Fifth-chroma temperaments: Difference between revisions
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Another omission is 70 & 80 & 84e & 94 which reduces by tempering out [[540/539|S12/S14]]; though the significance of this is less clear, it can be observed that it is similar to the other omission by having the latter two edos being an offset of 10 from the former two edos. | Another omission is 70 & 80 & 84e & 94 which reduces by tempering out [[540/539|S12/S14]]; though the significance of this is less clear, it can be observed that it is similar to the other omission by having the latter two edos being an offset of 10 from the former two edos. | ||
As a reminder then, the remarkable feature is that ''all of these edo joins are equivalent''* and refer to the same 13-limit tempered structure: the one which splits 25/24 into five equal parts of ~144/143 so that 11/9 and 16/13 are made fifth-complements. This structure maps various high-limit things onto the 2.3.7.11 subgroup, and is home to a family of lower-rank temperaments that introduce various extra equivalences, discussed in [[#Fifth-chroma temperaments]]. | |||
:: <nowiki>*</nowiki> (other than the ones indicated as specifying something different/more specific) | |||
=== Broad high-limit tuning results based on a hand-optimized measure of odd-limit approximation faithfulness === | === Broad high-limit tuning results based on a hand-optimized measure of odd-limit approximation faithfulness === | ||