Heptatonics Containing Forte 4-9

This is a follow-on from this post, when we discovered Forte 4-9 as the coscale of the octatonic you get from combining Vishwambari with Hatakambari (help with Forte numbers). Which makes it sound much more abstruse than it was in context (I think). But let's look at it as its own thing.

Forte 4-9 is a four-note structure that can be written as C-Db-F#-G -- that is, a semitone at the root (C-Db) and "echoed" at the tritone. Here's what it looks like on the fretboard in C, i.e. C-Db-F#-G:

This is symmetrical but it's not obviously related to anything in tonal music. You can also think of it as a combined Sus b2 (C-Db-G) and Sus #4 (C-F#-G), which is in line with some things we've been messing with lately. I've begun to think these kinds of chords are really crucial to master, and especially to be able to hear clearly, because of their importance in 20th century composition but their absence from more familiar tonal music.

Also in line with current practice, I looked at heptatonic scales in pairs, where the members of the pair invert to each other. I found 8 such pairs and I'm sure there are plenty more, but that's already too many to deal with in a blog post but there are three that really stand out.

Each of these three contains two copies of Forte 4-9, separated by semitones: one at the root and one at the b2. Since these must overlap on two notes that gives us six notes in total (two overlapping, then two more from each copy).

Here's how that looks -- the 4-9 at the root plus the yellow dots indicating the new notes we get from the 4-9 at the b2. It's a very obvious geometric pattern and easy to learn, but be sure to keep track of which note is which:

Salagam (1,b2,bb3,#4,5,b6,bb7) is obtained by adding a bb7 to this structure. Jalarnavam adds the b7 instead, and Jhalavarali (1,b2,bb3,#4,5,b6,7) adds the natural (major) 7. Salagam and Jhalavarali are inverses of each other while Jalarnavam is self-inverse so it doesn't come with a partner. These three scales seem to form a very special family.

Here are full fretboard diagrams for these three scales. To calm the colours down I've used dark blue for the root, light blue for the rest of the 4-9 notes (both copies) and yellow for the added bb7, b7 or 7 respectively:

Now the game here would be to find chords -- and sequences of chords -- in these scales that bring out both their many shared qualities and the individuality they get from the placing of their seventh notes. It would also, of course, be worth considering their coscales and whether they're part of anything larger and more interesting. But that's for another day.

There are lots of other heptatonics that contain only one copy of Forte 4-9; as you might expect, none of them is a common scale and all of them are interesting. In each case it would probably be worth cataloging all the things you can add to Forte 4-9 to get a heptatonic scale and seeing if anything interesting is to be found there.