Harmony
Short Description
Descripción: Harmony...
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Naval Education and Training Command
NAVEDTRA 12012 March 1990 0502-LP-213-0600
Special Publication
(SP)
Harmony
DISTRIBUTION
STATEMENT
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Nonfederal government personnel wanting a copy of this document must use the purchasing instructions on the inside cover.
S/N 0502-LP-213-0600
ACKNOWLEDGEMENT The contents of this manual were furnished by the courtesy of Headquarters, Department of the Army under the Interservice Mutual Support of Services and Training Agreement for exchange of training materials.
DISTRIBUTION
STATEMENT
A: Approved
for public release; distribution
is unlimited.
Nonfederal governmentpersonnelwanting a copy of this document must write to Superintendentof Documents, GovernmentPrinting Office, Washington,DC 20402OR CommandingOfficer, Naval Publicationsand FormsCenter, 5801 Tabor Avenue, Philadelphia, PA 19120-5099, Attention: Cash Sales,for price and availability.
*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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