Triples of Diminished Triads
Here's a little thing I found while experimenting with the complement of the quartal triad from this post (more on that to come). It turns out there are a few more ways to combine three diminished triads without any overlaps than I'd expected and, as usual, I found some unpromising globs of semitones with musical possibilities hidden inside them.
We may as well get the list out of the way -- here they all are:
| Combination | Resulting Notes | Forte Number |
|---|---|---|
| Cdim + C#dim + Ddim | ['C', 'C#', 'D', 'D#', 'E', 'F', 'F#', 'G', 'G#'] | 9-1 (Chromatic) |
| Cdim + C#dim + G#dim | ['C', 'C#', 'D', 'D#', 'E', 'F#', 'G', 'G#', 'B'] | 9-4A |
| Cdim + C#dim + Fdim | ['C', 'C#', 'D#', 'E', 'F', 'F#', 'G', 'G#', 'B'] | 9-4B (inversion of the previous one) |
| Cdim + Ddim + Edim | ['C', 'D', 'D#', 'E', 'F', 'F#', 'G', 'G#', 'A#'] | 9-6 |
| Cdim + Ddim + Gdim | ['C', 'C#', 'D', 'D#', 'F', 'F#', 'G', 'G#', 'A#'] | 9-9 |
| Cdim + Edim + G#dim | ['C', 'D', 'D#', 'E', 'F#', 'G', 'G#', 'A#', 'B'] | 9-12 (Messiaen Mode 3) |
These are mostly very chromatic, which isn't surprising when you're using 9 of the 12 available notes. If you play them as scalewise runs they're not likely to sound very interesting; the whole point is to think of them as congregations of diminished triads and see where that leads us. It's perhaps more interesting that 9-6 and 9-12 contain the Whole Tone scale -- making this out of diminished triads seems like an unhinged idea, and of course we get some extra notes as well but I think those tend to make whole tone harmony more spicy anyway.
In terms of common seventh chords and the augmented triad, all these scales contain at least one of each but in different proportions. 9-1 contains the fewest of each, which isn't too shocking. Apart from 9-9, the rest contain multiple augmented triads -- the most interesting of these might be the ones that aren't Whole Tone scale supersets. 9-12 contains a whopping six different Maj 7 chords. 9-4B contains five Min 7 chords (9-4A has "only" four). Unsurprisingly, perhaps, 9-12 contains the richest set of common chords, since its notes are the most evenly spread.
There's another way to see 9-4A and 9-4B that I think is suggestive for my general approach. Each of them is the Coltrane Cycle (three major 7 chords separated by major thirds) with an extra major seventh a semitone away from one of them -- this additional "side-slipped" chord is slipped down a step in 9-6A and up in 9-6B.
We may as well get the list out of the way -- here they all are:
| Combination | Resulting Notes | Forte Number |
|---|---|---|
| Cdim + C#dim + Ddim | ['C', 'C#', 'D', 'D#', 'E', 'F', 'F#', 'G', 'G#'] | 9-1 (Chromatic) |
| Cdim + C#dim + G#dim | ['C', 'C#', 'D', 'D#', 'E', 'F#', 'G', 'G#', 'B'] | 9-4A |
| Cdim + C#dim + Fdim | ['C', 'C#', 'D#', 'E', 'F', 'F#', 'G', 'G#', 'B'] | 9-4B (inversion of the previous one) |
| Cdim + Ddim + Edim | ['C', 'D', 'D#', 'E', 'F', 'F#', 'G', 'G#', 'A#'] | 9-6 |
| Cdim + Ddim + Gdim | ['C', 'C#', 'D', 'D#', 'F', 'F#', 'G', 'G#', 'A#'] | 9-9 |
| Cdim + Edim + G#dim | ['C', 'D', 'D#', 'E', 'F#', 'G', 'G#', 'A#', 'B'] | 9-12 (Messiaen Mode 3) |
These are mostly very chromatic, which isn't surprising when you're using 9 of the 12 available notes. If you play them as scalewise runs they're not likely to sound very interesting; the whole point is to think of them as congregations of diminished triads and see where that leads us. It's perhaps more interesting that 9-6 and 9-12 contain the Whole Tone scale -- making this out of diminished triads seems like an unhinged idea, and of course we get some extra notes as well but I think those tend to make whole tone harmony more spicy anyway.
In terms of common seventh chords and the augmented triad, all these scales contain at least one of each but in different proportions. 9-1 contains the fewest of each, which isn't too shocking. Apart from 9-9, the rest contain multiple augmented triads -- the most interesting of these might be the ones that aren't Whole Tone scale supersets. 9-12 contains a whopping six different Maj 7 chords. 9-4B contains five Min 7 chords (9-4A has "only" four). Unsurprisingly, perhaps, 9-12 contains the richest set of common chords, since its notes are the most evenly spread.
There's another way to see 9-4A and 9-4B that I think is suggestive for my general approach. Each of them is the Coltrane Cycle (three major 7 chords separated by major thirds) with an extra major seventh a semitone away from one of them -- this additional "side-slipped" chord is slipped down a step in 9-6A and up in 9-6B.
Rather than packing a lot in here, most of these probably deserve their own blog posts, so I'll get onto that.
[Unrelated coda: I finally moved house last month and set my sights on an ambitious (for me) studio build in the new place. "Do it the right way from the beginning," I said from the comfort of my armchair. Now of course I'm cursing my sensible former self because I don't have anything much to make music with and won't for a while yet -- instead I have a long list of tasks to get done, some of which involve skills on which I have only the most tenuous of grasps. I certainly won't bore you with all that but maybe I'll post some reflections on setting up a small home studio space if I think I've learned anything in the process...]
[Unrelated coda: I finally moved house last month and set my sights on an ambitious (for me) studio build in the new place. "Do it the right way from the beginning," I said to myself. Now of course I'm cursing my sensible former self because I don't have anything much to make music with and won't for a while yet -- instead I have a long list of tasks to get done, some of which involve skills on which I have only the most tenuous of grasps. I certainly won't bore you with all that but maybe I'll post some reflections on setting up a small home studio space if I think I've learned anything in the process...]
