Some Ways of Looking at 6-z38

The hexatonic set 6-z38 came up in relation to some material I was developing out of Yagapriya and at that time I put it aside for later. Well, later has arrived. Let's see what we can make of this awkward pile of semitones.

For the sake of concreteness I'll specifically refer here to 6-z38 by the notes C-Db-F-F#-G-Ab. Although it doesn't look like anything much I want to treat it with dignity, to look at some of the things it contains and to see whether we can get a better idea of what it is and how it might arise.

On the one hand, Db-F-Ab-C is DbM7. It's completed by Gb-G forming a chromatic line from the 4 to the 5, which we think of as belonging to the Blues Scale. So one way of looking at 6-z38 is as a weird "major seventh blues scale". The natural 4 (11) is an "avoid note" in the jazz textbooks -- this really might be more of a blues sound than a bebop-as-digested-by-academia one. This is a very easy way to find 6-z38 on the guitar.

On the other hand, C-Db-F#-G is a Lulu chord. This is a pair of semitones separated by a tritone. To make 6-z38, simply surround one of the semitones with a chromatic enclosure. This is an easy way to find 6-z38 on the piano and tends to point towards more atonal applications.

To see why I paired these two perspectives it's sufficient to gaze at the following diagram -- gold notes on the left are DbM7, on the right they're Lulu, green notes are added in each case to make 6-z38:

This seems to be to be a fruitful way to understand 6-z38 in terms of its subsets. What about its supersets? There are a few ways to add one note (shown here in square brackets) to it to get a heptatonic scale:

• Jhalavarali: C-Db-[D]-F-F#-G-Ab
• Mode of Pavani: C-Db-[Eb]-F-F#-G-Ab (Pavani is the mode starting on F#)
• Mode of Raghupriya: C-Db-[E]-F-F#-G-Ab (Raghupriya is the mode starting on E)
• Conian: C-Db-F-F#-G-Ab-[A]
• Apeliotean: C-Db-F-F#-G-Ab-[Bb]
• Salagam: C-Db-F-F#-G-Ab-[B]

Four of these are melakatas (or modes thereof); Apeliotean is one of what I call the Eight Winds; Conian is the dozenal name for a scale I don't know anything else about. I think we can see these as a family, unified by the rather interesting structure of 6-z38. Of course all the scales have a lot more in them besides that, too.

Here is, for each of these heptatonics, a couple of familiar-looking things it adds to 6-z38 that weren't there before; again, other interpretations are possible and probably interesting:

• Jhalavarali: C-Db-[D]-F-F#-G-Ab -- DMaj7b5, the quartal chord D-G-C-F.
• Mode of Pavani: C-Db-[Eb]-F-F#-G-Ab -- AbMaj7, C minor triad.
• Mode of Raghupriya: C-Db-[E]-F-F#-G-Ab -- C+, FmMaj7.
• Conian: C-Db-F-F#-G-Ab-[A] -- Db+, F major triad.
• Apeliotean: C-Db-F-F#-G-Ab-[Bb] -- Bbm7, Gm7b5.
• Salagam: C-Db-F-F#-G-Ab-[B] -- G7b5, F dim triad.

These might or might not be useful to you. You might be tempted to look at those pairs of chords as ways to move even further from where we started but the pairs all overlap a lot and don't seem very promising to me -- maybe you can make something of them, though.

What I think I can use from all this is the idea that 6-z38 is a unique combination of two very different ideas: (a) a major 7 with a "blues line" and (b) Lulu with a "chromatic enclosure". The first of these is at least superficially connected with jazz language while the second has much more Second Viennese vibes. There are multiple ways to extend this by adding an extra note, which can give us a wide variety of additional harmony options, many of which are again Major 7s but also some minor and diminished sounds.

When dealing with a lot of dissonance it's easy to end up saying "well this must be dominant language", which is a bit unhelpful (anything is dominant language if you're brave enough). Here we have a little island of dissonance that's very definitely leading us in a different direction, which is interesting in itself.

I'll sign off with Webern's Four Pieces for Violin and Piano. In The Structure of Atonal Music (p.126) Allan Forte provides a discussion of the third piece, in which 6-z38 and its complement 6-z6 play a crucial part:

In this part of the book Forte is focusing on demonstrating some ideas that I admit I'm not very au fait with but maybe I ought to look into it a bit more in the future. My interest in pc set theory bottoms out pretty fast, especially when it seems to point to "things that ought to work on paper" and away from "things people have actually used and that you can kind of hear if you listen". That part of the book smells more to me like the former than the latter but I might be wrong so I should do my homework before passing judgement.