Tonal harmony is the grammar of Western music. Understanding it does not constrain you — it gives you a language with which to think, and to deviate intentionally.
WHAT HARMONY DOES
Harmony creates context. A single note means nothing harmonically — it is a pure pitch. Two notes create an interval — a relationship. Three or more notes create a chord — a simultaneous harmonic event that implies tension or relaxation, direction or stability.
Tonal harmony organizes pitches around a central pitch (the tonic) and describes the relationships between all other pitches and chords in terms of their distance from and relationship to that center. The sense of "home" — of harmonic rest — is created by the tonic. All other harmonies create varying degrees of distance from home, with the dominant (the fifth scale degree and its chord) creating the maximum tension before return.
THE TRIAD
- The basic chord unit in tonal harmony is the triad: three notes arranged in thirds. Four triad qualities exist:
- Major triad: root, major third, perfect fifth (C–E–G). Sounds stable, bright.
- Minor triad: root, minor third, perfect fifth (C–E♭–G). Sounds stable, darker.
- Diminished triad: root, minor third, diminished fifth (C–E♭–G♭). Sounds unstable, tense.
- Augmented triad: root, major third, augmented fifth (C–E–G#). Sounds unstable, suspended.
The diminished triad is the most harmonically active — it wants to move to a stable chord.
DIATONIC TRIADS
Every major and minor scale generates seven diatonic triads — one built on each scale degree. In C major: I (C–E–G), ii (D–F–A), iii (E–G–B), IV (F–A–C), V (G–B–D), vi (A–C–E), vii° (B–D–F).
The Roman numeral system identifies chords by their scale degree. Uppercase = major; lowercase = minor; ° = diminished.
- The most important harmonic relationships:
- I: tonic — home
- V: dominant — maximum tension before resolution
- IV: subdominant — relaxed tension, often preceding V
- ii: often functions like IV, approaching V
- vi: relative minor — closely related to I
THE DOMINANT–TONIC RELATIONSHIP
The progression V → I is the engine of tonal music. The leading tone (the seventh scale degree, one semitone below the tonic) creates a strong pull upward to the tonic; and the dominant root in the bass pulls toward the tonic a fifth below. The resolution of V to I is the most fundamental motion in Western harmony.
The dominant seventh chord (V7: G–B–D–F in C major) adds a seventh to the triad, strengthening the pull toward I still further.
VOICE LEADING
- Voice leading is the art of moving smoothly from one chord to the next. The principles:
- Contrary motion: when the bass moves up, the upper voices tend to move down (and vice versa)
- Common tones: if two adjacent chords share a pitch, that pitch stays in the same voice
- Step motion: voices prefer to move by step (whole tone or semitone) rather than leap
- Avoid parallel fifths and octaves: two voices moving in parallel fifths or octaves merge into a single voice acoustically and obscure harmonic independence
Bach's chorales (370 of them, available on IMSLP) are the canonical models of voice leading. Analyzing them — identifying every voice, every progression, every exception — is the traditional path to harmonic fluency.
HARMONIC RHYTHM
The rate at which harmonies change is harmonic rhythm. Chopin's nocturnes often have one chord per bar or longer — broad, slow harmonic rhythm. Bach's inventions change harmony on every beat or more — rapid harmonic rhythm. Controlling harmonic rhythm is as important as choosing which harmonies to use.
CADENCES
- A cadence is a harmonic phrase ending — the punctuation of tonal music:
- Authentic cadence: V → I (full stop)
- Perfect authentic cadence: V → I with both chords in root position and tonic in the soprano
- Half cadence: any chord → V (question mark)
- Deceptive cadence: V → vi (expected I is replaced by its relative — a comma, not a period)
- Plagal cadence: IV → I (the "Amen" cadence — a softer ending)
FIGURED BASS AND THE ORIGINS OF MODERN HARMONY
Tonal harmony developed gradually from contrapuntal practice during the seventeenth century. The figured bass system — numerical shorthand notating which intervals above the bass line a keyboard player should fill in — was the practical training ground for generations of Baroque musicians. Bach taught his students harmony by giving them basses and asking them to realize the upper voices; Heinichen, Mattheson, and C.P.E. Bach published influential treatises explaining the system.
Figured bass numbers indicate the intervals above the bass: a "6" means a sixth above the bass; "6/4" indicates a six-four chord (a triad in second inversion); a slash through a number indicates raising it by a semitone. The system is efficient: it encodes complete harmonic information without spelling out every note. Studying figured bass realizations from Corelli, Handel, and Bach is one of the most direct ways to understand how tonal voice leading actually works in practice rather than in textbook abstraction.
FUNCTIONAL HARMONY AND THE THREE FUNCTIONS
The German theorist Hugo Riemann (1849–1919) systematized tonal harmony around three functions: tonic (T), subdominant (S), and dominant (D). Every chord can be analyzed as serving one of these three functions. In C major, I and vi are tonic-function chords; IV and ii are subdominant-function; V and vii° are dominant-function. The typical harmonic progression moves T → S → D → T — establishing home, departing, building tension, returning.
This three-function model is a simplification but a useful one. It explains why ii → V → I and IV → V → I work the same way (both are S → D → T progressions); why V → vi is a deceptive cadence (D goes to T, but to a less stable tonic chord); why iii is rarely used as a primary chord (it is functionally ambiguous, sharing notes with both I and V).
PHRASE MODELS AND HARMONIC SYNTAX
Harmony works at multiple levels simultaneously. At the local level, individual chord-to-chord movements follow voice leading rules. At the phrase level, harmonies group into characteristic phrase models: the prolongation of tonic, the move to a contrasting harmonic area, the cadential preparation, the cadence itself. At the section level, large-scale tonal motion (modulation between keys) provides architectural shape.
The standard Classical phrase model is approximately: I (tonic prolongation, possibly several bars) → ii or IV (predominant) → V or V7 (dominant) → I (cadence). This pattern can be heard in thousands of Classical and folk pieces. Recognizing it allows you to navigate harmonic landscapes quickly and to identify departures from the norm as expressive choices.
THE CIRCLE OF FIFTHS
The circle of fifths organizes the twelve keys by relationship: each key is a fifth from its neighbor. Moving clockwise adds sharps; moving counterclockwise adds flats. Adjacent keys (C and G, or C and F) share six of seven pitches; distant keys (C and F#) share only two (B and, enharmonically, F/E#). The circle of fifths is the map of tonal space — it tells you which keys are nearby (easy to modulate to) and which are far away (require more preparation).
Most Classical music modulates to closely related keys: tonic to dominant in major-key works, tonic to relative major in minor-key works. Romantic composers expanded the available territory, moving to mediant relationships (C to E major), chromatic third relationships (C to E♭ or A♭), and remote keys reached through enharmonic reinterpretation. Schubert is the great explorer of distant key relationships — his sonatas often visit keys that earlier composers would not have approached.
HARMONIC PROGRESSIONS IN POPULAR MUSIC
Many of the most enduring popular songs are built on a handful of harmonic patterns. The I–V–vi–IV progression appears in hundreds of pop and rock songs from "Let It Be" (Beatles) to "Don't Stop Believin'" (Journey) to countless contemporary hits. The 12-bar blues progression (I, I, I, I, IV, IV, I, I, V, IV, I, V) is the harmonic foundation of blues, early rock, and significant portions of jazz. The ii–V–I progression is the most common cadential motion in jazz standards.
Studying these recurring patterns is not just useful for writing popular music — it reveals what makes a progression memorable and effective. The patterns survive because they work.
COMMON HARMONIC PITFALLS
Several characteristic problems appear in early student harmonizations. First, harmonic stasis — using the tonic chord too much, leaving the music feeling stuck. Second, weak cadences — failing to use the V → I motion at phrase endings. Third, voice leading errors — parallel fifths and octaves, inadequate preparation of dissonance, awkward leaps in inner voices. Fourth, mismatched harmonic rhythm — changing chords too quickly or too slowly for the melodic surface. Fifth, ignoring the bass line — treating the bass as a chord root rather than a melodic voice in its own right.
The bass line is the second most important voice after the soprano (the melody). A strong bass line moves with melodic logic of its own — stepwise where possible, with occasional purposeful leaps, ending phrases on strong scale degrees. Studying the bass lines of Bach chorales reveals how a bass voice can be both harmonic foundation and independent melody simultaneously.
EXERCISE: HARMONIZING A MELODY
Take one of the melodies you wrote in the previous lesson and harmonize it. For each note of the melody, choose a chord that contains that note. Use mainly I, IV, V, and ii. End each phrase with a cadence. Sing or play the result. Is the harmony interesting? Are the chord changes smooth? Try two different harmonizations of the same melody and compare. Then play just the bass line you have created — does it have its own melodic logic, or does it merely outline chord roots? Revising the bass line independently of the melody is one of the most effective ways to improve a harmonization.