The Harmonic Field: the Chords a Scale Contains
A major scale is seven notes. Ask what chords can be built using only those seven, and the answer is not a matter of taste: exactly seven chords come out, in a fixed order of qualities, and that order is the same in every major key. The set is called the harmonic field of the scale, and it is the reason the chords of a song sound like they belong together — they were all drawn from the same seven notes.
Stacking thirds
The recipe is one move, repeated seven times. Stand on a degree of the scale, skip the next note, take the one after it, skip again, take the one after that. Three notes, each one a third above the last, every one of them already in the scale.
Do that on the first degree and you get a chord. Do it on the second, then the third, and so on to the seventh, wrapping around the octave when you run off the top. Seven degrees, seven chords, no notes borrowed from outside.
What comes out
Using C major as the example — the scale of the white keys — the seven chords are these:
| Degree | Notes | Quality | Numeral |
|---|---|---|---|
| 1 | C E G | major | I |
| 2 | D F A | minor | ii |
| 3 | E G B | minor | iii |
| 4 | F A C | major | IV |
| 5 | G B D | major | V |
| 6 | A C E | minor | vi |
| 7 | B D F | diminished | vii° |
Read the quality column on its own and it is the pattern worth keeping:
major – minor – minor – major – major – minor – diminished
That sequence is the same for every major scale, and for the same reason the scale formula itself is: nothing in the recipe mentions a particular note. Move the whole scale to a new tonic and every third moves with it, so the qualities cannot change. Learn the sequence once and you know the chords of all twelve major keys.
Why the qualities differ at all
Every chord here is built by the same move, so it is fair to ask why they do not all come out the same. The answer is that the steps of the scale are uneven.
A third taken inside the scale — a note, skip one, the next — spans 4 semitones in some places and 3 in others, depending on where the scale’s two semitone steps happen to fall. Two thirds stacked give the three qualities this field produces:
- 4 then 3 — a major chord;
- 3 then 4 — a minor chord;
- 3 then 3 — a diminished chord, two minor thirds, which the diminished and augmented chords lesson takes further.
The uneven scale is doing all the work. A ruler with evenly spaced marks would give seven identical chords and no harmony worth the name.
The roman numerals
The chords are numbered by degree, in roman numerals, and the numeral carries the quality in how it is written:
- uppercase — a major chord: I, IV, V;
- lowercase — a minor chord: ii, iii, vi;
- lowercase with a small circle — diminished: vii°.
The point of numbering rather than naming is that a numeral describes a position in the key, not a note. The progression I–V–vi–IV is one progression, playable in any of the twelve major keys, and a musician who reads it knows the shape of the music before knowing which key it will be played in. It is also why the same three chords keep appearing: I, IV and V are the three major chords of the field, and an enormous amount of music is built from little else.
Why the seventh degree is diminished
Six of the seven chords are ordinary major or minor triads. The seventh is not, and it is worth seeing why rather than filing it under exceptions.
The seventh degree is the leading tone, sitting one semitone below the tonic. Stack thirds on it and you take the seventh, the second and the fourth degrees. In C major that is B, D and F: B up to D is 3 semitones, D up to F is another 3. Two minor thirds — a diminished chord.
Both of the scale’s semitone steps are involved, and that is the whole cause. Each of those two thirds is squeezed to 3 semitones by one of them, and no other degree of the scale has both squeezed at once. The outer interval comes to 6 semitones, the tritone, the one interval of this size the scale contains — which is why vii° is the single unstable chord in an otherwise settled set, and why it tends to be used as something to move away from rather than a place to rest.
Common mistakes to avoid
- Reading the numerals as note names. V is “the chord on the fifth degree”, whatever key you are in. In one key it is one chord and in another it is a different one.
- Ignoring the case of the letters. ii and II are not the same chord. Lowercase is minor and it is the only thing on the page saying so.
- Expecting the pattern to shift between keys. It does not. Major-minor-minor-major-major-minor-diminished is every major key, always.
- Treating vii° as a mistake in the system. It is the direct consequence of the scale’s semitone steps, and it is where the tension in the key lives.
Now play
The exercise below drills the three qualities the harmonic field produces — major, minor and diminished — but it names each chord outright rather than asking which degree it sits on, so building “the chord on the fourth degree of G major” is something to practise away from the screen for now.
A good way to use it: before you build each chord, say which degree it would be if the key were the one that makes it the tonic chord. The building is the mechanical half; placing a chord inside a key is the half that turns into playing.