Re: Margarets 22 scale

Margo commented in the 22 tetrachord thread...

> If we start from C, for example, we get a "Pythagorean" diatonic scale
> like this:
>
> C D E F G A B C
> 0 4 8 9 13 17 21 22
> 4 4 1 4 4 4 1
>

I just thought I'd jump in with an update from my scale search
program. Now that I'm fairly content with the program, I'm just
working through various scales formats and writing the results
down for future investigation.

I started looking at the various 7 tone diatonic scales

transposable : BaBaBBa BBaBBBa ionian
non-tranposable : BBaaBBa BaBBBBa melodic minor
BBBaBaa aBBBBBa 'thing'
BBBBaaa

So far I've only looked in detail at the transposable
scales and melodic minor. I just thought I'd jump in
and say that 22-eq usually shows up at about the fifth
most favored scale in my system for the diatonics I've
looked at, a result I found surprising.

Margo's 22-pythagorean diatonic shows up in the BBaBBBa
but I thought I'd show the melodic minor. After a meantone,
pythagorean and some other interesting and unusual tunings
appears

0 218 273 491 709 937 1145
1/1 8/7 7/6 4/3 3/2 12/7 27/14

which prompted me to go off and look in a spreadsheet I
have with the question "what ED2 best approximates the
3/2 with 709c,... well I'll be jiggerred!"

One intrigueing aspect of this particular scale is
that the diminished fourth in this scale (from the seventh
to the third) is a somewhat wide 6:5 (5:3 in inversion).
I haven't listened so I can't say if it really is in a
more or less stable pocket than the 7:6, but it would
seem to have some interesting possibilitys.

Bob Valentine