Harmony in Yagapriya

I recently revisited this post in search of some new harmonic ideas and thought I'd take a closer look at Yagapriya, a rather exotic scale for us Westerners that's very far removed from the diatonic scales we're used to. It also doesn't harmonize easily using my usual tricks so I wanted to treat it more as a unique thing in itself and see where it led me. (As usual I'm using "Yagapriya" as the name for a 12EDO scale; I won't have anything to say about Carnatic music in this post.)

In terms of the major scale, Yagapriya is 1 #2 3 4 5 b6 bb7. If you look at the intervals, we have a groupd of three chromatic notes, #2-3-4, and another, 5-b6-bb7, separated by a whole tone. The only note that isn't in one of these groups is the root, which is a minor third away from both groups. So although it isn't symmetrical in the usual sense, it feels like it has a lot of symmetry to its structure. A clockface might make that more explicit:

As an aside, applying M5 or M7 to this scale produces this one, which is even more exotic and doesn't have a sensible name -- I'm not going to say anything more about this for now but these two scales do seem like they'd be quite closely related:

Anyway, back to Yagapriya. The easiest way to think of it as a scale is probably as a minor six pentatonic (1 b3 4 5 6) plus two notes: the major third and minor sixth. if you know the minor six pentatonic, that's probably enough to get you playing the scale but not enough to bring out its harmonic properties. I'll assume we're using C Yagapriya (C-Eb-E-F-G-Ab-A) as our source of notes, and yes I'm spelling it with flats because that's what makes the most sense to me for now.

I'm mostly interested in the unusual stuff but let's start by noticing some triad-based chords in the scale; I think these come in three pairs. One is the fairly obvious C6 and Cm6; another is FMaj7 and Fm7. notice these are both pairs of different chords with the same root note. the last pair is a slight variation: AbMaj7 and Am7, which means we also have Am7b5 too if we want it. Together these cover off all the notes of Yagapriya and nothing else and for such a dissonant scale they make rather tame, insipid harmony that just drifts from chord to chord without much in the way of tension. That might sometimes be useful but it's not very exciting (and it's an easy effect to get by much less convoluted means).

Now for the more spicy stuff. Yagapriya contains not one but two all-interval tetrachords, Eb-E-G-A and Eb-F-Ab-A. Both are 4-z15 and they're inversions of each other (shown here by the fact they're mirror images of each other):

Notice these two AITs also cover the whole scale except for the root, meaning they can express the scale quite well all on their own. However, AITs are great to play on the keyboard but not so much fun on guitar, where voicing options are limited and often a bit awkward. Here are some suggested ways to play them, assuming we're still in the context of C Yagapriya:

Another interesting tetrachord in this scale is Eb-E-Ab-A (Forte 4-8), which is a bit like a Lulu chord but different. In fact it appears in the major scale (as B-C-E-F in C major) and it's one of my favourite diatonic quartal chords so I was pleased to find it. Here are a few ideas for fingerings (don't try to play these across all 6 strings unless you're a bit more flexible than I am)

You might enjoy locating these in the major scale, too, as that kind of thing often opens up new approaches to old material.

I did run into one other interesting chord that deserves a bit more investigation: C-E-G-Ab, which you could think of as AbMaj7#5. I love this chord, especially as an arpeggio -- see my previous discussions of it here and here -- there's already a good bit of duplication between those two posts so I won't make it worse by repeating them again here. In case you think I just make all this stuff up, here's an article about using Maj7#5 chords in a jazz context.

I appreciate this amounts to a list of chords you can find in Yagapriya but doesn't really give you much harmony. My own approach to harmony tends to be more about voice-leading than "chord progressions" but it's useful to at least classify these chords by how they strike your ear. For me the AITs and the 4-8 can function a like quartal or suspended chords; they have more colour and "grit" than the triadic chords but only a little. The AbMaj7#5 is the only thing here that gives dominant vibes but even so it doesn't have a Db or G chord to resolve to. So although we've found a bit more dissonance I don't think we've strayed too far from the rather plain, open sounds of the triadic chords.

Naturally we can make more spikey sounds if we want -- for example, we have the chromatic trichords Eb-E-F and G-Ab-A if we want that. Here are some ways to play the Eb-E-F one:

But dissonance isn't the same as harmonic tension and I don't think these "call for resolution" in a way that could imply a dominant function either. This isn't too surprising given that Yagapriya is so far removed from the diatonic home of tonal harmony.

I'm inclined instead of think of Yagapriya as a kind of harmonic desert landscape, offering plenty of pretty vistas but not much in the way of clear routes forward: it suggests lingering and drifting rather than making progress. Indeed, it's a part of that much vaster wilderness of harmonies beyond the built-up regions of mostly-diatonic scales where the roads are paved and we already know where they lead.