Play a piece of music you know well and stop it one chord before the end. The room waits. Nobody has to be trained to feel that something is owed; the last chord is an answer, and you have just heard the question. Now play only the very last two chords, over and over: the first is tense, the second is home. Your ear has been keeping a ledger of tension and release since before you could read.
Harmony is the study of that ledger. It asks why some chords sit still and some lean forward, why a chord can be built from any note but only a few notes build useful ones, and why a good arranger moves each note of a chord as little as possible. This piece takes the six ideas a music graduate keeps. Every card makes sound if you tap Play (it is generated in your browser, nothing is downloaded), and every card also shows the notes, so it works with the sound off. Sound is not available in this reader, so the cards show notes and numbers only.
- Who takes it
- Every music major, usually in year 2 of a conservatory or university degree (the US accrediting body NASM, the UK subject benchmark for music and Berklee's core all include it), and songwriters and producers who want to know why their chords work.
- What it is for
- Naming chords, hearing where they want to go, and writing four voices that move well together.
- Comes after
- Music Fundamentals: Pitch, Rhythm & Notation (35/63).
- Leads to
- Counterpoint & Form (35/67), Western Music History: Chant to Now (35/70) and Jazz, Popular Music & the Recording Age (35/71); through counterpoint, Composition, Arranging & Orchestration (35/72).
- What this piece gives you
- You will not be able to harmonise a chorale to a professor's satisfaction. You will see how a scale builds its chords, what the dominant seventh's tritone is doing, why parallel fifths are frowned on, and that all of this is one system among several. Easier first reads: Music Theory Accelerators vols. 1 and 2 (09/05, 09/08), which this piece goes further than.
Stacking thirds: where chords come from
Take a major scale and skip: use a note, skip one, use the next, skip one, use the next. In C major, starting on C, that gives C–E–G. Start on D and you get D–F–A; on E, E–G–B. Seven starting points, seven chords, all from the same seven notes. This is the whole supply of chords in a key, and it explains why they belong together: they are the same scale, regrouped.
What makes them sound different is the size of the two thirds stacked. A major third is 4 semitones, a minor third is 3.
Run that down a major scale and a pattern falls out that every musician memorises: major, minor, minor, major, major, minor, diminished. Capital Roman numerals are major chords and small ones are minor, so a key reads I ii iii IV V vi vii°. The Roman numeral is the chord's job in the key, not its name; I–IV–V is the same story in G or in E♭. Letter names (C D E) and fixed-do solfège (do re mi, common across much of Latin America and Europe) name the same notes, and the card shows both.
Equal temperament, A4 = 440 Hz. The chord is stacked from the scale and moved down an octave if it would run off the staff. The clef is drawn as the letter G on purpose: that is what it began as.
Try the seventh. Stack one more third on the chord built on V (G–B–D, then F) and you get a chord that is not like the rest: a major triad with a minor seventh above it. Only the fifth degree makes it. That accident of the scale is the subject of the third idea.
Function and cadences: three jobs and a grammar
Seven chords do not have seven jobs. They have three. The tonic (I, with vi and iii as understudies) is rest. The predominant (ii and IV) is departure: it leaves home and prepares something. The dominant (V, V7 and vii°) is tension that asks to be resolved. A great deal of music from roughly Bach to Brahms is a path around that triangle.
Jean-Philippe Rameau, in his Traité de l'harmonie (1722), argued that chords have roots and that progressions move by those roots; Hugo Riemann later made the three-job picture explicit (tonic, subdominant, dominant). It is a theory of tendencies, not laws. The places where music stops make the tendencies audible, and they have names. A cadence is the punctuation at the end of a phrase: V–I is a full stop (authentic), ending on V is a comma or question (half), IV–I is a soft amen (plagal), and V–vi is a surprise, the full stop that did not arrive (deceptive).
In C major. Four voices, voiced with the nearest-note method of the fourth idea, plus a bass on each root. Eight chords at most. The wording of each move describes a tendency, not an error: none of these is wrong.
Build I–IV–V–I and read the description: it leaves home, builds to tension, resolves home. Build I–V–vi–IV, the pop loop from the accelerators, and the readout flags a deceptive-looking V–vi, but the loop never needed the grammar. Pop and blues often treat chords as colours, not as steps in a journey; they are explored in Jazz, Popular Music & the Recording Age (35/71).
The dominant seventh: a tritone that wants to move
Look back at the seventh chord on V: G–B–D–F. Between its B and its F is six semitones, exactly half an octave, the tritone. In equal temperament that is 600 cents, and the two notes are the one interval that is its own inverse: flip it and you still have six semitones. That symmetry makes it unstable in a way nothing else is, and the scale offers a single resolution: B steps up to C, F steps down to E, and the six semitones shrink to a major third (400 cents).
The pull is learned from the music you grew up with, not built into physics; European composers settled on this resolution during the 17th century. Once learned it is powerful, and it leads to one of jazz's favourite tricks. The chord D♭7 (D♭–F–A♭–C♭) contains the same F and, spelled differently, the same B (C♭), so it has the same tritone and can resolve to C just as well. That is the tritone substitution, and its bass moves down one semitone to the tonic instead of up a fourth.
Hold the tones, then drag the slider: two sine tones glide from the tritone to the major third. Played in equal temperament, with a triangle-wave bass. Upper voices only on the staff; the bass is in the readout.
Voice leading: move as little as you can
A chord on the page is a name; in a choir it is four people, each with a line to sing. Voice leading is the study of those lines. The golden rule is lazy: keep any note two chords share, and move the others by the smallest step. A hand on a keyboard works the same way, and it is why a chorale sounds like four singers, not four blocks.
The numbers are striking. With four voices, root position to root position, I to V drops every voice a fifth: 20 semitones of movement in total. With the nearest-note voicing the same two chords cost 8. I–IV–V–I in root position costs 80; voiced smoothly it costs 24. The card finds the cheapest of all 24 ways to assign the next chord's notes to the voices.
Four voices in C major, the first voicing with the root doubled. Upper staff row: both chords in root position. Lower row: the cheapest voicing. Voices are not allowed to cross or share a note; the cost counts semitones.
The classical four-part habits that grow from this (avoid big leaps, resolve the leading tone B up and the chord seventh F down, never double the leading tone) are the rules of one style, the one taught from Bach's chorales. They are good training because they force you to hear lines.
Independence: why parallel fifths are the first thing marked wrong
Two voices singing a fifth apart and moving together sound less like two voices than like one voice with a thicker sound. One common explanation: the third harmonic of any note is a fifth above its octave, so a second voice on that fifth reinforces an overtone the first voice already has, and the ear fuses them. David Huron's research on voice leading and auditory fusion argues that this blend is what the old rule protects against. A composer who wanted two independent lines would avoid the effect, and so textbooks forbid parallel fifths and octaves.
It is a style rule, not a law of nature. The first European part-music, in the ninth century, moved in strict parallel fifths and fourths on purpose (see Western Music History, 35/70). A rock guitarist's power chord is a fifth, played in parallel, and it is the sound. Debussy used parallel chords for colour. The rule describes what Bach, Haydn and Mozart did, and it is what graders look for because it trains independence.
The checker looks at each step between consecutive notes: both voices must move, and the interval (counted in semitones modulo an octave) must be 7 or 0 twice in a row. It also warns about direct motion into a perfect interval by a leap. It knows nothing about taste.
With the "all fifths" preset, five consecutive fifths are flagged. Load the contrary-motion line, where one voice rises while the other falls, and the report is clean. Contrary motion is the oldest advice in the book for a reason.
One system among several
Everything above is functional tonal harmony, the system of European music from about 1650 to 1900 and of most conservatory teaching. It is one way to explain how chords behave. The others disagree about the unit of analysis, and each hears something the others do not.
| Approach | Unit and claim |
|---|---|
| Rameau (1722) | Chords have roots; progressions move by fifths; the fundamental bass supports them. |
| Riemann (late 19th c.) | Every chord is a tonic, subdominant or dominant function. |
| Schenker (early 20th c.) | A piece prolongs a few structural lines; chords are surface. |
| Jazz (mid 20th c.) | Chords are labels for scales to improvise on; ii–V–I is the commonest pattern. |
| Pop and rock | Loops and modes; chords often colour a groove rather than lead somewhere. |
| Neo-Riemannian (1980s on) | Chords are points, linked by the smallest voice-leading move. |
Outside Europe harmony is often not the organising axis at all. A raga is a melodic grammar over a drone; maqam and dastgah are modes with their own melodic paths; gamelan layers parts by speed (see Music Traditions of the World, 35/69). Choral traditions such as Georgian polyphony use harmony in their own terms. "Harmony" in the textbook sense is one major achievement, not the definition of music.
The last card shows what the neo-Riemannian view sees. Start on C major. Three moves: P (parallel) flips major to minor on the same root, R (relative) goes to the relative minor, L (leading-tone exchange) goes to the minor chord a third up. In each, two notes stay and one moves by one or two semitones, so the chords are close neighbours however their "functions" read.
Triads are voiced to move as little as possible (three voices). P, L and R come from Hugo Riemann's dualism; the modern use is David Lewin (1987) and Richard Cohn (1990s).
What a graduate just sees
- Seven chords in a key, one major-minor-minor-major-major-minor-diminished pattern: the same pattern in every major key.
- Every chord has a job: rest, departure or tension; cadences are where the job is visible.
- The tritone in a dominant seventh is why V7 wants to go home, and a tritone substitute shares that pull.
- Good voice leading keeps common tones and moves the rest by step.
- Parallel fifths and octaves fuse voices; the rule is a style, not physics.
- Roman numerals describe a progression independent of key, so a song can be transposed by changing one number.
- Functional harmony is one theory among several, and a good arranger knows when it is the wrong lens.
Where it shows up next
- Counterpoint & Form (35/67) takes the independence of voices as far as it goes: lines first, chords as the by-product.
- Western Music History (35/70) is the story of this system being built, stretched (Wagner's Tristan chord) and broken.
- Jazz, Popular Music & the Recording Age (35/71) swaps function for chord-scale thinking and loops.
- In the world: the arranger writing a string pad, the songwriter choosing a bridge chord, the pianist reharmonising a standard, the game composer who makes a loop sound unresolved on purpose.
If you want to go deeper
- 📘 Textbook. Edward Aldwell and Carl Schachter, Harmony and Voice Leading (Schirmer/Cengage). Voice leading first; the book MIT's harmony course is built on.
- 📘 Textbook. Stefan Kostka and Dorothy Payne, Tonal Harmony (McGraw-Hill). The most widely assigned US text, with a workbook of exercises.
- 📘 Also. Steven Laitz, The Complete Musician (Oxford University Press). Integrates theory, ear training and analysis.
- 🌐 Gentler, free. musictheory.net lessons and the free open textbook Open Music Theory (search the title): short lessons with exercises.
- 🌐 Free course. MIT OpenCourseWare 21M.301 Harmony and Counterpoint I (Spring 2005), with assignments and exams.
- 🌐 IMSLP, the free library of public-domain scores: open a Bach chorale and label the chords.
A scale stacks into seven chords with three jobs among them, and the shortest path between chords is the one where each voice moves least. The tritone in V7 is the engine, the cadence is the punctuation, and parallel fifths are the first sign of a voice losing its identity. All of it is one rich system among several.
Try this: this week, pick a song you know, hum its last phrase and find the note it ends on. Then look for the note one step above or below it that, if the song stopped there instead, would feel unfinished. That wanting is the leading tone you now know how to name.
Sources. Triad qualities, functions and cadences are standard textbook material (Aldwell and Schachter; Kostka and Payne; Laitz). Rameau's Traité de l'harmonie (1722) and Riemann's functional theory are standard history. The explanation of fusion draws on David Huron's work on voice leading and auditory scene analysis. Neo-Riemannian theory: David Lewin, Generalized Musical Intervals and Transformations (1987) and Richard Cohn's articles. The MIT course page and its textbook were confirmed on ocw.mit.edu. All interactive numbers were computed in node. The detector and builder describe style tendencies, not rules of nature; a book edition number is not given because it was not confirmed.
- 🌐 MIT OCW 21M.301
- 🌐 musictheory.net
- 📘 Aldwell and Schachter, Harmony and Voice Leading
- 📘 Kostka and Payne, Tonal Harmony