Mint family: Difference between revisions

Cmloegcmluin (talk | contribs)
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
 
(3 intermediate revisions by 2 users not shown)
Line 1: Line 1:
The '''mint family''' of rank-3 temperaments tempers out [[36/35]], identifying both [[7/6]] with [[6/5]] and [[5/4]] with [[9/7]].
{{Technical data page}}
The '''mint family''' of [[rank-3 temperament]]s tempers out [[36/35]], identifying both [[7/6]] with [[6/5]] and [[5/4]] with [[9/7]].


== Mint  ==
== Mint  ==
 
[[Subgroup]]: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 36/35
[[Comma list]]: 36/35


[[Mapping]]: [{{val| 1 0 0 2 }}, {{val| 0 1 0 2 }}, {{val| 0 0 1 -1 }}]
{{Mapping|legend=1| 1 0 0 2 | 0 1 0 2 | 0 0 1 -1 }}


[[POTE generator]]s: ~3/2 = 698.6351, ~5/4 = 404.2809
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 698.6351, ~5/4 = 404.2809


{{Optimal ET sequence|legend=1| 4, 5, 7, 8d, 9, 12 }}
{{Optimal ET sequence|legend=1| 4, 5, 7, 8d, 9, 12 }}
Line 16: Line 16:


== Nickel  ==
== Nickel  ==
 
[[Subgroup]]: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 36/35, [[45/44]]
[[Comma list]]: 36/35, [[45/44]]


[[Mapping]]: [{{val| 1 0 0 2 -2 }}, {{val| 0 1 0 2 2 }}, {{val| 0 0 1 -1 1 }}]
{{Mapping|legend=1| 1 0 0 2 -2 | 0 1 0 2 2 | 0 0 1 -1 1 }}


[[POTE generator]]s: ~3/2 = 688.8370, ~5/4 = 391.8801
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 688.8370, ~5/4 = 391.8801


{{Optimal ET sequence|legend=1| 7, 9, 12, 21, 28 }}
{{Optimal ET sequence|legend=1| 7, 9, 12, 21, 28 }}
Line 30: Line 29:


=== 13-limit  ===
=== 13-limit  ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: [[27/26]], 36/35, 45/44
Comma list: [[27/26]], 36/35, 45/44


Mapping: [{{val| 1 0 0 2 -2 -1 }}, {{val| 0 1 0 2 2 3 }}, {{val| 0 0 1 -1 1 0 }}]
Mapping: {{mapping| 1 0 0 2 -2 -1 | 0 1 0 2 2 3 | 0 0 1 -1 1 0 }}


POTE generators: ~3/2 = 685.0048, ~5/4 = 390.2563
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 685.0048, ~5/4 = 390.2563


{{Optimal ET sequence|legend=1| 7, 9, 12f, 16, 21, 28 }}
{{Optimal ET sequence|legend=1| 7, 9, 12f, 16, 21, 28 }}
Line 44: Line 42:


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Mint]]
[[Category:Pages with mostly numerical content]]
[[Category:Mint family| ]] <!-- main article -->
[[Category:Mint| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]