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I'm reading about some jazz stuff, and get told there are ony two whole tone scales, and three diminished scales. The whole tones are pretty obvious - once you get past the second semitone, you're into a mode of the original one. But - I thought there were the whole/half and the half/whole diminished scales, so what's the third one? Unless the writer conflated scales and arpeggios, whereby the notes of say, Co, C♯o and Do are all different, but when we arrive at E♭o, that's a mode of the first, Co?

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  • whole + half = 3 half steps. If a pattern repeats every 3 half steps, it can only have 3 versions. Proof: the one starting on C goes C, D, Eb F Gb. Now look at the one starting on Eb, and you'll see it's the same collection of notes. The other way to look at it is C has 2 of them, but one of them doesn't have a C at all. Aug 17 at 2:09
  • They mean the somewhat abstract observation regarding counting scales as a set of pitch classes. So, up to starting note, there are only two distinct whole tone scales: 0, 2, 4, 6, 8, 10; and 1, 3, 5, 7, 9, 11. Similarly, there are only three distinct diminished scales up to starting note: 0, 1, 3, 4, 6, 7, 9, 10; 0, 2, 3, 5, 6, 8, 9, 11; and 1, 2, 4, 5, 7, 8, 10, 11.
    – Brian Tung
    Aug 18 at 19:56
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There are three unique whole-half (or half-whole) diminished scales starting a half-step apart from each other. Each one has an equivalent half-whole (or whole-half) diminished scale starting a whole step (or half step) above it.

Equivalences between whole-half and half-whole diminished scales

Whole-Half scale | Half-Whole scale
starting pitch   | starting pitch
-------------------------------------
C, Eb, Gb, or A  | D, F, Ab, or B
C#, E, G, or Bb  | C, Eb, Gb, or A
D, F, Ab, or B   | C#, E, G, or Bb

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  • So doesn't that make six different diminished scales..?
    – Tim
    Aug 16 at 16:19
  • Simple, really, innit?
    – Tim
    Aug 16 at 16:21
  • @Tim Another way to look at it is that W-H and H-W are two different scales, and there are three unique versions of each. In that way it's like saying there are 12 major scales and 12 (natural) minor scales, even though they only differ according to their starting pitches.
    – Aaron
    Aug 16 at 16:24
  • Thanks. I was considering that the writer (a certain Jamie) was considering a diminished seventh arp. as a scale - when there wuld in fact be three different ones - and their modes.
    – Tim
    Aug 16 at 16:27
  • 1
    Calling H/W and W/H the "same" is like say phrygian and lydian are the same, because they are rotations of the diatonic scale. Aug 16 at 17:20
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only two whole tone scales, and three diminished scales.

They just mean that when you account from transposing the scales there are only 2 unique sets of tones for the whole tone scale, and 3 for a diminished scale.

But they are overlooking there are two diminished (or octatonic) scales.

In terms of interval structure there is one whole tones scale - all whole steps, and two octatonic scales - one alternating whole and half steps, the other alternating half and whole steps.

When you transpose a whole tone scale by a whole tone, you get the same set of tones.

When you transpose a diminished/octatonic scale by a minor third, you get the same set of tones.

If you take the rotations, or modes, of the scales instead of transpose them, something funny happens. All rotations of a whole tone scale produce the same set of tones just like transposing by a whole step. But, with the diminished scale, every other rotation produced the same set of tones or the "opposite" diminished scale, for example take second rotation of a W/H diminished scale and you get a H/W diminished scale.

If, for some reason, you treat the first and second rotation of a diminished scale to be the same thing, then there are only 3 diminished scales.

If you treat octatonic scales as just embellishments of a diminished seventh chord, then I guess it sort of makes sense to treat W/H and H/W as the same.

If you realize that W/H octatonic has a perfect fourth above the tonic, and H/W has diminished sixth - enharmonically equivalent to a perfect fifth - that's a significant structural difference, and W/H and H/W are different scales. With H/W you can construct major, minor, and diminished triads above the tonic.

Coincidentally, I recently was looking at my scale syllabus from a certain Jamey, for a dominant seventh flat nine chord. He gives the diminished scale, but only the H/W version. That makes sense, because it provides the flat nine. But, that also underscores the two diminished scales are not necessary to be treated as the same.

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  • I think it's the way he phrased the whole thing. There were a couple of other iffily phrased bits too. Producing 'educational' documents, I feel it's of paramount importance to eliminate all statements which may, even in the least, be construed as ambiguous.
    – Tim
    Aug 16 at 17:24
  • I find a lot of jazz pedagogy unclear and, at least for me, prompts lots of follow up questions. It's almost always confusion about the wording and terminology. Aug 16 at 18:19
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As far as I’m concerned there are 12 whole tone scales, 12 W/H diminished scales and 12 H/W diminished scales. The two diminished scales I mentioned are separate entities. I’ve never agreed with the “there are only 2 whole tone scales” etc. explanation. Of course several of the scales share notes but I approach them as individual entities. Just as I don’t think of E Phrygian as a C scale from E to E I don’t think of a E whole tone scale as a C whole tone scale from E to E. The tonal center of a scale should have some importance, even if it shares notes with 4 or 6 other scales.

Based on his logic of “only 2 whole tone scales”, the writer is definitely thinking of a single diminished scale in 3 chromatic positions, C, C#, D and saying everything else just comes from there.

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  • We may be getting into the realm of 'when is a mode a scale, when is a scale a mode' territory...
    – Tim
    Aug 17 at 7:01
  • @Tim I’d say pretty much always in both cases… Aug 17 at 16:43
  • I can't make up my mind - a scale is a set of notes put into an order - ascending/descending. But Dorian, Phrygian, Lydian, etc., are almost always referred to as modes. To me, a mode is an inversion of a known (accepted) scale. A question may be coming on...
    – Tim
    Aug 17 at 16:49
  • @Tim Everyone brace yourselves! Aug 17 at 16:53

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