5

I think there's some confusion about the definition of the word 'diatonic'. I'm not using it here to refer to the the prominent primal pattern of the heptatonic scale that has a group of two and three whole steps separated by half steps, but rather as an adjective to describe a note, chord, etc. as being 'of the scale'. In the major scale, I know the diatonic chords to include a major 1, 4, & 5, a minor 2, 3, & 6, and a diminished 7. I'm trying to find out what the diatonic chords would be in a diminished scale. I've done some work down below, and think I've arrived at the conclusion that all eight chords will be diatonic if they are diminished, whether in the half-whole or whole-half dim scale. Is this a correct conclusion? I'm also open to any insight about chord progressions in a diminished key. Note - For the purpose of this question, I'm not concerned with extended chords like 7ths, etc. Only triads with a tonic, third interval, and fifth interval.

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    So would you consider C-E-G to be "of the C half-whole diminished scale"? – Your Uncle Bob Jul 7 at 20:34
  • I don't believe there's a 'diminished key'. Certainly diminished scales, but that doesn't mean there will be a 'key'. There's the 'whole tone scale', but no 'whole tone key'. – Tim Jul 8 at 4:25
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    Several of the note names should be spelled enharmonically. – Tim Jul 8 at 4:31
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    I'm confused about your destructive edit: it seems that you have some good comments and answers here, and I don't see any snide comments.... – ex nihilo Jul 8 at 14:58
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    @EthanRichardson, I really hope you restore your question, because it is a good one. In my answer I tried to explain about the scale spellings which was the point of one of the comments about the source you used. Keep in mind you got 2 up votes on your question. That indicates the community believes it a good question!!! – Michael Curtis Jul 8 at 15:03
5

If you consider every chord made up of notes from a diminished scale to be "of the scale", then a diminished scale contains not just diminished triads. The diminished scale is highly symmetrical, so to find triads in a diminished scale you only have to consider a small number of candidates, which you can then transpose to get the full list.

Let's look at the C half-whole diminished scale:

C  C# D  Eb E  F  F# G  Ab A  Bb B
*  *     *  *     *  *     *  *

We'll only look at triads starting on C or C#:

C  C# D  Eb E  F  F# G  Ab A  Bb B
*        *        *       (*)       Cdim
*        *           *              Cm
*           *        *              C
   *        *        *       (*)    C#dim

To get the full list of triads, we transpose these four chords in steps of three half-tones:

Cdim    Ebdim    F#dim    Adim
Cm      Ebm      F#m      Am
C       Eb       F#       A
C#dim   Edim     Gdim     Bbdim

This is the list of 16 triads for C half-whole diminished, but also for:

C  half-whole diminished
Eb half-whole diminished
F# half-whole diminished
A  half-whole diminished
C# whole-half diminished
E  whole-half diminished
G  whole-half diminished
Bb whole-half diminished

because these eight diminished scales are enharmonic, they are made up of the same notes. There are two further "families" of diminished scales: the scales above transposed 1 half-tone step up, and the scales above transposed 1 half-tone step down.

To find the 16 triads for a diminished scale from one of the other two "families", check whether it is a scale in the list transposed a half-tone up or down, and then transpose the 16 triads a half-tone up or down.

You will notice that the list of 16 triads for one "family" of enharmonic diminished scales contains 4 major triads, 4 minor triads, and 8 diminished triads. This means that two non-enharmonic diminished scales share 4 diminished triads, but no major or minor triads. E.g. the C half-whole diminished scale and the C# half-whole diminished scale share these triads:

C#dim   Edim     Gdim     Bbdim

while the C half-whole diminished scale and the B half-whole diminished scale share these triads:

Cdim    Ebdim    F#dim    Adim
2

Yes.

The diminished scale is symmetrical: every third is the same distance as all the other thirds. Since all the thirds are minor thirds, all the chords that naturally occur in the scale will be m3+m3 = a diminished triad.

The same will be true of the whole tone scale: every third is a major third, so every triad will be augmented.

1

The other answers provide a lot of information and go into a lot of technical detail. I could list all the nuts and bolts as well, but it seems like you are just discovering music and want a simpler algorithm to memorise, perhaps.

There are 2 diminished scales, each has 8 notes per octave. You can think of those notes as being odd or even in number (for the C half-whole diminished scale, note 1 would be C, the root, and note 2 would be C#).

In terms of chords, both half-whole and whole-half diminished scales follow a very predictable pattern:

  1. The half-whole diminished scale

    Every odd note produces a major triad[1], a minor triad[2] and a diminished chord[3]. Every even note produces just the diminished triad.

  2. The whole-half diminished scale

    The pattern gets reversed: now every odd note produces just the dimished triad, and every even note produces a major triad, a minor triad and a diminished chord.

It's that simple!


1 The formula for the major triad is 0-4-7 (where 0 is the root, and every other number denotes how many semitones away from the root the next note is) or R-W+W-W+H (where W is a whole tone and H is a semitone).

2 The formula for the minor triad is 0-3-7 or R-W+H-W+W.

3 The formula for the diminished triad is 0-3-6 or R-W+H-W+H.

1

The diminished scale is often used with the 7b9 family of chords. C half-whole diminished is associated with the C7b9 chord:

C E G Bb Db

(the whole scale is C Db D# E F# G A Bb... notice that you have a major 3rd between C and E thanks to skipping over both Db and D#)

Edim7 is the same chord as C7b9 without C in the bass, so they're often completely interchangeable.

You can create very nice extended chords by adding-in other notes from the C diminished scale:

  • C E G Bb Db A (C13b9)
  • C E G Bb Dd F# (C7b9#11)
  • C E G Bb Db D# (C7b9#9)
1

This question seems to hinge on how things are spelled - including enharmonic spellings - and the effect of spelling on interval names.

If the diminished scales are spelled as two superimposed diminished seventh chords, we get...

|C  |Eb  |Gb  |Bbb  |
|  D|   F|  Ab|   Cb| 

...or...

|C  |Eb  |Gb  |Bbb  |
| Db|  Fb| Abb|  Cbb|

Let's use the second scale for examples. We can make a chord C Fb Abb and enharmonically re-spell it to C E G. The first chord C Fb Abb is a diminished fourth and a minor third. The other spelling is a major third and a minor third.

We could re-spell the scale so that the two superimposed diminished seventh chords structure is obscured:

|C  |Eb |F# |A  |
| Db|  E|  G| Bb|

With that spelling we can make C E G without any enharmonic re-spellings.

Of course the issue here is the gamut (the seven letters) are for a heptatonic diatonic scale, but the diminished scales are octatonic, and the naming of intervals is first based on the position in the letter sequence and then qualified by the size in semi-tones.

When tertian chords are built the spelling details matter. C E G is two stacked thirds where the specific qualities are major third and minor third. C Fb Abb is NOT two stacked thirds. It is a diminished fourth and a minor third. If our "diatonic" chords are to be tertian triads in root position, then C Fb Abb is not a diatonic chord, but C Eb Gb or Db Fb Abb would be diatonic chords.

For what it's worth, when the second scale of superimposed diminished seventh chords is used and we have chord like Abb Cbb Db it's is enharmonically equivalent to a diminished triad, but as spelled it is an inverted diminished seventh chord with the third tone omitted.

Are all diatonic [of the scale] chords in the diminished scale diminished?

I think "yes" provided that the chords are tertian and the scale is spelled as two superimposed seventh chords.


EDIT

Part of the discussion with this question is about the possibility to construct a major triad in the diminished scale and should that be considered diatonic.

In my initial answer where the diminished scales were constructed from superimposed diminished seventh chords I said "no" because the chord spelling used a diminished fourth.

However, you could construct the diminished scale using superimposed major triads and get different spellings...

scale degree: 1  2  3  4  5  6  7  8  1  2  3  4
              C  Db Eb E  Gb G  A  Bb C  Db Eb E
              | (C#)|  |  |  |  |  |    (C#)   |
              ----------------  |  |     |     |
                    |     |  |  |  |     |     |
                    ----------------     |     |
                          |     |  |     |     |
                          ----------------     |
                                |        |     |
                                ----------------

The three chords are C, Eb, Gb, and A all major triads in a sequence of chromatic mediants. The A chord needs an enharmonic respelling of Db to C#.

You could then harmonize the scale with a series of alternating root and first inversion triads:

C A6/3 Eb C6/3 Gb Eb6/3 A Gb6/3 | C

Now you could say all the 'diatonic' chords of the diminished scale are major triads.

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    I think of chords that come from enharmonic spellings of scales as potential scale applications, but might say in a sloppy moment that those chords are in the scale. In practice, these enharmonic applications make melodic minor, harmonic minor, and pentatonic scales (to name the most common) very flexible. – ex nihilo Jul 8 at 15:03
  • "potential scale applications..." sure. I don't mean to say C E G or other enharmonic spellings could not be used. But I don't think that is the main point of the question. It seems to be about unpacking the meaning of diatonic when switching from heptatonic to octatonic. – Michael Curtis Jul 8 at 15:15
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    When I asked "would you consider C-E-G to be of the C half-whole diminished scale?" the OP said "yes, I would consider the notes and the C major chord they form as being of the diminished scale". This (and his anger about terminology nitpicking in the comments) led me to believe that his question was quite practical, and not concerned with the subtleties of whether C-E-G and C-Fb-Abb are the same. – Your Uncle Bob Jul 8 at 20:49
  • I don't think I would call anything 'practical' when working with an octatonic scale! I only wanted to point out that the spelling of the scale can make a difference deciding what "diatonic" should mean in an octatonic system. – Michael Curtis Jul 9 at 13:37

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