Superparticulars

I looked for superparticular ratios whose prime factors were no larger than 23
and whose numerators were less than or equal to ten million (10 ^7) as that
seemed the practical limit of my computer at thattime (1997, XH (17).

My source was a paper by Bernd Streitberg and Klaus Balzer, 1988, The
Sound of Mathematics, Proceedings of the 1988 International Computer
Music Conference 158-165. They searched at the five limit to 10 ^12
and found only 10 (2/1, 3/2, 4/3, 5/4, 6/5, 9/8, 10/9, 16/15, 25/24
and 81/80).

I found only 240 at the 23 limit. I've summarized the numbers at each
prime limit and the cumulative totals below:

Limit Number Total
2 1 1
3 3 4
5 6 10
7 13 23
11 17 40
13 28 68
17 40 108
19 58 166
23 74 240

I'm not sure what the question was about lengths (?) at
each limit; I hope these data help answer it.

--John

--- In tuning-math@y..., John Chalmers <JHCHALMERS@U...> wrote:

> I'm not sure what the question was about lengths (?) at
> each limit; I hope these data help answer it.

What's really best would be the data itself, and not a summary, but
if that is too onerous the largest for each prime would be nice.