Today I spent some time analysing and messing about with Ganamurti, one of the Carnatic melakata scales. This actually happened by accident -- I intended to look at something else, which I'll come back to, but wrote it down wrong on my way to the studio and didn't check until much later. I thought the results were quite nice so I'm counting this as a happy accident.

What is Ganamurti Anyway?

Ganamurti, as a 12EDO scale, is 1 b2 bb3 4 5 b6 7; starting on C we get C Db D F G Ab B. It's characterised in part by the cluster of four semitones around the root -- one below and two above -- that provide a lot of melodic options but can easily trip us up.

Here's the CAGED diagrams from the book:

Here's a lovely live Carnatic performance in Ganamurti:

The Tritone Pair

Notice that Ganamurti has no major or minor third, so the root harmony is a bit weird -- a sus 2 or sus 4 chord, most likely. The tonal ambiguity is a really nice feature of this scale but it can make it sound a bit untethered from anything familiar. One way to connect with it is to play other common chords and arpeggios the scale contains without losing sight of the supposed tonal gravity of the root note.

There aren't too many options for this, but the ones we have are quite nice. To make it simple I'll assume the root note is C. Then we can play Db7 or G7, a "tritone pair" that's easy to find if you know about the tritone substitution idea in mainstream jazz. Remarkably, Ganamurti is the scale you get when you start with the tonic and play all the notes of the dominant 7 and its tritone sub.

A couple of things help us to start thinking of this pair of chords in an expanded way, as a sort of "system" over the C root. One is that in both cases we can add the b9 and #11 and stay in the scale.

These aren't very weird things to add to the G7, although it's a bit odd to add them both at the same time -- in jazz terms, the b9 implies an "altered dominant" function where the fifth would be omitted, but it isn't, and the #11 alongside the fifth implies a "Lydian dominant" function (or lack thereof) that the b9 clashes with. In this respect It's kind of similar in a mirror-image way to the way the whole tone scale contains a natural 9 (suggesting Lydian dominant) but altered fifths (suggesting altered dominant).

The ambiguity is compounded by the fact that the unaltered 11 of G is C natural, which of course is also in the scale (it's the root!). That's typically an "avoid note" in the jazz textbooks and pulls us back towards mixolydian territory. Treating G as the root, we can therefore use this scale (now spelled 1 b2 3 4 b5 bb6 b7) as a sort of "spicy Lydian dominant", using the 4 with caution if a more diatonic flavour is wanted (I'll say more about that in a moment).

The other major triad is Db, which expands to Db7, again with the added b9 and #11. This time we do not also get the natural 11; instead the extra note is the root of C Ganamurti, which is the major seventh of Db7. So there's an asymmetry here that's important to notice. The V7 has the natural 11, which paradoxically interferes with its ability to function as a jazzy dominant chord, whereas the bII7 has the natural 7, which also messes with its usual function, but in a different way.

Playing lines that shift between the two dominant arpeggios, including their b9s and #11s at will, produces to stuff that I certainly wouldn't usually think of.

In addition, we do have a diminished seventh chord (in C Ganamurti the chord is Ab-B-D-F). It falls a semitone above the roots of either of those dominant chords, so it tends to want to resolve down to them. Yet it's a semitone below the root of the whole scale, so when resolving to that it tends to move upwards instead.

There's also a Lulu (b2-2-5-b6, Db-D-G-Ab in C Ganamurti) should you fancy a different kind of crunchy symmetrical chord. Its notes are nothing but the root and fifth of the two dominant chords -- G7 (G, D) and Db7 (Db, Ab). Studying how these resolve to the notes in the other dominant chord can certainly help with building nice voice-leading from this scale.

The 5 Dom Pentatonic

Ganamurti is a pretty far-out scale so it's perhaps surprising that it contains a pentatonic that lives entirely in the major scale -- specifically, C Ganamurti (C Db D F G Ab B) contains five of the notes in C major (C D F G B). The easiest way to find them, though, is to think of them as a G7 arpeggio suspended over the C root:

Much as we might expect this scale to be very symmetrical about the tritone, it's not and we can't do the same with the Db7. What's interesting to me, I guess, is that we have 5 notes shared with the major scale but we can't really think of Ganamurti as "a major scale with two alterations" -- yes it has a b6, but where's the third gone and where did that extra b2 some from? I just don't think it's helpful to think about it that way, so it's surprising to find this quite substantial diatonic chunk hiding in there.

When I first found this scale my ears lied to me and told me it was Pelog, another diatonic subset. It isn't, but that's still enough of an excuse to post Neil Ardley's delightful album Kaleidoscope of Rainbows, a sort of prog-jazz-Terry-Riley thing written entirely in the pelog scale that has some really killer playing on it:

The Tritone Substitution Heptatonics

OK so this is how my stupid brain works -- if you can make Ganamurti by adding a note to a pair of dominant chords a tritone apart, what else can we make that way? There are actually two more ways to do it. I should start by saying that Ganamurti is by far the most "natural" of these to someone with the kind of mess of approximately-jazz-college-harmony knowledge most people are working with these days. But that doesn't mean the others won't be interesting.

You get a mode of the scale I call Augmented #6 by shifting the tritone sub down a minor third relative to the root -- that is, we keep the root as C but now play E7 and Bb7. This gives the scale C-D-E-F-G#-Bb-B. This is a mode of Namanarayani and is something I've never really explored before.

The other possibility is to move the tritone sub down another semitone, keeping the root C and playing Eb7 and A7, giving the scale I call Natakapriya b4 (C-Db-Eb-E-G-A-Bb). This is a mode of Ramapriya, and also of Melodic Minor b5 which my book says Allan Holdsworth included in one of his lists of frequently-used scales. I can't attest to the Holdsworth connection being accurate (I heard somewhere that those lists were often coaxed out of him by well-meaning producers and not necessarily things he put much stock by) but it's a connection to something, and those seem to be surprisingly hard to come by in this sphere.

To summarise:

• C Ganamurti: C root + G7/Db7
• C Augmented #6: C root + E7/Bb7
• C Natakapriya b4: C root + Eb7/A7

Now, an important thing to note is that each of these is nothing but an octatonic diminished scale (Half-Whole or Whole-Half) with one note deleted, and if you're familiar with that scale's symmetrical structure it won't be surprising that there are only thee of those. Nor will it be a surprise that this arises from the tritone sub, again if you're already aware of how that works. But threse seven-note scales are very much not the diminished scale -- with its symmetry broken, its character changes radically. This is something I failed to appreciate for a rather long time -- it's one of those things that's only really clear when you play music with these resources instead of juggling them on paper.

All the modes are worth investigating of course and I might come back with more findings on those if there are any. Note that for all three of these you can still add the b9s and #11s at will to these dominant arpeggios, which produces some very unusual effects. Incidentally, you're unlikely to find success with these over actual dominant chords in a jazz setting -- I don't do much of that kind of thing at the moment but I can almost guarantee it'll be a "discuss first or get vibed" kind of deal due to the unaltered fifths in both dominant chords. But I'm more interested in these as paths towards new melodic lines in non-functional contexts anyway.

Until next time -- here's something beautiful in Ramapriya to send you on your way: