Report On the Transpositions of 12TET/EDO "Nested" Inversions of Blues...

...Tetrachord 1-2-3 (4-13):

I just finished drawing out all 12 transpositions
of the "nested" inversions of the blues tetrachord
with scale steps 1-2-3 (pitch class set 4-13),
and I hit the jackpot and got 12 structurally
distinct superscales with the following characteristics:

1. one symmetrical pentachord

2. three asymmetrical hexachords and three
symmetrical hexachords

3. one asymmetrical septachord

4. four symmetrical octachords

Because this particular tetrachord has 12
structurally distinct superscales, I will
designate it as a "hyper-differentiating" (HD)
nested tetrachord.

Notice that there are four asymmetrical
superscales, so that those could be further
"nested" with their various superscale inversions to
produce another "generation" of raw scalar
material.

I will be continuing my exploration of nested
tetrachords, pentachords, and hexachords
and posting the results at my primary
theoretical Yahoo group:

/12TET_TuningSystemSpecificity/

MIDI files of all 17 of the 12TET nested tetrachords
can be accessed/listened to here:

/BluesNestedTetrachord4ToneScales
/

Note: you must join the group in order to be
able to access/listen to the MIDI files, which
are in the group's Files section.

Bill.Flavell at GMail.com