Reply to Jon from MakeMicroMusic

--- In MakeMicroMusic@yahoogroups.com, "Jonathan M. Szanto"
<JSZANTO@A...> wrote:

> I really think
> that anything getting to around 2 [keyboard] octaves or so
*without* a repeating
> symmetry in some fashion (like maybe 18 or 24, or less notes per
octave)
> really isn't something I'm going to try and just _play_,

Hi Jon.

My new paper, which you're kindly helping me with at the moment, has
some things to offer you, or anyone like you, here.

If you're looking to approximate harmonies with a prime limit of 5,
my paper offers:

24 notes: 1 scale
23 notes: 2 scales
22 notes: 6 scales
21 notes: 0 scales
20 notes: 2 scales
19 notes: 6 scales
18 notes: 1 scale
17 notes: 3 scales (incl. the Wilson/medievalArabic schismatic scale)
16 notes: 3 scales
15 notes: 4 scales
14 notes: 0 scales
13 notes: 5 scales
(should I go lower?)

If you're looking to approximate harmonies with a prime limit of 7,
my paper offers:

24 notes: 2 scales
23 notes: 1 scale
22 notes: 7 scales
21 notes: 3 scales (including Blackjack)
20 notes: 1 scale
19 notes: 9 scales
18 notes: 1 scale (+ one more if you include Ennealimmal[18])
17 notes: 5 scales
16 notes: 3 scales
15 notes: 7 scales
14 notes: 5 scales
13 notes: 4 scales
(should I go lower?)

Each of the scales has 2 step sizes, distributed as evenly as
possible around the octave.

The number of possibilities goes way up if you count different modes
(i.e., rotations) of these scales as different, and up still higher
if you include permutations of the step sizes (which means, for
example, turning the major scale LLsLLLs into the melodic minor
ascending scale LsLLLLs).

If anyone is interested in a particular number of notes, let me know,
and I can detail the relevant scales here.

Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> My new paper, which you're kindly helping me with at the moment, has
> some things to offer you, or anyone like you, here.

Duly noted. Mr. Tenney is giving me a headache, but beyond that...

Cheers,
Jon