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Transforming one temperament to another

🔗Gene Ward Smith <genewardsmith@juno.com> <genewardsmith@juno.com>

12/9/2002 11:26:42 PM

I've mentioned that one 1-comma (planar, for 7-limit) temperament can be transformed to another by mapping the comma. The same is true with more than one comma; one simply applies the map to the kernel. Here is an example:

The Nonkleismic temperament has map and wedgie

[[1, -1, 0, 1], [0, 10, 9, 7]] [10, 9, 7, -9, 17, -9]

Error, complexity and badness:

3.320167 27.531739 2516.675764

Generators:

[1200., 309.9514712]

and a kernel generated by <126/125, 1728/1715>. Mapping this by
2-->2, 3-->8/3, 5-->32/7, 7-->32/5 sends the above kernel to
<343/360, 875/864>, a temperament whose corresponding values are

[[1, 4, 4, 5], [0, -10, -7, -9]] [10, 7, 9, 1, 14, -12]

21.487964 27.215263 15915.502350

[1200., 290.6218997]

It's not a very good temperament, but it certainly counts as one. Probably there are better examples.