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.