Co-Melakatas: Pentatonic Shadows of Carnatic Scales

Regular readers will know that whenever I study almost any resource, I take an interest in whatever isn't in it. I guess this is a habit I picked up early, when somebody pointed out that not only are the white notes on a piano the major scale but the black notes -- all the ones that aren't in the major scale -- form a major pentatonic. Switching between a scale, chord or whatever and its complement is something I find very musically useful. So I was surprised to realise I've never studied melakatas this way. What do their complements look like?

You can download all the Scala files for this post here as a zip file -- look under scala/melakata_complement_tunings for the ones in this post.

Every melakata is a scale of seven notes, so that leaves five notes unaccounted for: these are the complements of melakatas or, because inventing fancy jargon helps me remember things, the "co-melakatas". Essentially, we imagine putting the notes from the melakata on the white keys and the five leftover notes on the black keys, then playing just the black keys. (By the way, if you really want to you can make Scala files that do this for you so you don't have to do any thinking, assuming you're using an instrument that can load them of course.)

If two melakatas are modes of each other then their co-melakatas will be too, and vice verse. Funnily enough we have 36 distinct melakatas, but that isn't because each of the 72 is a mode of one other; the picture is really messy, and as far as I can tell the number being exactly half is a coincidence. I think it would have to be a factor of 72, but there are a few other reasonable options it could have been.

Anyway, there are 36 co-melakatas corresponding to the 36 modal groups of melakatas. All 36 are contained in other melakatas, and quite a lot of melakatas contain copies of their own complements just like the Major Scale does.

I'm a bit daunted by the complexity and messiness of the picture here and maybe there's not much in it. But here we have 36 different pentatonic scales that relate to the melakatas in intricate and musically promising ways, and that isn't nothing.

At the very least, we can do the trick we did previously and play these scales with equally-spaced notes on the in-between keys. In this case we'll put the pentatonic co-melakata on the black keys and tune the white keys exactly in between their neighbours. This allows you to lazily play any co-melakata on the black keys and to intersperse its notes with other, alien notes. These are sometimes other notes from 12-EDO but they're mixed up with a selection of quarter-tones and third-tones. The resulting palettes of twelve pitches are weird, lumpy and hard to define. Maybe you'll get a kick out of them; there are certainly some pretty strong melodic flavours to be discovered there.