chord between the first and last chords. Pedals voice with the Tenor voice used for analysis is called an inverted

occurring

in three or more

and must be non-harmonic occur primarily

in the Bass

and figured bass. A pedal in the Soprano

pedal. A pedal in the Tenor or Alto voices is called an internal

voice pedal.

Pedals occurring in two voices are called double pedals. The lowest moving voice is used for analysis and figured bass. The tonic and dominant scale degrees are the commonly used pedal notes.

FIGURE

8.21: Pedal

43

SIMULTANEOUS More

than

NON-HARMONIC

one

non-harmonic

non-harmonic

tones normally

octave

when

through

occurs

tone

TONES may

form harmonic

two passing

occur

at

intervals

a given of thirds,

tones move in contrary

motion.

point. sixths,

Simultaneous or octaves.

The

This is called passing

the octave.

FIGURE

Simultaneous

non-harmonic

8.22: Passing

Through

tones may be figured two ways. Vertical

figured with the numerals arranged from highest which the non-harmonic tones occur.

FIGURE

8.23: Vertical

the Octave

Figuring

to lowest,

for Simultaneous

44

combinations

regardless

Non-Harmonic

of the voices

Tones

are in

Linear movement

of individual

voices is figured starting

from the figuring

of the chord’s

position.

FIGURE

Non-harmonic

8.24: Linear Figuring

tones or auxiliaries.

analysis

may occur (auxiliary

FIGURE

six-four.

Non-Harmonic

tones of the same kind can occur simultaneously.

passing

Another

for Simultaneous

Some have become

The most common

used that a change

are

of chord

6. ). +

8.25: Passing

kind of simultaneous

so widely

Tones

Tones and Auxiliaries

use is the appoggiatura

It uses the 6 to 5 and 4 to 3 voice leading

45

used Simultaneously

six-four.

and appears

It is similar to a cadential in a strong-weak

rhythmic

relationship, or IV

but not at a cadence.

The two uses of the appoggiatura

six-four are the I . to V

to I.

FIGURE

Non-harmonic an example auxiliary.

tones of different

of the use of passing

FIGURE 8.27: Comparison Non-Harmonic Tones

CHORDAL

8.26: Appoggiatura

Six-Four

kinds also occur simultaneously.

tones, passing

of Passing

through

Six-Four

and

A passing

the octave, combined

Simultaneous

Use

six-four

is

with a lower

of Different

SEVENTHS

Chapter 15, Basic Music (TC 12-41/NAVEDTRA 10244) defines chordal sevenths. Care should be taken when using a non-harmonic tone which would be a chordal seventh. Under most circumstances, the treatment of the seventh of the Dominant Seventh chord discussed in Chapter VII is an excellent guide.

46

FIGURE

8.28: Chordal

Sevenths

VOICING Non-harmonic tones may occur in any voice. They occur less frequently in the Bass voice and are generally limited to unaccented passing tones, auxiliaries, and pedals.

FIGURE

8.29: Voicing

Non-Harmonic

47

Tones

...

CHAPTER9

Secondary Secondary which

triads reinforce

reinforce

tonality.

modality.

Secondary

Triads

They do not occur as frequently triads

are used in harmonic

as primary

progressions

triads,

to create

variety. CHORD

PROGRESSION

Principles of chord progression may be discussed primary triads. The tonic chord is considered progression

because

are assigned chords. GROUP

all chord progressions

to Groups

(Classifications)

with the addition of secondary triads to separately when describing chord

move toward which

relate

the tonic. The remaining generally

to the function

chords of the

1

Group 1 (First Classification) chords are the major dominant and diminished leading tone chords and have a dominant function. The first inversion augmented mediant triad found in harmonic and ascending melodic minor is in this group because of its similarity to the dominant GROUP

chord.

2

Group 2 (second

Classification)

have a subdominant

function.

GROUP

chords

are the subdominant

and supersonic

chords

and

3

The Group

3 (Third

Classification)

chord

is the submediant

and may have a tonic

function. GROUP

4

The Group dominant

4 (Fourth

Classification)

chord

FIGURE

9.1: Chord Chart 49

——.

is the mediant

function.

and may have

a tonic

or

Dominant

relationship

apart. Dominant through

Group

is the association

relationship

prevails

whose

roots area

when the chord Groups are assembled

perfect

fifth

from Group 4

1 and then the tonic.

FIGURE

An established

of two chords

9.2: Dominant

tonic chord occurs whenever

Relationship

a dominant

function

chord progresses

to the

tonic chord. Any chord may follow an established tonic chord. Any chord may follow itself. Chords generally change from weak to strong rhythmic position unless they are of long duration.

FIGURE

Normal

chord progression

from left to right through

9.3: Chord

Progression

occurs after an established

each successive

group.

50

tonic chord, when chords progress

.Z .—.—---—.—.

FIGURE

Elision

in a chord

progression

9.4: Normal

occurs

Chord

when one chord

movement. Elision must be followed by normal vi(VI) to V(V#) are common examples of elision.

FIGURE

A neutral

tonic chord occurs

FIGURE

Retrogression Retrogression

occurs is usually

when

move

by normal

appears

Tonic

iii(III)

to IV(iv)

and

between

any two chords

in a

from

Chord

right

movement.

9.7: Retrogression 51

__

progression.

in left to right

9.5: Elision

9.6: Neutral

chords

followed

group is skipped

of the same chord. Neutral tonic chords usually occur

FIGURE

_ _

chord

when a tonic chord

progression or between two positions with normal progression.

Progression

to left

on the

chord

chart.

+6 The III chord $ dominant chord. non-harmonic

in minor The chord

often

has a dominant

may be described

chord

it is similar

to the

with an unresolved

9.8: III

in Minor

BASS

The principles

LEADING

as a dominant

because

tone.

FIGURE

FIGURED

function

of figured

TONE

bass remain

the same with the addition

of secondary

triads.

TRIAD

Basic Music (TC 12-41/NAVEDTRA 10244) describes leading tone triad. This chord is often called a dominant

the spelling and quality of the seventh with root omitted. The

third is normally doubled to avoid doubling a note of the tritone. The root and fifth of the chord ascend to the root and fifth of the tonic chord often producing unequal fifths. It is used exclusively

in first inversion.

FIGURE

9.9: Leading 52

Tone Triad

The fifth of the chord is doubled

FIGURE

when it appears

9.10: Doubled

Fifth on Leading

An Intermediate may appear

Cadence occurs with a vii 06 at any cadence but final.

FIGURE

COMMON The vii”tj followed

FUNCTION chord

in the Soprano

voice.

Tone Triad

to I(i) progression

9.11: Intermediate

at a cadence

point. It

Cadence

SUCCESSION

may follow

only by the dominant

a dominant seventh

triad within

(V7).

53

a progression.

A vii06

can be

SUPERTONIC Basic

Music

supersonic

TRIAD (TC 12-41/NAVEI)TRA

triad. It occurs primarily

chord may appear in root position note).

with doubled

FIGURE

In major

keys, the supersonic

10244) descr ibes the spelling and quality of the with doubled third (tonal note). The

in first inversion

chord

root (modal

note) or doubled

9.12: Supertonic Triad

may be used in second

inversion

six-four.

FIGURE

third (tonal

9.13: Second

Inversion

54

Supersonic

Triad

as a passing

The

supersonic

ascending

melodic

chord

may

may also be a non-harmonic

FIGURE

SUBMEDIANT

be used

minor. The leading

to harmonize

the raised

tone may be harmonized

sixth

scale

degree

with the V# or

in it

tone.

9.14: Harmonizing

the Raised

Sixth in Minor with Supersonic

Chord

TRIAD

Basic Music (TC 12-41/NAVEDTRA 10244) describes the spelling and quality of the submediant triad. It appears primarily in root position. In major keys the root (modal note) or third (tonal note) may be doubled. In minor keys the root is usually doubled because of the major quality

of the triad.

FIGURE

9.15: Submediant

55

Triad

In minor, the third must be doubled when there is elision (VI to V#) or retrogression VI). Augmented doubled.

melodic

FIGURE

intervals,

parallels,

9.16: Submediant

or large

leaps

with Doubled

occur

(V# to

if any other note is

Third in Minor

The Deceptive Cadence is a V to vi or V# to VI progression at a cadence point. It may occur at any cadence but final. The submediant triad replaces the tonic. The third of the submediant (tonic scale degree) is doubled. normally follow the submediant,

FIGURE

This cadence

9.17: Deceptive

56

is followed

Cadence

by a chord that would

First inversion unresolved

of the submediant

triad occurs primarily

as a tonic chord with resolved

or

appoggiatura.

I

FIGURE

9.18: First Inversion

The chord may progress create stepwise first inversion.

Submediant

as Appoggiatura

to a Group 2 chord from first inversion.

motion in the Bass Voice to a Group 1 chord (elision).

FIGURE

9.19: First Inversion

57

Submediant

It may also be used to The third is doubled in

MEDIANT Basic

TRIAD

Music

(TC 12-41/NAVEDTRA

10244) describes

the spelling

and quality

of the

mediant triad. In major keys, it may appear in root position with doubled root (modal note) or occasional doubled third (tonal note). In first inversion the third is normally doubled.

FIGURE

In minor inversion

keys, the major

with doubled

the submediant

quality

9.20: Mediant

mediant

Triad

triad may appear

root. The fifth of the chord (subtonic

scale degree.

FIGURE

9.21: Mediant

58

in root position

or first

scale degree) must descend

Chord in Minor

to

The Augmented quality mediant triad may appear in root position in first inversion with doubled third.

FIGURE

SUBTONIC Basic subtonic

Music

9.22: Augmented

Mediant

with doubled

root, or

Triad

TRIAD (TC 12-41/NAVEDTRA

10244) describes

triad. This chord is not considered

in the chord

the spelling chart because

and quality

of the

it only occurs

in

minor and has an unusual character. It occurs in root position or first inversion with doubled root progressing to the major quality mediant chord. The subtonic chord maybe preceded

by either i or iv.

FIGURE

9.23: Subtonic

59

Triad

SUBTONIC

SCALE

DEGREE

The subtonic scale degree may be harmonized with the subtonic or the minor quality dominant chords. The following chord will be the subdominant or submediant. The effect of such movement

is that of passing

FIGURE

chords

without

9.24: Subtonic

60

progression.

Scale Degree

CHAPTER 1O

Diatonic

Sevenths

Diatonic sevenths are created by adding a seventh above the root of each diatonic triad. The approach to the seventh and its resolution is the same as that for the dominant seventh chord (Chapter

7). Acceptable

chord progression

must be maintained.

The chord following

the diatonic seventh chord normally contains the note of resolution. A delayed resolution of the seventh occurs when the seventh is sustained or repeated in the following chord. Ultimately dominant

it must resolve.

TONE

The leading

tone seventh

is a min7

resolving

either to a root position

result in parallel

fifths.

n major keys and a dim7 in minor keys. It may to a root position tonic chord; in first inversion it may

or first nversion

tonic chord.

fifths,

vii

.6

minor.

10.1. Leading

When chord roots are chromatically (Roman

numeral)

FIGURE

t)h

Tone Seventh

In major, should

the vii

to I will

be borrowed

from the

Chords

altered and the chord appears

in root position, the

must reflect the alteration.

10.2. Analysis

of Chromatically 61

-.

is the same as that for the

(bh)

To avoid the parallel

FIGURE

analysis

sevenths

SEVENTH

occur in root position

parallel

bass for diatonic

seventh.

LEADING

resolve

Figured

Altered

Roots

SUPERTONIC The supertonic appears

SEVENTH seventh

in root position

third inversions.

is a min 7 in major keys and a min 7in and all inversions;

First inversion

minor keys. In major it

in minor it appears

is used most frequently

in root position,

to approach

first, and

a cadence.

Figure 10.3. Supertonic Seventh Chords

Chords the leading resolution

following

the supersonic

tone triad or leading

seventh

are the dominant

tone seventh,

or the

triad or dominant

seventh,

The I ~ (i ~) delays

of the seventh.

FIGURE 10.4. Supertonic to Seventh Chord

62

the

SUBDOMINANT

SEVENTH

The subdominant seventh is a Maj7 in major keys and a min7 in minor keys. Major sevenths are dissonant and occur infrequently. Inversions produce minor seconds or minor ninths; therefore, the IV7 in major occurs primarily in root position and occasionally in first inversion. In minor, the iv7 occurs only in root position. The IV7 (iv7) progresses either to a dominant to the subtonic

triad (seventh)

or leading

tone triad (seventh).

In minor it may also progress

chord.

FIGURE

10.5. Subdominant

Sevenths

The IV7 (iv7) frequently occurs before the supersonic seventh chord. Resolution of the seventh occurs while the remaining voices sustain. It can be figured as a supersonic seventh with appoggiatura.

FIGURE

10.6. Progression

of the Subdominant 63

Seventh

to Supersonic

Seventh

SUBMEDIANT

SEVENTH

The submediant

seventh

occurs in root position, or first inversion.

It is used primarily

of the submediant the supersonic

is a min7 in major keys and a Maj7 in minor keys. In major it

first inversion,

seventh

In minor it occurs in root position

to Group 2 chords. Regular

chord occurs when the subdominant

resolution

scale degree is doubled

on

chord.

FIGURE

MEDIANT

or third inversion. as an approach

10.7. The Submediant

Seventh

SEVENTH

The mediant

seventh

is a min7 in major

keys and a Maj7 in minor keys. In major,

it

occurs in root position or first or third inversions. In minor, it occurs in root position or first inversion. It progresses to the submediant or subdominant chord. Descending root movement

should

be avoided.

The III+7 in minor rarely occurs.

64

FIGURE

10.8. The Mediant

Seventh

Occasionally the mediant seventh in minor will have a lowered normally followed by iv. It may also be followed by VI.

FIGURE

10.9. The Mediant

Seventh

65

with Lowered

seventh.

Seventh

This III

is

TONIC

SEVENTH

The tonic (leading

seventh

is a Maj7

in major

keys and a min7 in minor

tone) in minor is never used. The tonic seventh

rarely follows

keys. A min\Maj7 a dominant

function

chord. It usually follows an established tonic triad or occurs as a neutral I (i). In major, it occurs in root position or first inversion. In minor, it occurs in all positions. When required, an irregular

resolution

will be used. This will cause the subtonic

FIGURE SUBTONIC The subtonic must progress

10.10. The Tonic

in minor to ascend.

Seventh

SEVENTH seventh is a dom7 chord. It occurs in root position, to the III chord.

FIGURE

10.11. The Subtonic 66

Seventh

first or third inversion.

It

DIATONIC

SEVENTH

When the seventh the chord sustaining,

SEQUENCE

of a diatonic

seventh

a new diatonic

FIGURE

chord resolves

seventh

regularly

chord is created,

10.12. The Diatonic

67

Seventh

with the remainder

forming

Sequence

a SEQUENCE.

of

68

CHAPTER

Extensions Extended chords

Chords

contain

are discussed

11

on Diatonic in Basic

five or more pitches,

which

Music

Chords

(TC 12-41\NAVEDTRA

requires

a selection

10244). These

of notes for four parts.

Chords with extensions appear primarily in root position. An extension may be analyzed as an essential harmonic tone or as an unessential non-harmonic tone (appoggiatura or accented MAJOR

passing

tone). Extensions

appear

primarily

seventh

or supersonic

seventh

chord.

the fifth of the chord is omitted.

The major ninth on a dominant seventh

voice.

NINTH

Major ninths appear in major keys on the dominant Normally,

in the soprano

(appoggiatura)

seventh

resolves down by step to the root of the dominant

or to the fifth of the tonic at the change

of chord. The third of the

dominant seventh is occasionally omitted and the ninth functions as an upward resolving appoggiatura to the third. Figuring for chords in root position with a ninth is the single numeral 9.

FIGURE

The dominant ninth 7 6 for first inversion. El

11.1. The Major Ninth in Root Position

may appear

FIGURE

in inversion.

11.2. First Inversion 69

Figuring

for inversion

of the Major Ninth

is:

6 5 for second inversion.

The second inversion

of the dominant

ninth chord is better analyzed

(4 omitted) 0(.j as vii s.

FIGURE 11.3. Second

Inversion

of the Major Ninth

for third inversion.

FIGURE 11.4. Third Inversion

70

of the Major Ninth

for fourth inversion

(rare) resolving

FIGURE

The major supersonic

ninth

6 to a I d .

11.5. Fourth Inversion

on a supersonic

chord (appoggiatura),

seventh

of the Major Ninth

resolves

down

to the fifth of the dominant

by step:

to the root of the

chord (supersonic),

third of the leading

or to the

tone chord (supersonic). An interval of a major seventh exists between the third and ninth of this chord. The third and ninth should not be voiced in adjacent appear in voices when they form a minor second. The supersonic ninth may occasionally the first inversion

FIGURE

11.6. The Major Ninth on the Supersonic

71

Seventh

MINOR

NINTH

The minor ninth appears in minor keys on the dominant must resolve Inversions

down by step. The minor ninth should

are rare. The fourth inversion

FIGURE

seventh chord. The minor ninth

never be reduced

to a minor second.

is forbidden.

11.7. The Minor Ninth and Inversions

ELEVENTH Major

chords

with

an eleventh

are referred

to as sus4

chords

in Basic

Music

(TC 12-41/NAVEDTRA 10244). The eleventh appears primarily over the dominant seventh chord. The seventh and ninth usually appear with an eleventh, omitting the third and fifth. Chords with elevenths are used exclusively eleventh chord may resolve in three ways: (1) Directly

to the tonic chord with the eleventh

tonic, the ninth and seventh

resolving

(2) The eleventh ninth.

resolves

down

(3) The eleventh

and ninth resolve

in root position.

repeating

to become

the root of the

tone, forming

a dominant

normally.

by step to the leading

simultaneously,

72

The dominant

forming

a dominant

seventh.

FIGURE

11.8. The Dominant

Eleventh

THIRTEENTH The thirteenth root position

appears

on the dominant

seventh

with the fifth, ninth, and eleventh

chord

omitted.

only. It appears

The thirteenth

exclusively

in

may resolve down

by step to the fifth of the dominant seventh (appoggiatura) or by leap to the root of the tonic chord. When the latter occurs, the Bass voice must ascend to avoid an objectionable hidden octave.

FIGURE

11.9. The Dominant

73

Thirteenth

74

CHAPTER

Simple

12

Modulation

Modulation is the process of moving from one tonality to another. Simple modulation is movement to a closely related key. Closely related keys are those adjacent to a key on the circle of fifths and their relative keys. Therefore, any one key has five closely related keys.

FIGURE

12.1. Closely

Related

Keys

KEYS Terms applied to keys in modulation are original key, old key, and new key. The original key is the beginning key. Usually, music begins and ends in the original key. In a modulation, the music moves from the old key to the new key retaining the key signature of the original key, sufficient

key. When a series of modulations phrases

must remain

FIGURE

has taken the music far from the original

to work back to the original

12.2. Modulation

key.

Series in a Composition

75

PIVOT

CHORD

A pivot

chord

is used to effect

a modulation.

In simple

modulation

a common

chord

(diatonic in the old and new keys) is used as a pivot chord. For example, the tonic chord in C major could be used as the pivot chord to modulate to G major as the subdominant chord. Pivot chords are analyzed in both the old and new keys. The pivot chord should not be the dominant chord of the new key.

FIGURE

Accidentals accompanied

12.3. Pivot Chord Modulation

used to create notes in a new key need not be indicated

in figured bass when

with analysis.

FIGURE

12.4. Figuring

of Accidentals

76

in a Modulation

ESTABLISHING

KEYS

Chords on each side of a pivot chord must establish the tonality and modality of each key. The new key must be established by the end of the phrase in which the pivot chord appears.

FIGURE

12.5. Establishment

of Old and New Key in a Modulation

77

78

CHAPTER

Secondary

13

Chords

Secondary chords relate to the key of the chord which follows (key of the moment) but do not effect a modulation. For example, the secondary chords to the supersonic chord in C major come from the key of d minor. A secondary chord contains at least one chromatically altered note; the chromatically altered note is never doubled. Secondary chords usually have dominant function, Chords must be major or minor in quality to be preceded by secondary

chords.

ANALYSIS Two Roman numerals separated by a slash are used to analyze secondary chords. The first numeral shows the function and quality of the secondary chord in relation to the following chord; the second numeral shows the following chord.

FIGURE

SECONDARY Secondary extensions seventh

of Secondary

Chords

DOMINANTS dominants

(elevenths

may be triads, are rare).

chord, the momentary

to become

13.1. Analysis

When

leading

dominant a secondary

sevenths, dominant

or dominant progresses

tone (third of the chord) may descend

the seventh.

79

sevenths

with

to a diatonic by a half step

The V/V or

occurs in major or minor as a chromatically

It is used in any position inversion.

FIGURE

Because chromatic dominant dominants

the

In minor

13.2. Secondary

is the tonic

alteration seventh

in major.

in the tonic

chord, chord.

may be used because

Dominants

In minor,

be used in major the secondary

both are altered

80

except

chord. second

of the Dominant

the must

may be used in all positions.

altered supersonic

it is used in any position

tonic chords.

dominant

to have triad

These secondary

a or

FIGURE

Dominants

of the Subdominant

The or V occurs in major as a chromatically in all positions except second inversion.

altered submediant

FIGURE

13.3. Secondary

13.4. Secondary

Dominants 81

of the Supersonic

chord. It is used

occurs in major as a chromatically altered mediant chord. It is used The or in all positions except second inversion. In minor, the secondary dominant seventh must be used so that a chromatic alteration occurs on the mediant chord usable in all positions; second inversion occurs only in a descending involves

the subtonic

13.5. Secondary

Dominants

The V / iii occurs in major as a chromatically

of the Submediant

altered leading

positions except second inversion. In a minor key the triad and subtonic seventh chord. Although no alteration as secondary

is it

scale degree.

FIGURE

analyzed

line because

dominants.

82

tone chord and is used in all

and occurs,

are the these chords could be

FIGURE

is used in all positions

13.6. Secondary

Dominants

of the Mediant

occurs in minor as a chromatically except second inversion.

FIGURE

13.7. Secondary

Dominants

83

altered subdominant

of the Subtonic

chord. It

SECONDARY Secondary

LEADING Leading

TONE CHORDS

Tone chords

FIGURE

constructed

13.8. Secondary

84

using the key of the moment.

Leading

Tone Chords

CHAPTER

Borrowed BORROWED

14

Chords

CHORDS

Chords in a major key may be borrowed from the parallel key may be borrowed from the parallel major. Continuous effect a modulation BORROWED When writing

to the parallel

FROM

minor and chords in a minor use of borrowed chords may

key.

MINOR

in a major key, the following

chords

may be borrowed

minor:

FIGURE

14.1. The Borrowed

Supersonic

FIGURE

14.2. The Borrowed

Leading

85

from Minor

Tone Seventh

from the parallel

Subdominant (min) in aPlagal cadence

FIGURE

Extensions

14.3. The Borrowed

on the dominant

FIGURE

Submediant

Subdominant

in a Plagal

chord

14.4. Borrowed

Extensions

on the Dominant

(Maj)

FIGURE

Cadence

14.5. The Borrowed 86

Submediant

Non-harmonic

tones occurring

with borrowed

chords must be borrowed

from the parallel

minor.

FIGURE

14.6. Non-harmonic

Overuse of borrowed modulation may occur.

BORROWED

FROM

When writing

chords

Tones

Used with Borrowed

and accompanying

non-harmonics

Chords

should

be avoided

as

MAJOR

in a minor key, the following

chords

may be borrowed from the parallel

major: Dominant

(maj.) and Dominant

Seventh

Leading

tone triad (dim.)

Picardy

third on tonic chord (maj.)

Supersonic ascending Non-harmonic

chord

(min.)

when

harmonizing

form of melodic

minor scale.

tones occurring

with borrowed

major.

87

the

raised

sixth scale degree in

chords must be borrowed

from the parallel

88

CHAPTER

Chromatic Chords

may be chromatically

chord tone. Chromatically RAISED

15

Alterations

altered. The fifth of a chord is the most frequently

altered

altered notes are never doubled.

FIFTH

The raised fifth may appear on dominant, tonic, and subdominant chord in major keys. The raised fifth (raised supersonic scale degree) of the dominant chord must ascend to the third of the tonic chord. This will result in an acceptable doubled third of the tonic chord in first inversion. The augmented dominant chord may be used in root position or first inversion.

FIGURE

The raised fifth submediant scale acceptable doubled chord may be used

15.1. The Augmented

Chord

(raised dominant scale degree) of the tonic chord must ascend to the degree (subdominant or submediant chord). This will result in an third of the subdominant chord in first inversion. The augmented tonic in root position or first inversion when approaching the subdominant

chord. It is used only in root position

FIGURE

when approaching

15.2. The Augmented 89

I

Dominant

the submediant

Tonic

Chord

chord.

A raised fifth (raised tonic scale degree) of the subdominant chord must ascend to the supersonic scale degree (supersonic or dominant chord). The augmented subdominant chord may be used in root position or first inversion when approaching the dominant chord. It is used only in root position when approaching the supersonic chord.

FIGURE

LOWERED

15.3. The Augmented

Subdominant

Chord

FIFTH

The lowered fifth may appear on the dominant chord; it must descend to the tonic scale degree. The dominant chord with lowered fifth may be used in root position or first inversion.

90

FIGURE

RAISED Chords dominant

15.4. The Dominant

with Lowered

Fifth

ROOT constructed

on the raised

scale degrees were previously

tonic,

supersonic

identified

91

(in major),

as secondary

subdominant,

leading

tone chords.

and

92

CHAPTER Augmented

16

Sixth

Chords

The augmented sixth chords are named Italian, French, and German. Augmented sixth chords are often identified using an abbreviation of their respective names. Augmented sixth chords progress to a dominant chord or to a tonic six-four followed by the dominant chord. The dissonant the dominant Commonly

augmented octave.

sixth interval

Tendencies

used approach

normally

occurs in outer voices and resolves

of the chromatically

chords

are supersonic,

altered

subdominant,

notes

to

must be followed.

or submediant

chords.

ITALIAN The Italian first inversion

sixth is constructed with doubled

on the raised subdominant

fifth. It is analyzed

FIGURE

16.1. The Italian

and figured

Augmented

scale degree

and is used in

as

Sixth

FRENCH The French inversion.

sixth

is constructed

It is analyzed

on the supersonic

and figured

6 as II4. 3

93

scale degree

and is used in second

FIGURE

16.2. The French

Augmented

Sixth

GERMAN There are two forms of the German sixth. The first is constructed on the raised subdominant scale degree and is used in first inversion. It will progress to the dominant chord in major or minor. It may also progress to the tonic six-four followed by the dominant chord

in minor.

resolving

It is analyzed

$ as IVb5. The parallel fifths that occur in 3 are acceptable, but they should not appear in the outer

and figured

this chord to the dominant

voices.

FIGURE

16.3 The German

Augmented

94

Sixth on the Raised

Subdominant

he

second form of the German

and is used in second dominant

inversion.

chord in major.

FIGURE

Occasionally,

sixth is constructed It will progress

It is analyzed

16.4. The German

other forms

on the raised supersonic to the tonic

and figured

Augmented

of augmented

sixth

six-four

scale degree

followed

by the

6 as II ~. 3

Sixth on the Raised

are used in different

Supersonic

inversions

or are

constructed on other scale degrees leading to other than dominant chords. The interval relationships must remain intact and chromatic tendencies must be followed.

95

96

CHAPTER

Neapolitan A Neapolitan

sixth

chord

is a major

degree and is used in first inversion. a subdominant

function.

The N6 chord progresses

Sixth

It is analyzed

on the lowered

supersonic

and figured as The

scale

chord has

doubled.

17.1. The Neapolitan

to dominant

Chord

triad constructed

The third is always

FIGURE

17

harmony

Sixth Chord

or dominant

harmony

decorated

by tonic

six-four. When resolving to the dominant chord the lowered supersonic (root of N6) moves to the leading tone (third of V). This produces a cross relation which is not objectionable.

FIGURE

17.2. Progressions

97

of the Neapolitan

Sixth

chord may occur in root position progressing The Neapolitan chord. The fifth will ascend to the tonic to avoid parallel fifths.

FIGURE 17.3. Voice Leading

of the Neapolitan

The Neapolitan sixth chord may be preceded dominant seventh chord.

FIGURE 17.4. The Neapolitan

Chords

similar to the Neapolitan

to other than dominant

chord maybe

chords.

98

tonic

Chord in Root Position

by its secondary

Sixth Preceded

to a root position

dominant

by Secondary

or secondary

Dominant

found on other scale degrees progressing

CHAPTER

Advanced

18

Modulation

Advanced modulation is the process of moving to a distantly related key or to a closely related key using advanced modulation techniques. All pivot chords may be described as:

old key

.... ........ ..

Diatonic

...............

Diatonic.

new key Diatonic

. . . . . . . . . . . . . Chromatic

Chromatic.

. . . . . . . . . . . . . Diatonic

Chromatic.

. . . . . . . . . . . Chromatic

Pivot chords

may be enharmonically

DIATONIC

TO DIATONIC

The pivot chord will be diatonic

spelled.

in both the old and new keys using diatonic

to diatonic

modulations.

FIGURE

18.1. Modulation

Using

the Diatonic

99

to Diatonic

Pivot Chord

DIATONIC

TO CHROMATIC

The pivot diatonic

chord

will be diatonic

to chromatic

FIGURE

CHROMATIC The pivot chromatic

in the old key and chromatic

in the new key using

modulations.

18.2. Modulation

Using the Diatonic

to Chromatic

Pivot Chord

TO DIATONIC chord

will be chromatic

to diatonic

FIGURE

in the old key and diatonic

in the new key using

modulations.

18.3. Modulation

Using

the Chromatic

100

to Diatonic

Pivot Chord

CHROMATIC The pivot chromatic

TO CHROMATIC chord

will be chromatic

in both the old and new keys using

chromatic

to

modulations.

FIGURE

18.4. Modulation

ENHARMONIC An enharmonic

the Chromatic

to Chromatic

Pivot Chord

MODULATION modulation

and is enharmonically

FIGURE

Using

occurs when the pivot chord sounds the same in both keys spelled in the new key.

18.5. Modulation

Using

the Enharmonically

101

Spelled

Pivot Chord

CHANGE OF MODE A change of mode is a modulation parallel

that occurs when a major or minor key modulates

key.

FIGURE 18.6. Change

102

of Mode

to its

- ___ ~_—=_ .== ______________

—...-..++=—

-=.5=---–---.>----------

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