The harmonic field figure
A scale on one wheel, home on top, and the chord on every degree built in front of you — its notes marked one by one, the rest closed, the chord extracted — with a row of small wheels beneath, one a degree, each in its own frame.
Stack thirds on every note of a scale and you get the scale's chords — its harmonic field. This figure builds them in front of you, on the wheel rather than the neck, because the argument it serves is about which notes a chord has and which it lacks, and a fretboard shows one voicing and no missing note. It is the figure of Why the major modes.
What it shows
One big wheel is the scale, home on top, its notes named round the rim in the scale's own spelling — G♯ in A harmonic minor, not A♭. A row of small wheels beneath it, one per degree, is the chord built on each, and every small wheel is drawn in its own frame with its root on top. That is what lets a row be read at a glance: a major scale's row is three of one picture, three of another and one odd one; an augmented triad's symmetry is visible; a diminished one looks like nothing else in the row.
The build is the app's own choreography. For one degree at a time, the chord's notes are marked on the big wheel one after another — root, third, fifth, the stack as it is stacked — then the rest of the scale closes and the colors shift so the chord's root wears the root color: the chord extracted. Then the scale reopens and the next degree is up. The small wheel being built lifts while it is.
A pentatonic tried on every degree is what the app never shows and this figure exists for. Where the triad's third is major the attempt is a major pentatonic, where minor a minor one; a note the attempt needs and the scale doesn't have is a hollow wedge — dashed, no fill — where it would be. The attempt marks it like the others and then fails: nothing is extracted, the hollow wedges fade, and the degree's small wheel keeps its hole. In a major scale six degrees succeed and only the seventh fails; in A harmonic minor every one fails.
Every degree counts. The diminished and augmented chords are drawn like the rest, never hidden — unlike the app's nest explorer, which drops a chord with a tritone above its root.
What you can do
- Triads · Tetrads · Pentatonics change the size of chord built on each degree.
- With a minor scale up, natural · harmonic · melodic minor switch between the three; the alternatives are the essay's argument.
- Tap a small wheel to hold that degree — the chord built once and left extracted — and hear it, in pure sines. Tap again and the cycle goes on.
- Left alone, the figure cycles through the degrees while it is on screen, and stops when it isn't.
The state is in the address: #field=A.harmonicMinor.triads is a scale, …triads.3 holds the chord on its third degree, and .gaps holds the scale still with its semitone pairs marked and the notes rather than the chords beneath — the essay's sections about the steps rather than the chords. A chromatic type, all twelve in gray with a cluster on every degree, and a fifths.<n> walk are reachable by link too.
Where it appears
Pinned under Why the major modes, sharing a frame with the circle of fifths — the circle for the walk that opens the essay, the field from "look what is inside" on — and on the Why Major Modes? page in the curriculum.