Some 13 limit temperaments

Letting E be max error and C minimal Graham complexity, I looked at
EDOs with a badness figure of E * C^(3/2) less than 0.5 up to 2000.
The results were dominated by hercules, the 224&270 temperament, for
which 494 does such a good job. Filtering further by requiring that
any division, to appear on the list, has to beat all smaller divisions
with the same minimal temperament gives the following: 145, 494, 730,
1178, 1258, 1506, 1802. Here 145 appears supporting mystery; 232 does
also, but does not beat 145. 494 of course supports hercules; 1258
beats it and so appears also. 270 does *not* appear since its best
temperament is also hercules, and it doesn't make the cut.

Woolhouse's 730 appears supporting the 80&270 temperament, for which I
am suggesting the name "woolhouse", despite the fact that Paul will
hate it. I think it is easy to remember what it means. 1178 is a
strong 13-limit system, and has a minimal temperament 494&684. 1506 is
an even stronger 13-limit system, with minimal temperament 24&494.
1802 appears in support of the 320&494 temperament, which has a
half-octave period and a major third generator.

This new method seems skewed toward larger EDOs.

-Carl

At 12:47 PM 5/9/2005, you wrote:
>Letting E be max error and C minimal Graham complexity, I looked at
>EDOs with a badness figure of E * C^(3/2) less than 0.5 up to 2000.
>The results were dominated by hercules, the 224&270 temperament, for
>which 494 does such a good job. Filtering further by requiring that
>any division, to appear on the list, has to beat all smaller divisions
>with the same minimal temperament gives the following: 145, 494, 730,
>1178, 1258, 1506, 1802. Here 145 appears supporting mystery; 232 does
>also, but does not beat 145. 494 of course supports hercules; 1258
>beats it and so appears also. 270 does *not* appear since its best
>temperament is also hercules, and it doesn't make the cut.
>
>Woolhouse's 730 appears supporting the 80&270 temperament, for which I
>am suggesting the name "woolhouse", despite the fact that Paul will
>hate it. I think it is easy to remember what it means. 1178 is a
>strong 13-limit system, and has a minimal temperament 494&684. 1506 is
>an even stronger 13-limit system, with minimal temperament 24&494.
>1802 appears in support of the 320&494 temperament, which has a
>half-octave period and a major third generator.

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> This new method seems skewed toward larger EDOs.

Definately, but partly that is just the different point of view, which
does not measure complexity in terms of the size of the division.