harmony-analysis

Harmony Analysis

Harmony is the vertical dimension of music — the simultaneous sounding of pitches and the principles governing how those sonorities connect across time. Harmonic analysis decodes the function of each chord within a key, traces the path of individual voices between chords, and reveals the large-scale tonal architecture of a piece. This skill covers diatonic and chromatic harmony, voice leading rules, cadence identification, modulation techniques, and the translation between classical and jazz chord notation systems.

Agent affinity: rameau (harmonic function, fundamental bass theory), bach (voice leading, chorale harmonization)

Concept IDs: harmony, chord-progressions, song-form

Part I — Chord Vocabulary

Triads

A triad is a three-note chord built in thirds above a root. Four qualities exist in tonal music:

| Quality | Intervals | Example on C | Symbol | |---|---|---|---| | Major | M3 + m3 (P5 total) | C-E-G | C or CM | | Minor | m3 + M3 (P5 total) | C-Eb-G | Cm or c | | Diminished | m3 + m3 (d5 total) | C-Eb-Gb | Cdim or c-degrees | | Augmented | M3 + M3 (A5 total) | C-E-G# | Caug or C+ |

In a major key, the diatonic triads are: I (major), ii (minor), iii (minor), IV (major), V (major), vi (minor), vii-degrees (diminished). This distribution of qualities is not arbitrary — it arises from the pattern of whole and half steps in the major scale.

Seventh Chords

Adding a third above the triad's fifth produces a seventh chord. The five principal types:

| Type | Construction | Diatonic location (major key) | Jazz symbol | |---|---|---|---| | Major seventh | Major triad + M7 | I7, IV7 | Cmaj7, C-triangle-7 | | Dominant seventh | Major triad + m7 | V7 | C7 | | Minor seventh | Minor triad + m7 | ii7, iii7, vi7 | Cm7, C-7 | | Half-diminished seventh | Dim triad + m7 | vii-ø-7 | Cm7b5, C-ø-7 | | Fully diminished seventh | Dim triad + d7 | vii-degrees-7 (minor key) | Cdim7, C-degrees-7 |

The dominant seventh is the most harmonically active of these — its tritone (between the third and seventh of the chord) creates a strong pull toward resolution.

Inversions

Triads have three positions; seventh chords have four:

| Triad position | Bass note | Figured bass | Seventh chord position | Bass note | Figured bass | |---|---|---|---|---|---| | Root position | Root | 5/3 (or blank) | Root position | Root | 7 | | First inversion | Third | 6 or 6/3 | First inversion | Third | 6/5 | | Second inversion | Fifth | 6/4 | Second inversion | Fifth | 4/3 | | — | — | — | Third inversion | Seventh | 4/2 or 2 |

Second-inversion triads (6/4 chords) are unstable and appear in three standard contexts: cadential 6/4 (I-6/4 resolving to V), passing 6/4 (connecting two root-position or first-inversion chords), and pedal 6/4 (upper voices move over a stationary bass).

Part II — Roman Numeral Analysis

Roman numeral analysis identifies each chord by its scale-degree root and quality relative to the prevailing key. This is the standard analytical language of Western tonal music.

Notation conventions:

• Uppercase Roman numeral = major triad (I, IV, V)
• Lowercase Roman numeral = minor triad (ii, iii, vi)
• Superscript circle = diminished (vii-degrees)
• Superscript plus = augmented (III+)
• Arabic numerals indicate inversions (figured bass shorthand)
• Slash notation for applied (secondary) chords: V/V means "V of V"

Worked analysis: Bach Chorale "Ich bin's, ich sollte bussen" (St. Matthew Passion, No. 16)

Key: E major

Soprano:  E   | D#  | E   F# | G#  | F#  E   | D#  | E
Alto:     B   | B   | B   D# | E   | D#  C#  | B   | B
Tenor:    G#  | F#  | G#  A  | B   | B   A   | F#  | G#
Bass:     E   | B   | E   D# | C#  | D#  A   | B   | E
Roman:    I   | V   | I  V6/5/iv| vi  |V6/4/V IV| V   | I

Measure-by-measure:

1. I — Tonic establishes the key.
2. V — Dominant in root position; standard tonic-to-dominant motion.
3. I to V6/5 of vi — The tonic resolves, then a secondary dominant (applied chord) targets vi.
4. vi — The secondary dominant resolves to its target; this is a tonicization, not a modulation (the key does not change).
5. Cadential 6/4 to IV — The cadential 6/4 functions as a dominant preparation; IV provides plagal color.
6. V — The dominant, prepared by IV.
7. I — Authentic cadence. The progression V-I closes the phrase.

This chorale phrase demonstrates three fundamental harmonic principles: (1) tonic-dominant polarity frames the phrase, (2) secondary dominants create momentary tonal tension without leaving the key, and (3) the cadential 6/4 is a voice-leading event over dominant harmony, not an independent tonic chord.

Part III — Voice Leading

Voice leading governs how individual voices (soprano, alto, tenor, bass) move from one chord to the next. Good voice leading produces smooth, singable lines and avoids forbidden parallels.

The Four Rules

1. No parallel fifths. Two voices moving in parallel perfect fifths (e.g., C-G to D-A) produce a hollow, medieval sound that undermines harmonic independence. This was the first prohibition codified in Renaissance counterpoint.

1. No parallel octaves. Two voices moving in parallel octaves (or unisons) reduce four-part texture to three effective voices. The doubling adds power but removes independence.

1. Resolve the leading tone. In a V-I progression, the seventh scale degree (the leading tone) must resolve up by step to the tonic, especially when in the soprano. Exception: in inner voices, the leading tone may descend to the fifth of the tonic chord to achieve a complete chord.

1. Resolve the chordal seventh. In any seventh chord, the seventh (the dissonant note) resolves down by step. In V7-I, the seventh of V (the fourth scale degree) resolves down to the third of I.

Voice Leading Principles (Beyond the Rules)

• Common tones. When two successive chords share a note, keep it in the same voice. This is the simplest form of smooth voice leading.
• Stepwise motion. Move the remaining voices by the smallest possible interval. Leaps larger than a fourth should be followed by stepwise motion in the opposite direction.
• Contrary motion with the bass. When the bass leaps, the upper voices should move in contrary motion (opposite direction) to achieve balance.
• Spacing. Adjacent upper voices (soprano-alto, alto-tenor) should be no more than an octave apart. The tenor-bass gap may be larger (up to two octaves in orchestral writing).

Worked Example — Harmonizing V7 to I in C Major

Soprano:  B  ->  C    (leading tone resolves up to tonic)
Alto:     F  ->  E    (chordal seventh resolves down by step)
Tenor:    D  ->  C    (common tone available, but stepwise descent
                        to tonic also valid; here resolves down)
Bass:     G  ->  C    (root motion: V to I, descending fifth)

Result: V7 (G-B-D-F) resolves to I (C-C-E-C). The I chord is incomplete (tripled root, no fifth) — this is normal and expected when properly resolving all tendency tones.

Part IV — Cadences

A cadence is a harmonic arrival point that articulates phrase structure. Four principal types:

Authentic Cadence (AC)

V (or V7) to I. The strongest cadence. A perfect authentic cadence (PAC) has: root-position V, root-position I, and the tonic in the soprano on the final chord. An imperfect authentic cadence (IAC) weakens one of these conditions (inverted V, inverted I, or non-tonic note in soprano).

Harmonic weight: Conclusive. Used at the ends of sections and pieces.

Half Cadence (HC)

Any chord to V. The phrase ends on the dominant, creating an open, unresolved feeling — like a comma in prose. Common approaches: I-V, ii-V, IV-V, vi-V.

Harmonic weight: Suspensive. Demands continuation.

Deceptive Cadence (DC)

V to vi (or another non-tonic chord). The ear expects I after V; the substitution of vi creates surprise. The deceptive cadence works because vi sh