Sane and insane temperaments: Difference between revisions
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The 2.9.5 restriction of 2.3.5 81/80 (meantone) is a weak restriction that is not insane. The resulting temperament is generated by the tempered 2/1 and 9/8. The original subgroup of 2.9.5 contains 9/1 as an interval but not 3/1. However, since 9/1 is a generator of this temperament, there is no way to "split" it further to obtain an unmapped 3/1, so it is not insane. The kernel is 81/80, which is a saturated lattice of the 5-limit, so we have a sane temperament. | The 2.9.5 restriction of 2.3.5 81/80 (meantone) is a weak restriction that is not insane. The resulting temperament is generated by the tempered 2/1 and 9/8. The original subgroup of 2.9.5 contains 9/1 as an interval but not 3/1. However, since 9/1 is a generator of this temperament, there is no way to "split" it further to obtain an unmapped 3/1, so it is not insane. The kernel is 81/80, which is a saturated lattice of the 5-limit, so we have a sane temperament. | ||
[[Category:Regular temperament theory]] | |||
[[Category:Math]] | |||