Let me share what I've been playing with during past weeks...
For sake of thought exercise and experiment I decided to limit myself and explore 7 note scales, more precisely scales which contain exactly 7 different notes, and where 2 half-steps in sequence are not allowed ( e.g. B/C/C# is illegal because C can be regarded as a "passing note" in such situation). How many of such scales are there possible in our tempered system?
If I got things correctly there are 72 of such scales possible, and they can be classified into 6 nonoverlaping types (patterns), each containing 12 scales.
I decided then to find their signatures and put them onto "circles of fifths" (close to distant relationship?). So I got 6 circles, of which the first one is of course the circle of Lydian scales, another circle contains all Lyd Diminished scales, the next one Lydian Augmented and so on... Now, I wanted to stack those circles one above the other (which one is above the other is not so important, but it's important which scales form together a column) and rotate them until they "lock" into some "logical" position. What does "logical" mean here? Well, something that sounds (and looks) close-related. For example, thanks to LCCOTO we immediately acknowledge that LD (Lydian Diminished) is related to Lydian scale built on the same Lydian Tonic, so these two circles should be rotated so that F Lyd and F LD get close together (one above the other). But what should be done with LFS (Lyd 7b) and LA (Lyd +5), as they are actually members of the same circle/type/pattern? I played these things on the piano, and so far I feel that LFS is a closer relative of the Lyd than LA. Maybe I'm doing something wrong, but so far I decided to rotate this circle so that F LFS gets close to (under) F Lyd, and F LA is then treated as G LFS and falls under the G Lyd...
So, I went on with this, and if anyone cares to take a look at the final result, it is here:
https://drive.google.com/file/d/0BzznNG ... sp=sharing
It was interesting to see all those crazy signatures... Maybe they are something totally normal to all of you more familiar with jazz and modern music, but I've certainly never seen them yet printed this way (although it could well be that I've heard music relying on such patterns, but my solfegge abilities are not on the level which would have made me aware of that).
It was for me interesting then to see this L+2 scale, which sounds to me also very nice, but I don't remember seeing it mentioned in the book, though I know it's used (for example Eb L+2 is used in Klezmer music and they call it Freylekhs).
I apologize if I'm doing something stupid, you can see that I'm quite a beginner - I would be interested to hear/read any critique if you see some flaws in my approach. But all this exploration (inspired by the book) is so interesting and enjoyable... I should probably stop theorizing now, and go back to my instrument more...
All the best,
m
edit: changed the 6th type's relation to other scales, updated pdf...