AP Music Theory Unit 3 Cheat Sheet: Music Fundamentals III

The basics

What it covers: How chords are built and labeled — the four triad qualities, diatonic chords and Roman numerals, chord inversions and figured bass, and the five common seventh chords.

Exam weight: AP Music Theory is weighted by section, not by unit (45% multiple choice, 45% free response, 10% sight-singing). Unit 3's chord vocabulary underlies all of the harmony and voice-leading on the exam.

The big question: How are chords built from stacked thirds, and how do Roman numerals and figured bass describe their quality and position?

Big Ideas covered: Pitch (BI 1), Music Design (BI 4).

Key topics at a glance

Building Triads

A triad is a root, a note a 3rd above, and a note a 5th above — two stacked thirds. Re-stack any chord in thirds to find its root.

The Four Triad Qualities

Major = M3 + m3 (C–E–G). Minor = m3 + M3 (C–E♭–G). Diminished = two m3 (B–D–F). Augmented = two M3 (C–E–G♯).

Roman Numerals

Uppercase = major, lowercase = minor, ° = diminished, + = augmented. The numeral gives the scale degree of the chord's root.

Diatonic Triads

Major: I ii iii IV V vi vii°. Harmonic minor: i ii° III+ iv V VI vii° (raised leading tone gives a major V and diminished vii°).

Inversions & Figured Bass

Bass note decides inversion: root position (no figure), 1st inv = 6, 2nd inv = 6/4. The figures count intervals above the bass.

Seventh Chords

Triad + a 7th. Five qualities: MM7 (major), Mm7 (dominant), mm7 (minor), ø7 (half-diminished), °7 (fully-diminished).

Seventh-Chord Inversions

Figures: root = 7, 1st inv = 6/5, 2nd inv = 4/3, 3rd inv = 4/2.

Finding Root & Quality

Re-stack the notes into thirds; the bottom is the root. Then measure the 3rd, 5th (and 7th) above it to name the quality.

The key terms you must know

Triad — a three-note chord of root, third, and fifth (two stacked thirds).
Chord quality — major, minor, diminished, or augmented, set by the sizes of the stacked thirds.
Root position & inversions — which chord tone is in the bass: root, third (1st inv), or fifth (2nd inv).
Figured bass — numbers under the bass showing intervals above it (6, 6/4, 6/5, 4/3, 4/2).
Roman numeral — labels a chord's scale degree and quality by case and symbol.
Diatonic chord — a chord built only from notes of the key.
Leading-tone chord — vii° (or vii°7 / viiø7), built on scale degree 7.
Seventh chord — a four-note chord: a triad plus a seventh above the root.
Dominant seventh (Mm7) — major triad + minor 7th; the V7 that drives to tonic.
Half-diminished vs. fully-diminished 7th — diminished triad + a minor 7th (ø7) vs. + a diminished 7th (°7).
Inversion figures — the shorthand (7, 6/5, 4/3, 4/2) for seventh-chord positions.

Key themes to remember

Everything is stacked thirds. Triads and seventh chords are just thirds piled on a root — re-stack to analyze any chord.
Quality comes from the thirds. Whether each third is major or minor determines major, minor, diminished, or augmented.
Case carries meaning. In Roman numerals, uppercase vs. lowercase (plus ° and +) tells you the quality at a glance.
The bass note names the inversion. Figured bass counts intervals above whatever pitch is in the bass.
The dominant seventh is special. Its tritone (between 3 and 7 of the chord) gives V7 its strong pull toward tonic.

Common exam traps

Spell the chord in thirds first. Notes written out of order still form a triad — re-stack them before naming the quality.
Diminished vs. minor. A diminished triad has a diminished 5th (two minor 3rds); don't confuse it with a plain minor triad.
Roman-numeral case is not optional. Writing "V" for a minor chord (or "v" for major) is marked wrong — case shows quality.
6 means first inversion, not "a sixth chord." Figured-bass numbers describe intervals above the bass, not the chord's name.
Half-diminished ≠ fully-diminished. ø7 has a minor 7th; °7 has a diminished 7th. The top interval is the difference.
In minor, watch the leading tone. The raised 7th makes V major and vii° diminished — natural-minor v and VII behave differently.