No-fives subgroup temperaments: Difference between revisions

Switch to Sintel's badness, WE & CWE tunings (10/)
- dubious extensions
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[[Comma list]]: 24576/24389
[[Comma list]]: 24576/24389


[[Mapping]]: [{{val|1 2 5}}, {{val|0 3 -1}}]
{{Mapping|legend=2| 1 2 5 | 0 3 -1 }}


[[CTE tuning|CTE generator]]: ~32/29 = 166.067
[[Optimal tuning]]s ([[CTE]]): ~32/29 = 166.067{{c}}


{{Optimal ET sequence|legend=1| 7, 22, 29, 94, 123, 152j, 275jj, 427jjj }}
{{Optimal ET sequence|legend=1| 7, 22, 29, 94, 123, 152j, 275jj, 427jjj }}


=== Sematology ===
=== Sematology ===
This temperament tempers out 4107/4096 and thus equates 2 [[37/32]]'s with [[4/3]].
This temperament tempers out [[4107/4096]] and thus equates a stack of two [[37/32]]'s with [[4/3]].


[[Subgroup]]: 2.3.37
[[Subgroup]]: 2.3.37
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[[Comma list]]: 4107/4096
[[Comma list]]: 4107/4096


[[Gencom]]: [2 37/32; 4107/4096]
{{Mapping|legend=2| 1 1 5 | 0 -2 1 }}


[[Mapping]]: [{{val|1 1 5}}, {{val|0 -2 1}}]
[[Optimal tuning]]s ([[POTE]]): ~37/32 = 249.075{{c}}
 
[[POTE generator]]: ~[[37/32]] = 249.075


{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 53, 77, 130 }}
{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 53, 77, 130 }}
==== 2.3.7.37 subgroup ====
[[Subgroup]]: 2.3.7.37
[[Comma list]]: 4107/4096, 259/256
[[Gencom]]: [2 37/32; 4107/4096 259/256]
[[Mapping]]: [{{val|1 1 1 5}}, {{val|0 -2 -1 1}}]
[[POTE generator]]: ~[[37/32]] = 247.782
{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 53d }}
==== 2.3.5.37 subgroup ====
It is difficult to extend sematology to include 5, due the 5th harmonic being quite high-complexity.
[[Subgroup]]: 2.3.5.37
[[Comma list]]: 4107/4096, 17592186044416/17562397269605
[[Gencom]]: [2 37/32; 4107/4096 17592186044416/17562397269605]
[[Mapping]]: [{{val|1 1 4 5}}, {{val|0 -2 -8 1}}]
[[POTE generator]]: ~[[37/32]] = 251.393
{{Optimal ET sequence|legend=1| 5, 14c, 19, 43, 62 }}
===== 2.3.5.7.37 subgroup =====
[[Subgroup]]: 2.3.5.7.37
[[Comma list]]: 4107/4096, 17592186044416/17562397269605, 259/256
[[Gencom]]: [2 37/32; 4107/4096 17592186044416/17562397269605 259/256]
[[Mapping]]: [{{val|1 1 4 1 5}}, {{val|0 -2 -8 -1 1}}]
[[POTE generator]]: ~[[37/32]] = 251.204
{{Optimal ET sequence|legend=1| 5, 14c, 19 }}


=== Reversed mavila ===
=== Reversed mavila ===
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[[Comma list]]: 81/74
[[Comma list]]: 81/74


[[Gencom]]: [2 4/3; 81/74]
{{Mapping|legend=2| 1 1 0 | 0 -1 12 }}


[[Mapping]]: [{{val|1 1 0}}, {{val|0 -1 12}}]
[[Optimal tuning]]s ([[POTE]]): ~4/3 = 521.397{{c}}
 
[[POTE generator]]: ~4/3 = 521.397


{{Optimal ET sequence|legend=1| 5l, 7l, 9, 16l }}
{{Optimal ET sequence|legend=1| 5l, 7l, 9, 16l }}
Line 1,328: Line 1,283:
{{Main| Reversed meantone }}
{{Main| Reversed meantone }}


Subgroup: 2.3.41
[[Subgroup]]: 2.3.41


[[Comma list]]: 82/81
[[Comma list]]: 82/81


[[Gencom]]: [2 4/3; 82/81]
{{Mapping|legend=2| 1 2 7 | 0 -1 -4 }}


[[Mapping|Sval mapping]]: [{{val|1 2 7}}, {{val|0 -1 -4}}]
[[Optimal tuning]]s ([[POTE]]): ~4/3 = 494.509{{c}}
 
[[Tp tuning|POL2 generator]]: ~4/3 = 494.509


{{Optimal ET sequence|legend=1| 5, 12, 17 }}
{{Optimal ET sequence|legend=1| 5, 12, 17 }}
==== 2.3.7.41 subgroup ====
Subgroup: 2.3.7.41
[[Comma list]]: 64/63, 82/81
[[Gencom]]: [2 4/3; 64/63 82/81]
[[Mapping|Sval mapping]]: [{{val| 1 2 2 7 }}, {{val| 0 -1 2 -4 }}]
[[POTE generator]]: ~4/3 = 490.0323
[[TOP tuning|TOP generator]]s: ~2 = 1197.2342, ~4/3 = 488.9029
{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 49 }}
==== 2.3.7.11.41 subgroup ====
Subgroup: 2.3.7.11.41
[[Comma list]]: 64/63, 82/81, 99/98
[[Gencom]]: [2 4/3; 64/63 82/81 99/98]
[[Mapping|Sval mapping]]: [{{val| 1 2 2 1 7 }}, {{val| 0 -1 2 6 -4 }}]
[[POTE generator]]: ~4/3 = 492.1787
[[TOP tuning|TOP generator]]s: ~2 = 1197.9683, ~4/3 = 491.3454
{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 39d }}


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Subgroup temperaments]]
[[Category:Subgroup temperaments]]
[[Category:Rank 2]]
[[Category:Rank 2]]