31st-octave temperaments: Difference between revisions
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→217 & 1178: fulfill + music |
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== 217 & 1178 == | == 217 & 1178 == | ||
The 217 & 1178 temperament combines two multiples of 31, which are large equal divisions consistent in the 21-odd-limit. 1395edo, also consistent in 21-odd-limit, is also a tuning. | The 217 & 1178 temperament combines two multiples of 31, which are large equal divisions consistent in the 21-odd-limit. 1395edo, also consistent in 21-odd-limit, is also a tuning. | ||
Subgroup: 2.3.5.7 | |||
Comma list: 4375/4374, {{monzo|-153 42 7 25}} | |||
{{Mapping|legend=1| 31 2 -38 197 | 0 3 7 -7 }} | |||
: mapping generators: ~562711519881/549755813888 = 1\31, ~67108864/47258883 = 608.167 | |||
[[Optimal tuning]] ([[CTE]]): ~14553/10240 = 608.167 | |||
[[Support]]ing [[ET]]s: {{EDOs|217, 744c, 961, 1178, 1395, 1612, 2573}} | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 4375/4374, 820125/819896, {{monzo|-37 12 -1 6 1}} | |||
{{Mapping|legend=1| 31 2 -38 197 -97 | 0 3 7 -7 13 }} | |||
: mapping generators: ~45/44 = 1\31, ~14553/10240 = 608.167 | |||
[[Optimal tuning]] ([[CTE]]): ~14553/10240 = 608.167 | |||
[[Support]]ing [[ET]]s: {{EDOs|217, 961e, 1178, 1395, 1612, 2573}} | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 4225/4224, 4375/4374, 225000/224939, 18753525/18743296 | |||
{{Mapping|legend=1| 31 2 -38 197 -97 99 | 0 3 7 -7 13 1 }} | |||
: mapping generators: ~45/44 = 1\31, ~14553/10240 = 608.167 | |||
[[Optimal tuning]] ([[CTE]]): ~14553/10240 = 608.167 | |||
[[Support]]ing [[ET]]s: {{EDOs|217, 961e, 1178, 1395, 1612, 2573}} | |||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 4225/4224, 4375/4374, 14400/14399, 14875/14872, 56595/56576 | |||
{{Mapping|legend=1| 31 2 -38 197 -97 99 111 | 0 3 7 -7 13 1 1 }} | |||
: mapping generators: ~45/44 = 1\31, ~1989/1400 = 608.167 | |||
[[Optimal tuning]] ([[CTE]]): ~1989/1400 = 608.167 | |||
[[Support]]ing [[ET]]s: {{EDOs|217, 961e, 1178, 1395, 1612, 2573}} | |||
=== 19-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
Comma list: 4200/4199, 4225/4224, 4375/4374, 5929/5928, 5985/5984, 14875/14872 | Comma list: 4200/4199, 4225/4224, 4375/4374, 5929/5928, 5985/5984, 14875/14872 | ||
{{Mapping|legend=1| 31 2 -38 197 -97 99 111 6 | 0 3 7 -7 13 1 1 8 }} | |||
: mapping generators: ~112651/110160 = 1\31, ~665/468 = 608.166 | |||
[[Optimal tuning]] ([[CTE]]): ~665/468 = 608.166 | |||
[[Support]]ing [[ET]]s: {{EDOs|217, 961e, 1178, 1395, 1612, 2573}} | |||
; Music | |||
* ''[https://www.youtube.com/watch?v=c9e7MTsIDc4 Listening]'' by [[Eliora]] (2023) - 217 & 1178 and enneadecal in 1178edo tuning | |||
== Prajapati == | == Prajapati == | ||