The formless form of divine light that dwells in all the temples of Kartikeya sounds like it would be pretty far out, if it were a musical scale, and indeed it is. Jyoti Swarupini is an unusual Carnatic scale that hasn't come up too often before in these parts so I thought I'd have a look at it. No more mangling of Hinduism, I promise.

What is Jyoti Swarupini?

We'll start with a bit of music, although I don't know the name of the performer or anything else about this one:

Here's the scale's entry from the book:

A jazz-inclined Westerner will likely see this as a dominant chord with added #9, #11 and b13. The #11 and b13 are easy to find as a chromatic enclosure around the fifth and the #9 is a b3, which can come off as a "blue note". If the 5 wasn't there, this would be a very straightforward altered dominant sound that belonged in a jazz setting, but it is and that puts the #11 and b13 on a more tonally uncertain footing.

However, I'd like to look at this another way. Considering C to be the root, mix the notes of the C7 and Ab7 arpeggios; they overlap on the note C and cover the whole scale. This is a peculiar pairing of chords -- you could maybe think about it as C7 - D7, with Ab7 being the tritone sub for D7, but that seems like a stretch. It sounds more like Debussy than Bird.

Anyway, my business here is to look at Jyoti Swarupini (JS) as this combination of two dominant sevenths a major third apart. The main motivation for this is that while JS itself is pretty easy to find and understand, all its modes are quite far out and very much not the kind of thing I'd be likely to organically think of playing.

The Modes of Jyoti Swarupini

In each case I'll always take the root note to be C and talk about how to find the pair of dominants relative to that. When you write it down that seems like a lot of steps but it works out a bit easier on the instrument once you get used to it. Here's a quick list, using names from the book:

• Suspended Augmented Scale: Bb7/D7 over C root (1 2 #3 #4 #5 6 b7). This does indeed have a pretty suspended quality due to its lack of either a third or a fifth.
• Semidominant Augmented Scale: C7/E7 over C root (1 2 3 ##4 #5 #6 7). The mode that has the other dominant chord at the root, but this is more of a major 7 sound to me as it's a near neighbour to the Coltrane Cycle, where we'd play EMaj7 over CMaj7.
• Kolikapriya #5 Scale: Db7/F7 over C root (1 b2 b3 4 #5 6 7). The chromatic enclosure of the root with major seconds either side of it gives this a somewhat Neapolitan quality; it works similarly as a mysterious minor 6 sound but the #5 distances it a bit more from triadic harmony.
• Phrygian Semidominant Scale: D7/F#7 over C root (1 b2 bb3 b4 b5 6 b7). Weirdly close to Lydian Dominant, but with the leading tone b2 instead of a nice stable 5.
• Semidiminished Scale: E7/G#7 over C root (1 2 b3 b4 b5 b6 7). Again, the E7 makes this sound Coltrane-Cycle-adjacent to me with a nice altered Harmonic Major kind of vibe. I think this could make for pretty melodic material.
• Ultra Locrian bb5 Scale: F7/A7 over C root (1 b2 b3 b4 bb5 bb6 bb7)

A More Systematic Perspective

The Coltrane Cycle connection is a clue to how to unify this into something more like a "system" by looking at the combination of three dominant chords separated by major thirds, for example C7 (C-E-G-Bb), E7 (E-G#-B-D) and Ab7 (Ab-C-Eb-Gb).

This leads us to think of the modes in triples of dominant chords build on the notes of augmented triads. The result is three groups of three scales, which includes a pair of octatonics that arise as hypermodes of Jyoti Swarupini with the root added back in (I'll say a bit more about them shortly). Here they all are, again with C as the root throughout, and with my very subjective impression of their prevailing effect:

• The C7/E7/G#7 complex: Jyoti Swarupini, Semidominant Augmented, Semidiminished -- altered dominant sounds
• The Db7/F7/A7 complex: Kolikapriya #5, Ultra Locrian bb5, Forte 8-19 (Db7/A7 over C) -- diminished sounds
• The D7/F#7/A#7 complex: Suspended Augmented, Phrygian Semidominant, Forte 8-24 (F#7/A#7 over C) -- Lydian Dominant sounds

We should note that there's another triple Eb7/G7/B7 that gives all octatonics if you take C to be the root. Those seem to be quite a lot messier than the others but they have an intriguing sound that's much harder to squeeze into a jazz frame so they're probably worth investigating further.

Observations about 8-19 and 8-24

These arise from the fact that some pairs of dominant chords discussed above don't contain the root note (C), so when we add that in we get eight notes instead of seven. I feel like in this context they're best understood as part of their three-arpeggio complexes but it's worth having a look to see what they contain.

Forte 8-19 is the complement of the minor-major seventh chord -- the EbmM7 chord to be precise. Forte 8-24 is the complement of B7#5. These are interesting chords but I don't think they help us make much sense of these octatonics in connection with the general system of "dominants going around augmented arpeggios".

Instead let's look at what these octatonics share -- both contain the hexatonic 6-z4, which is two clusters of three semitones separated by a whole tone. For example, with root C, 8-19 contains the 6-z4 instance [G-G#-A]-[B-C-C#] while 8-24 contains [C-C#-D]-[E-F-F#]. This structure bunches all six notes down one half of the octave, leaving major third (between G and B inclusive) available to be filled in.

Visually we could represent the available notes using zeros: 00000. We're looking at ways to fit two notes into this gap but we don't want to spoil the character of 6-z4 so we'll avoid adding a note that directly abuts it. That leaves three notes in the middle, and three possible ways to add two notes: 00110 (adding A and A#), 01010 (adding G# and A#) or 01100 (adding G# and A). The first is 8-19 (Db7/A7 over C), the second is 8-24 (F#7/A#7 over C) and the third is 8-19 in inverted form.

The inverted 8-19 doesn't include a pair of diminants a major third apart so it isn't really part of this story, but it can be thought of in a rather different and interesting way -- as a major triad with a pair of augmented triads one and two semitones below it. This makes it a sort of hypermodal application of the Augmented Hexatonic and that's going to have to be a tale for another day.

What Can We Do With All This?

I think we can start playing dominant chords around the cycle of major thirds just like I already like to do with major sevenths, and the analysis above points to four different sounds we can get from that approach. As usual we have a few obvious approaches in jazz-adjacent situations:

• Play one of the arpeggios as an upper structure
• Combine two arpeggios to create melodic material
• Play fragments of any of the three arpeggios as chord subs

Although I'll tell anyone who'll listen that I'm "not a jazz guy", this kind of thinking is embedded too firmly in my brain to shake off so I may as well take advantage of it. I'm not sure whether "proper jazz" can benefit from any of these ideas but they help me hear the differences between them and use them in a mroe refined way.