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Copop hemiwuerschmidt

🔗Gene Ward Smith <gwsmith@svpal.org>

7/4/2004 2:46:17 PM

If you take the poptimal range for wuerschmidt and divide it by 2, and
compare to the poptimal range for 7 or 9 limit hemiwuerschmidt, you
find they are almost the same. 229 works as a poptimal et for
hemiwuerschmidt in the 7 or 9 limit, and wuerschmidt in the 5 limit.

In the 11-limit, we get a temperament with the same TOP tuning,
11-limit hemiwuerschmidt, from

<<16 2 5 -90 -34 -37 -198 6 -216 -270||

This has a common poptimal generator with 5, 7, and 9 limit
(hemi)wuerschmidt of 6^(1/16) for hemiwuerschmidt, 6^(1/8) for
wuerschmidt, so 229 works well here also, and 359 is almost exact.
However, it has a high complexity and so a high badness,

<<16 2 5 40 -34 -37 8 6 86 95||

is much better in terms of badness; 421 is poptimal for this. This
temperament has a TM basis of {243/242, 441/440, 3136/3125} and is
reasonable in terms of badness; it can be described as 31&130. The 421
val for it, derivable from the 68/421 generator, is
<421 667 978 1182 1457|

I've listed this before as hemiwuerschmidt, but the tuning is too
different. Worseschmidt?