Schismatic family: Difference between revisions
m 147 is lower error in 7-limit garibaldi |
m unfortunately thats not how optimal ET sequences work. it's a defined thing by fumica's temperament evaluator. the standard ive been abiding by is that missing entries are to be discussed on a case-by-case basis |
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Garibaldi tempers out the [[garischisma]], equating the [[64/63|septimal comma]] with both the [[syntonic comma]] and the [[Pythagorean comma]]. The 7/4 is found at -14 fifths, represented by the double-diminished octave (C–C𝄫), or down-minor seventh (C-vB♭) with the down-arrow representing the comma step. It necessitates a sharper fifth than pure. Its [[S-expression]]-based comma list is {[[5120/5103|S8/S9]], [[225/224|S15]]}. | Garibaldi tempers out the [[garischisma]], equating the [[64/63|septimal comma]] with both the [[syntonic comma]] and the [[Pythagorean comma]]. The 7/4 is found at -14 fifths, represented by the double-diminished octave (C–C𝄫), or down-minor seventh (C-vB♭) with the down-arrow representing the comma step. It necessitates a sharper fifth than pure. Its [[S-expression]]-based comma list is {[[5120/5103|S8/S9]], [[225/224|S15]]}. | ||
[[147edo]] (from 94+53) is a [[patent val]] tuning with 5 and 7 very close to equally out-of-tune in opposite directions s.t only 7/5 and 10/7 are inconsistent in the 9-odd-limit, so might be considered for (EG) a 41-note subset ([[12L 29s]]). | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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* 7- and 9-odd-limit [[diamond tradeoff]]: ~3/2 = [701.711, 702.915] | * 7- and 9-odd-limit [[diamond tradeoff]]: ~3/2 = [701.711, 702.915] | ||
{{Optimal ET sequence|legend=1| 12, 29, 41, 53, 94 | {{Optimal ET sequence|legend=1| 12, 29, 41, 53, 94 }} | ||
[[Badness]] (Sintel): 0.548 | [[Badness]] (Sintel): 0.548 | ||