Fundamental Scales

One last attempt to get a bite ---

1. It is possible to match up Steiners in the Double Steiner system to create 11 fundamental septads. These cut up the set theoretical space in an organized way. (hexads and pentads).

2. With one move, you can go to fundamental scales (Major, Melodic Minor or Harmonic Minor). Moving by a tritone or a major third.

3. Since these fundamental scales can be described in terms of diminished and augmented tuning, so can the fundamental DSS scales.

For example, take major

CDEFGABC. It contains 3 major thirds, and 4 minor thirds, (never in order). As a chain, DFACEGBD. (3,4,3,4,3,4,3) Now the rule being that notes that drag a connection maintain the connection to 3 and/or 4, and in these DSS scales, they always hook up anew with the same (a new 3 or a new 4). The rule being that if you create extra major or minor thirds, they are ignored if they didn't transport from the same.

(Such as going from Major to 0,1,3,4,5,7,8 scale, going from 10 to 4 creates two more major thirds which are ignored.

As a chain, this is Eb major so F,Ab,C,Eb,G,Bb,D,F; going to EE scale which is D,F,Ab,C,Eb=E split and G tail. This is composed of
3,3,4,3=4 split and 4 or 3 tail.

4. It might be possible to create a DSS scale system which is all fundamental scales (if you include Major Locrian, Hungarian, etc)

5. This concept can be extended to M22 (S(3,6,22)) M24, (S(5,8,24)) and the like, in a variety of 5-limit comma bases.