Whole-Tone and Diminished Scales: Structure, Spelling and Sound
The whole-tone scale uses only whole steps, and the octatonic scales alternate whole and half steps. Here are their spellings on C and the chords they fit.
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The whole-tone scale is six notes separated only by whole steps, and on C it is C, D, E, F♯, G♯, B♭. The diminished scale, also called octatonic, has eight notes that alternate whole and half steps. It comes in two forms: whole–half, which starts with a whole step, and half–whole, which starts with a half step. Each form fits a different family of chords, which is the practical reason to learn them.
Six notes, all whole steps
Every step in the whole-tone scale is two semitones, so the notes sit at 0, 2, 4, 6, 8 and 10 semitones above C. Six whole steps make exactly one octave.
The scale has no half step, so no note pulls strongly toward another. It has no leading tone, because B is missing, and no perfect fifth, because G is missing. Those absences are the sound. The scale does not sound like a key, and a listener has no clear sense of where home is. Debussy built much of Voiles, from the first book of Préludes, on this scale, and the Debussy and impressionism article places that music in context.
Only two whole-tone sets exist. The set that starts on C♯ (or D♭) is D♭, E♭, F, G, A and B. Starting on any other note produces one of these two. The sets share no notes, and together they contain all twelve pitches.
Every interval inside the scale is an even number of semitones: 2, 4, 6, 8 or 10. A perfect fourth, a perfect fifth and a minor third span 5, 7 and 3 semitones, all odd numbers, so none of them occurs inside the scale. That arithmetic explains much of the sound. The intervals a listener uses to find a key are missing.
Because the two sets are the even and the odd pitch classes, a half step always moves a melody from one set to the other. A melody that uses both sets is therefore using a half step at every change of collection.
Augmented triads and voice leading
The only triads the scale contains are augmented, with two notes four semitones apart and a third note four above that. The set on C holds two of them, C–E–G♯ and D–F♯–A♯, and the set on C♯ holds C♯–F–A and D♯–G–B.
Moving from the first augmented triad to the second keeps every note inside the set. C moves to D, E to F♯ and G♯ to A♯, so each voice rises by a whole step. Because all three voices move by the same interval, the chord changes without any voice crossing another, and the sound stays inside the collection. Each augmented triad is symmetrical, so any of its three notes can serve as its root. That is why whole-tone harmony moves between chords without a clear root, and why a listener hears the change as a change of colour rather than of key.
Eight notes, two orders
The octatonic scale alternates whole and half steps, and it has two forms. Messiaen grouped both collections among his modes of limited transposition, calling the whole-tone scale his first mode and the octatonic his second, because each has only a few distinct transpositions. Each octatonic collection repeats every three semitones, so there are three distinct versions of each.
| Scale | Steps | Spelled on C | Pitch classes | Distinct transpositions | Chords it fits |
|---|---|---|---|---|---|
| Whole-tone | W W W W W W | C D E F♯ G♯ B♭ | 0 2 4 6 8 10 | 2 | augmented triads |
| Whole–half | W H W H W H W H | C D E♭ F G♭ A♭ A B | 0 2 3 5 6 8 9 11 | 3 | fully diminished sevenths |
| Half–whole | H W H W H W H W | C D♭ E♭ E F♯ G A B♭ | 0 1 3 4 6 7 9 10 | 3 | dominant sevenths with a flat ninth |
An octatonic scale cannot spell each letter once. Eight notes need more letters than the seven available, so one letter must carry two notes. The whole–half scale on C repeats A, and the half–whole scale on C repeats E. Those repeats are a consequence of the step pattern, and a score chooses the spelling that matches each note’s role.
Starting on C, the whole–half scale is C, D, E♭, F, G♭, A♭, A and B. It contains the fully diminished seventh chords on C, C–E♭–G♭–A, and on D, D–F–A♭–B. A player who knows the diminished seventh chords article can use this scale over either of them.
Each octatonic collection contains two of the three fully diminished seventh chords, and the third lies outside it. The two forms on the same note are different collections. C whole–half and C half–whole share the four notes of the C diminished seventh and differ on the other four.
Half–whole and the dominant chord
The half–whole scale on C is C, D♭, E♭, E, F♯, G, A and B♭. Its step pattern is H W H W H W H W, and it fits dominant seventh chords with a flat ninth. Spell G7♭9 as G, B, D, F and A♭. Relative to the root, the chord uses 0, 1, 4, 7 and 10 semitones. The half–whole scale on G is G, A♭, B♭, B, C♯, D, E and F, and it contains all five of those pitches.
The same scale fits G7♯9, spelled G, B, D, F and A♯, because the sharp ninth sits three semitones above the root, inside the set.
Finding the scale in a passage
To identify the collection in a passage, list the pitch classes that appear and reduce them to numbers from C. A few pitch classes that fit inside one set do not identify it on their own, because many small groups belong to more than one collection, so check the whole passage before naming the scale. Six classes that are all even numbers from C, or all odd, point to a whole-tone set. Eight classes that alternate by one and two semitones point to an octatonic set. For the octatonic case, read the steps upward from the lowest note. A first step of a whole tone means the whole–half form, and a first step of a half tone means the half–whole form. The names of the chords a passage implies then tell you which collection to expect.
Where this misleads people
The names describe a step pattern, not a mood. “Diminished” comes from the fully diminished sevenths the octatonic scale contains, and it does not describe a dark sound. Reading the name as a mood leads a player to choose the octatonic scale for the wrong reason.
The whole-tone scale has no tonic, so a passage built on it does not establish a key. A player who wants a key centre has to return to a scale with a leading tone. Using the whole-tone scale as a substitute for a major scale removes the pull that makes the major scale work, and the result tends to sound unanchored.
Whole–half and half–whole on the same note are different collections, as the C example above shows. Playing one where the other belongs changes which chords a player can reach, so the spelling and the step pattern have to be checked together.
What to do with it
Play the C whole-tone scale and the D♭ whole-tone scale, and sing each from its lowest note. Notice that the two sets share no notes. Then spell the whole–half scale on E♭ as E♭, F, G♭, A♭, A, B, C and D, and find its two fully diminished sevenths. Last, play the G7♭9 chord on the virtual piano, then the half–whole scale on G above it, and listen for which notes of the scale are chord tones. The church modes article gives the seven-note scales to compare against these six- and eight-note collections.
Questions
What is a whole-tone scale?
A whole-tone scale is six notes separated only by whole steps. Starting on C it is C, D, E, F♯, G♯ and B♭. It has no leading tone and no perfect fifth, which gives it a suspended, unanchored sound.
How many different whole-tone scales are there?
Two. One starts on C and the other on C♯ or D♭. A whole-tone scale started on any other note contains the notes of one of these two sets, so the collection has only two transpositions.
What is the difference between the whole-half and half-whole diminished scales?
Both have eight notes. The whole-half scale starts with a whole step and contains fully diminished seventh chords. The half-whole scale starts with a half step and fits dominant seventh chords with a flat ninth.
Which composer built music on the whole-tone scale?
Claude Debussy built much of Voiles, from the first book of Préludes, on the whole-tone scale. The scale's missing leading tone and missing fifth account for much of the piece's unanchored sound.
