Chapters 1 and 2: Pitch and Intervals
All pitches within a one-octave span.
Dyads are pairs of pitches played either in sequence (melodic) or simultaneously (harmonic).
They are named after the distance between the two pitches. This distance is called an interval.
Intervals are measured in half-steps, the smallest possible distance between two pitches.
Number of half-steps Full interval name Abbreviation Scale Degree
between pitches Function
0 Perfect Unison P1 1
1 Minor 2nd m2 b2 / b9
2 Major 2nd M2 2/9
3 Minor 3rd m3 b3
Augmented 2nd A2 #2 / #9
4 Major 3rd M3 3
5 Perfect 4th P4 4 / 11
6 Tritone TT
Augmented 4th A4 #4 / #11
Diminished 5th d5 b5
7 Perfect 5th P5 5
8 Minor 6th m6 b6 / b13
Augmented 5th A5 #5
9 Major 6th M6 6 / 13
Diminished 7th d7 bb7
10 Minor 7th m7 b7
11 Major 7th M7 7
12 Perfect Octave P8 1
1
Unisons occur when the same pitch is played twice.
Octaves occur when two pitches with the same name are played one octave apart.
Melodic Intervals: Ascending
Melodic Intervals: Descending
Harmonic Intervals
2
Interval Nomenclature
There are two components to an interval’s name: a quality followed by a number.
The number indicates how many letter names are spanned between the two pitches, inclusive.
In this example, A ascends to G. Seven letter names are spanned: A-B-C-D-E-F-G. Therefore,
this interval is some kind of 7th.
In this example, A descends to G. Only two letter names are spanned: A-G. Therefore, this
interval is some kind of 2nd.
Qualities include Perfect, Minor, Major, Diminished, and Augmented.
Unisons, 4ths, 5ths, and Octaves can be Diminished, Perfect, or Augmented.
2nds, 3rds, 6ths, and 7ths can be Diminished, Minor, Major, or Augmented.
The table below summarizes which intervals are Perfect and which are Minor/Major, their
abbreviations, and how the quality is transformed when the interval is increased or decreased
by a half-step.
Interval Quality Abbreviation +1 Half-Step -1 Half-Step
(case-sensitive)
Perfect (1, 4, 5, 8) P Augmented Diminished
Minor (2, 3, 6, 7) m Major Diminished
Major (2, 3, 6, 7) M Augmented Minor
Diminished d Perfect or Minor
Augmented A Perfect or Major
3
Chapter 3a: Basic Triads
Triads contain three different pitches. Basic Triads are built by stacking pairs of third intervals.
The lowest pitch in one of these stacks is called the Root. The pitch a third above the Root is
called the Third, and the pitch a fifth above the Root is called the Fifth.
Triad Type Interval: Root Interval: Third Interval: Root Formula
and Third and Fifth and Fifth
Diminished, d, ° m3 m3 d5 1 b3 b5
Minor, m m3 M3 P5 1 b3 5
Major, M M3 m3 P5 135
Augmented, A, + M3 M3 A5 1 3 #5
Inversions are generated by changing which pitch appears in the low voice. A triad is in first
inversion when the Third is in the low voice. A triad is in second inversion when the Fifth is in
the low voice. A consequence of inversion is that the various intervals between the three voices
(Low, Middle, and High) change.
Triad Type Inversion Interval: Low Interval: Middle Interval: Low Formula
and Middle and High and High
Diminished 1st m3 A4 M6 b3 b5 1
Diminished 2nd A4 m3 M6 b5 1 b3
Minor 1st M3 P4 M6 b3 5 1
Minor 2nd P4 m3 m6 5 1 b3
Major 1st m3 P4 m6 351
Major 2nd P4 M3 M6 513
4
Chapter 3b: Advanced Triads
Advanced Triads are built by stacking pairs of fourth intervals. These are called Quartal triads.
Triad Type Interval: Low and Interval: Middle and Interval: Low and
Middle High High
Q P4 P4 m7
Q+ P4 A4 M7
+4Q A4 P4 M7
Each inversion is treated as its own unique triad, and its lowest note is reinterpreted as a new
Root.
Triad Type Inversion Name Formula Interval: Interval: Interval:
Low and Middle and Low and
Middle High High
Q 1st sus4 145 P4 M2 P5
Q 2nd sus2 125 M2 P4 P5
Q+ 1st Lydian 1 #4 5 A4 m2 P5
Q+ 2nd Locrian 1 b2 b5 m2 P4 d5
+4Q 1st sus4b5 1 4 b5 P4 m2 d5
+4Q 2nd Phrygian 1 b2 5 m2 A4 P5
5
Chapter 4: Sevenths
Seventh chords are formed when a 7th is added above a Triad’s Root.
6
Base Triad Added 7th Name of 7th Chord Formula
Major M7 Major 7 1357
Major m7 7 1 3 5 b7
Dominant 7
Minor M7 Minor Major 7 1 b3 5 7
Minor m7 Minor 7 1 b3 5 b7
Diminished M7 Diminished Major 7 1 b3 b5 7
Diminished m7 Half-diminished 7 1 b3 b5 b7
Minor 7 b5
Diminished d7 Diminished 7 1 b3 b5 bb7
Augmented M7 Augmented Major 7 1 3 #5 7
sus4 M7 Major 7 sus4 1457
sus4 m7 7sus4 1 4 5 b7
Dominant 7 sus4
sus2 M7 Major 7 sus2 1257
Lydian M7 Lydian Major 7 1 #4 5 7
Lydian m7 Lydian Dominant 7 1 #4 5 b7
Phrygian M7 Phrygian Major 7 1 b2 5 7
Phrygian m7 Phrygian Dominant 7 1 b2 5 b7
7
Chapter 5: Tonal Progressions
The Major scale is a set of seven pitches built on any given Root.
Scale Degree Number Scale Degree Name Interval Above Root
1 Tonic P1
2 Supertonic M2
3 Mediant M3
4 Subdominant P4
5 Dominant P5
6 Submediant M6
7 Leading tone M7
A triad can be built in diatonic thirds on each scale degree. “Diatonic” means that only pitches
from the scale are used.
Scale Degree Triad Quality Roman Numeral Function
1 Major I Tonic
2 Minor ii Pre-Dominant
3 Minor iii Tonic
4 Major IV Pre-Dominant
5 Major V Dominant
6 Minor vi Tonic
7 Diminished vii° Dominant
8
A seventh chord can be built in diatonic thirds on each scale degree.
Scale Degree Seventh Quality Roman Numeral Function
1 Major 7 IMaj7 Tonic
2 Minor 7 ii7 Pre-Dominant
3 Minor 7 iii7 Tonic
4 Major 7 IVMaj7 Pre-Dominant
5 Dominant 7 V7 Dominant
6 Minor 7 vi7 Tonic
7 Half-diminished viiø7
Minor 7 b5
Roman Numeral Nomenclature
Chord Type Case Additional Symbol
Diminished Lower-Case °
Minor Lower-Case
Major Upper-Case
Augmented Upper-Case +
9
The Minor scale is a set of seven pitches built on any given Root.
Note that compared to the Major scale, the third, sixth, and seventh scale degrees are flattened.
Scale Degree Number Scale Degree Name Interval Above Root
1 Tonic P1
2 Supertonic M2
b3 Mediant m3
4 Subdominant P4
5 Dominant P5
b6 Submediant m6
b7 Subtonic m7
A triad can be built in diatonic thirds on each scale degree.
Scale Degree Triad Quality Roman Numeral
1 Minor i
2 Diminished ii°
b3 Major bIII
4 Minor iv
5 Minor v
b6 Major bVI
b7 Major bVII
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Tonal Progressions Minor Key
The progressions in this module combine chords in Root Position with chords in 1st Inversion.
This means that a given bass note can potentially support several chords.
Scale Degree in the Bass Root Position Chord 1st Inversion Chord
1 i bVI
2 ii° bVII
b3 bIII i
4 iv ii°
5 v bIII
5 V
b6 bVI iv
b7 bVII v
11
Chapter 6: Secondary Chords
In a Major key, secondary dominant chords are the V7 and vii°7 chords of ii, iii, IV, V, and vi.
x V7/x vii°7/x
Dm (ii) A7 C#°7
Em (iii) B7 D#°7
F (IV) C7 E°7
G (V) D7 F#°7
Am (vi) E7 G#°7
12
Chapter 7a: Added-Note Chords
Added-Note Chords are formed when a 2nd, 4th, or 6th is added above a Triad’s Root.
13
Base Triad Added 2, 4, or 6 Name of New Chord Formula
Major m2 Phrygian Major 1 b2 3 5
Major M2 Major add 2 1235
Major P4 Major add 4 1345
Major A4 Lydian Major 1 3 #4 5
Major m6 Major add b6 1 3 5 b6
Major M6 Major 6 1356
Minor m2 Phrygian Minor 1 b2 b3 5
Minor M2 Minor add 2 1 2 b3 5
Minor P4 Minor add 4 1 b3 4 5
Minor A4 Lydian Minor 1 b3 #4 5
Minor m6 Minor add b6 1 b3 5 b6
Minor M6 Minor 6 1 b3 5 6
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Chapter 7b: Extended Chords
Extended Chords are formed when a 9th, 11th, or 13th is added above a Seventh chord’s Root.
Note: 9ths, 11ths, and 13ths are equivalent to 2nds, 4ths, and 6ths.
Base Seventh Chord Added 9, 11, or 13 Name of Chord Formula
Major 7 M9 Major 9 13579
Major 7 A11 Major 7 #11 1 3 5 7 #11
Major 7 M13 Major 13 1 3 5 7 13
Minor 7 M9 Minor 9 1 b3 5 b7 9
Minor 7 P11 Minor 11 1 b3 5 b7 11
Minor 7 M13 Minor 13 1 b3 5 b7 13
Minor Major 7 M9 Minor Major 9 1 b3 5 7 9
Minor Major 7 P11 Minor Major 11 1 b3 5 7 11
Minor Major 7 M13 Minor Major 13 1 b3 5 7 13
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Chapter 8: Rhythm
x note-heads in the sheet music, and shaded cells in the graphs denote the click.
Quarters
1 2 3 4
5 6 7 8
Eighths
1 + 2 +
3 + 4 +
Sixteenths
1 e + a
2 e + a
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Chapter 9: Scales
Ionian
Major
Dorian Phrygian Lydian
Mixolydian Aeolian Locrian
Melodic Minor
Melodic Minor
Dorian b2 Lydian Augmented Mixolydian #11
Mixolydian b6 Locrian Natural 2 Altered Dominant
Harmonic Minor
Harmonic Minor Locrian Natural 6 Ionian Augmented Dorian #4
Phrygian Major Lydian #9 Altered Dominant bb7
Dominant Diminished
Symmetrical
Tonic Diminished Whole-Tone Augmented
Major Pentatonic
Pentatonic/Blues
Major Blues Minor Pentatonic Minor Blues
Major Bebop
Bebop
Minor Bebop Dominant Bebop Melodic Minor Bebop
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Modes of the Major Scale
Ionian 1 2 3 4 5 6 7
Dorian 1 2 b3 4 5 6 b7
Phrygian 1 b2 b3 4 5 b6 b7
Lydian 1 2 3 #4 5 6 7
Mixolydian 1 2 3 4 5 6 b7
Aeolian 1 2 b3 4 5 b6 b7
Locrian 1 b2 b3 4 b5 b6 b7
Modes of the Melodic Minor Scale
Melodic Minor 1 2 b3 4 5 6 7
Dorian b2 1 b2 b3 4 5 6 b7
Lydian Augmented 1 2 3 #4 #5 6 7
Mixolydian #11 1 2 3 #4 5 6 b7
Mixolydian b6 1 2 3 4 5 b6 b7
Locrian Natural 2 1 2 b3 4 b5 b6 b7
Altered Dominant 1 b2 b3 b4 b5 b6 b7
#2 3 #5
Modes of the Harmonic Minor Scale
Harmonic Minor 1 2 b3 4 5 b6 7
Locrian Natural 6 1 b2 b3 4 b5 6 b7
Ionian Augmented 1 2 3 4 #5 6 7
Dorian #4 1 2 b3 #4 5 6 b7
Phrygian Major 1 b2 3 4 5 b6 b7
Lydian #9 1 #2 3 #4 5 6 7
Altered Dominant bb7 1 b2 b3 b4 b5 b6 bb7
#2 3 #4 #5 6
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Symmetrical Scales
Dominant Diminished 1 b2 #2 3 #4 5 6 b7
Tonic Diminished 1 2 b3 4 b5 #5 6 7
Whole Tone 1 2 3 #4 #5 b7
Augmented 1 b3 3 5 #5 7
Pentatonic and Blues Scales
Major Pentatonic 1 2 3 5 6
Major Blues 1 2 #2 3 5 6
b3
Minor Pentatonic 1 b3 4 5 b7
Minor Blues 1 b3 4 #4 5 b7
b5
Bebop Scales
Major Bebop 1 2 3 4 5 #5 6 7
b6
Minor Bebop 1 2 b3 4 5 b6 b7 7
Dominant Bebop 1 2 3 4 5 6 b7 7
Melodic Minor Bebop 1 2 b3 4 5 #5 6 7
b6
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Chapter 10: Modal Voicings
Modes are compared side-by-side. Shaded cells indicate the differences between modes.
Ionian 1 2 3 4 5 6 7
Lydian 1 2 3 #4 5 6 7
Dorian 1 2 b3 4 5 6 b7
Aeolian 1 2 b3 4 5 b6 b7
Phrygian 1 b2 b3 4 5 b6 b7
Locrian 1 b2 b3 4 b5 b6 b7
Ionian 1 2 3 4 5 6 7
Mixolydian 1 2 3 4 5 6 b7
Melodic Minor 1 2 b3 4 5 6 7
Locrian Natural 2 1 2 b3 4 b5 b6 b7
Dorian b2 1 b2 b3 4 5 6 b7
Altered Dominant 1 b2 b3 b4 b5 b6 b7
#2 3 #5
Lydian 1 2 3 #4 5 6 7
Lydian Augmented 1 2 3 #4 #5 6 7
Mixolydian #11 1 2 3 #4 5 6 b7
Mixolydian b6 1 2 3 4 5 b6 b7
Harmonic Minor 1 2 b3 4 5 b6 7
Phrygian Major 1 b2 3 4 5 b6 b7
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Altered Dominant 1 b2 b3 b4 b5 b6 b7
#2 3 #5
Altered Dominant bb7 1 b2 b3 b4 b5 b6 bb7
#2 3 #5 6
Locrian Natural 6 1 b2 b3 4 b5 6 b7
Dorian #4 1 2 b3 #4 5 6 b7
Ionian Augmented 1 2 3 4 #5 6 7
Lydian #9 1 #2 3 #4 5 6 7
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Chapter 12: Modal Harmony
Modal Triads include all non-diatonic Major and Minor triads.
Major Tonic
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Modal Triads in C Major
Roman Numeral Triad
bII Db
bii Dbm
II D
bIII Eb
biii Ebm
III E
iv Fm
bV Gb
bv Gbm
v Gm
bVI Ab
bvi Abm
VI A
bVII Bb
bvii Bbm
VII B
vii Bm
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Minor Tonic
24
Modal Triads in C Minor
Roman Numeral Triad
bII Db
bii Dbm
II D
ii Dm
biii Ebm
III E
iii Em
IV F
bV Gb
bv Gbm
bvi Abm
VI A
vi Am
bvii Bbm
VII B
vii Bm
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Chapter 13: Bitonal Harmony
Bitonal Harmony includes voicings that pair a bass note with a Major or Minor triad built on
another note. The resulting voicings are also known as “slash chords”, or “triads over bass
notes”. In these examples, all triads are paired with a C bass note.
Major Triads
Root of Triad Name Harmonic Analysis
b2 Db/C DbM7 (3rd inv)
Phrygian
2 D/C D7 (3rd inv)
Lydian
b3 Eb/C Cm7
3 E/C CM7#5
4 F/C F (2nd inv)
b5 Gb/C C7b5 b9
Altered / Dom. Dim
5 G/C CM9
b6 Ab/C Ab (1st inv)
6 A/C C13 b9 (Dom. Diminished)
b7 Bb/C C9sus4
7 B/C C°M7 (Tonic Dim)
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Minor Triads
Root of Triad Name Harmonic Analysis
b2 Dbm/C DbmM7 (3rd inv)
C7b9 #5 (Altered)
2 Dm/C Dm7 (3rd inv)
b3 Ebm/C Cm7b5
3 Em/C CM7
4 Fm/C Fm (2nd inv)
b5 Gbm/C C13 b9 b5 (Dom. Diminished)
5 Gm/C C9
b6 Abm/C Ab Min/Maj (2nd inv)
Dominant Diminished
6 Am/C Am (1st inv)
b7 Bbm/C C7sus4 b9
7 Bm/C CM9 #11
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