This one comes from the condition ln(p-q)/ln(q) < 3/4, cents < 50. One

way to think of the first condition is as follows: writing the comma p/q

as 1 + a/q, if ln(a)/ln(q) < e then a < q^e. We thus have a weaker

condition than requiring a to be less than a constant, by limiting its

size relative to q.

250/243, 1638400/1594323, 128/125, 1594323/1562500, 1990656/1953125,

3125/3072, 20000/19683, 531441/524288, 81/80, 2048/2025,

67108864/66430125, 129140163/128000000, 78732/78125, 393216/390625,

2109375/2097152, 15625/15552, 1600000/1594323, 1224440064/1220703125,

10485760000/10460353203, 6115295232/6103515625, 32805/32768,

274877906944/274658203125, 7629394531250/7625597484987

What do people think of this as a list of 5-limit temperaments?

--- In tuning-math@y..., Gene W Smith <genewardsmith@j...> wrote:

> This one comes from the condition ln(p-q)/ln(q) < 3/4, cents < 50.

One

> way to think of the first condition is as follows: writing the

comma p/q

> as 1 + a/q, if ln(a)/ln(q) < e then a < q^e. We thus have a weaker

> condition than requiring a to be less than a constant, by limiting

its

> size relative to q.

>

> 250/243, 1638400/1594323, 128/125, 1594323/1562500,

1990656/1953125,

> 3125/3072, 20000/19683, 531441/524288, 81/80, 2048/2025,

> 67108864/66430125, 129140163/128000000, 78732/78125, 393216/390625,

> 2109375/2097152, 15625/15552, 1600000/1594323,

1224440064/1220703125,

> 10485760000/10460353203, 6115295232/6103515625, 32805/32768,

> 274877906944/274658203125, 7629394531250/7625597484987

>

> What do people think of this as a list of 5-limit temperaments?

not bad, i'd say -- this could be justified in terms of the heuristic

combined with an appropriate badness function of complexity and error.