Whole-Tone and Octatonic Scales

Every scale so far has had uneven spacing. The major scale runs whole-whole-half-whole-whole-whole-half; Dorian runs whole-half-whole-whole-whole-half-whole. That unevenness is what gives a scale a face.

It is also what lets you hear where the tonic is. With only two half steps, their positions serve as landmarks telling you where you are.

This lesson takes up evenly spaced scales.

Whole-tone — an octave of whole steps

Stacking whole steps alone divides twelve half steps into twos, returning to the octave after six notes.

This scale has no face. Starting from any note produces the same shape, so listening gives you no way to tell where you are.

Concretely, here is what is lost.

• no leading tone — nothing sits a half step below the tonic
• no perfect 5th — every pair of notes spans a multiple of two half steps, never seven
• no major or minor triads — stacking thirds always produces an augmented triad

The absence of the perfect 5th is decisive. Without the interval that frames a chord, the machinery of functional harmony cannot be assembled.

And there are only two whole-tone scales. Starting from C or from D collects the same six notes. One group is C, D, E, F♯, G♯, A♯ and the other D♭, E♭, F, G, A, B. The twelve pitches divide in two, and that is all of them.

Whole-tone against the major scale

▶C major scale▶Whole-tone on C▶Augmented triad

Check: The first is an ordinary major scale, and reaching the top feels like arriving. The second is whole-tone, and going up produces no sense of landing, because with no half steps anywhere the ear cannot decide where the endpoint is. The third is an augmented triad drawn from it, where again no note can be identified as the root. The price of evenness is the loss of a center.

two half steps

Check

Why does stacking thirds in a whole-tone scale always produce an augmented triad?

There are two kinds of minor 3rdThere is no fifth degreeSkipping every other note always gives a major 3rd, and two stacked major 3rds make an augmented 5thThe scale does not have seven notes

Check answer

Octatonic — alternating whole and half steps

Alternating whole and half steps returns to the octave after eight notes.

There are two ways to begin, hence two names.

Name	Pattern	On C
Whole-half diminished	W H W H …	C D Eb F Gb Ab A B
Half-whole diminished	H W H W …	C Db Eb E Gb G A Bb

The two are the same scale. Reading the whole-half form from its second note gives the half-whole form. Which name you use depends on which note you are treating as the root.

• whole-half — used over a diminished seventh chord
• half-whole — used over a dominant seventh

And there are only three octatonic scales, because raising the root by half steps returns to the original collection on the third move.

Diminished seventh chords are limited to three for the same reason

The diminished seventh chord of Unit 3 was three stacked minor 3rds. A minor 3rd is three half steps, so counting from the root gives 0, 3, 6, 9 — and the next stack reaches 12, exactly an octave.

Four minor 3rds make exactly an octave. That evenness is what makes the diminished seventh chord symmetrical.

So a diminished seventh chord may be assigned any of its notes as root. Cdim7 is equally E♭dim7, G♭dim7, and B♭♭dim7. That ambiguity is a second doorway into the enharmonic modulation of Unit 8: one diminished seventh can resolve in four directions.

Raising a diminished seventh by half steps

▶Cdim7▶C#dim7▶Ddim7▶D#dim7

Check: Starting from Cdim7 and moving up a half step each time. The first three should sound distinct from one another. Listen to the fourth again — it has returned to exactly the collection of the first. The cycle closes after three, so there are only three diminished seventh chords in existence.

first

Where altered tensions come from

The previous lesson listed four altered tensions for the dominant seventh. Those are not improvised decoration; they are extracted from a symmetrical scale.

The half-whole diminished scale on C is C D♭ E♭ E G♭ G A B♭. Remove the notes of C7 (C E G B♭) and what remains is D♭, E♭, G♭, A.

Remaining note	Relative to C7
Db	♭9
Eb (= D♯)	♯9
Gb (= F♯)	♯11
A	13

Superimposing the half-whole diminished scale on a dominant seventh yields ♭9, ♯9, ♯11, and 13 automatically. The claim in the previous lesson that altered notes are freely available above a dominant seventh rests on this scale sitting behind them.

Note, however, that ♭13 is not in the scale — on C7 that would be A♭, and the half-whole scale has the natural 13th A instead. Producing a ♭13 calls for a different scale, typically one derived from the whole-tone collection. The notes of C7(♯5♯11) — C, E, G♯, B♭, F♯ — all belong to the whole-tone scale on C.

Check

What is the most accurate reason symmetrical scales were used as color in the twentieth century?

They had not been used in older musicThey contain many notesThey are difficult to performNeither tonic nor leading tone is fixed, so they produce sonorities detached from tonal gravity

Check answer

▶ Play the whole-tone scale in the scale dictionary On the keyboard the notes are evenly spaced rather than alternating white and black in the usual pattern. Switch to the two diminished scales on the same screen and compare Scale Dictionary →

Symmetrical scales trade a center for evenness. The next lesson exploits symmetry the other way, using the symmetrical structure of the dominant seventh’s tritone to replace one chord with another.