60th-octave temperaments: Difference between revisions
→Minutes: improve optimal gpv, it can be worked out manually if all the patent vals are known |
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{{Infobox fractional-octave|60}} | |||
[[60edo]] is a highly composite EDO, and some its multiples are notable for their consistency limits, such as 2460edo, which is a zeta edo. | [[60edo]] is a highly composite EDO, and some its multiples are notable for their consistency limits, such as 2460edo, which is a zeta edo. | ||
==Minutes== | |||
== Minutes == | |||
Defined as the 2460 & 4320 temperament, starting with the 13-limit. Named "minutes" for period-60, since there's 60 minutes in an hour. In light of 12 being a divisor of 60, minutes tempers out the [[Kirnberger's atom]], and in the limits below 13, it's a contorted atomic temperament. | Defined as the 2460 & 4320 temperament, starting with the 13-limit. Named "minutes" for period-60, since there's 60 minutes in an hour. In light of 12 being a divisor of 60, minutes tempers out the [[Kirnberger's atom]], and in the limits below 13, it's a contorted atomic temperament. | ||
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Optimal tuning (CTE): ~3/2 = 701.948 | Optimal tuning (CTE): ~3/2 = 701.948 | ||
Optimal | {{Optimal ET sequence|legend=1|1860, 2460, 6780, 7380}} | ||
=== 17-limit === | === 17-limit === | ||
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Optimal tuning (CTE): ~216/175 = 364.387 | Optimal tuning (CTE): ~216/175 = 364.387 | ||
{{Optimal ET sequence|legend=1|540, 1380, 1920, 2460, 3000, 3840, 4380, 4920, 6300, 6840e}} | |||
=== 19-limit === | === 19-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17.19 | ||
Comma list: 9801/9800, 10241/10240, 13377/13376, 5929/5928, 89376/89375, 23409/23408 | Comma list: 9801/9800, 10241/10240, 13377/13376, 5929/5928, 89376/89375, 23409/23408 | ||
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Optimal tuning (CTE): ~7533637632/6103515625 = 364.385 | Optimal tuning (CTE): ~7533637632/6103515625 = 364.385 | ||
{{Optimal ET sequence|legend=1|540jn, 1380jn, 1920, 2460, 3000jjnn, 3840jn, 4920jn 4380, 6300, 6840}} | |||
==== 2.3.5.7.29.43 subgroup ==== | ==== 2.3.5.7.29.43 subgroup ==== | ||
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Optimal tuning (CTE): ~216/175 = 364.385 | Optimal tuning (CTE): ~216/175 = 364.385 | ||
{{Navbox fractional-octave}} | |||
[[Category:60edo]] | [[Category:60edo]] | ||