No-twos subgroup temperaments: Difference between revisions

Cleanup (2/); - catalogs that don't fit
Cleanup (3/3)
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= Other tritave-based subgroups =
= Other tritave-based subgroups =
== Aldebaran ==
== Aldebaran ==
{{main|Aldebaran}}
{{Main| Aldebaran }}


[[Subgroup]]: 3.5.13
[[Subgroup]]: 3.5.13
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[[Comma list]]: 3159/3125
[[Comma list]]: 3159/3125


[[Sval]] [[mapping]]: [{{val|1 0 5}}, {{val|0 1 -2}}]
{{Mapping|legend=2| 1 0 5 | 0 1 -2 }}
 
[[Optimal tuning]] ([[CTE]]): ~5/3 = 887.76{{c}}


[[Support]]ing [[ET]]s: 15, 17, 13, 32, 47, 28, 11[-13], 19[+13], 43, 9[-13], 7[-13], 49[+13], 21[+13], 41[-13]
[[Support]]ing [[ET]]s: 15, 17, 13, 32, 47, 28, 11[-13], 19[+13], 43, 9[-13], 7[-13], 49[+13], 21[+13], 41[-13]
[[CTE tuning|CTE generator]]: ~[[5/3]] = 887.76


== Keladic ==
== Keladic ==
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[[Comma list]]: 351/343
[[Comma list]]: 351/343


[[Sval]] [[mapping]]: [{{val| 1 1 0 }}, {{val| 0 1 3 }}]
{{Mapping|legend=2| 1 1 0 | 0 1 3 }}
 
: mapping generators: ~3, ~7/3
Sval mapping generators: ~3, ~7/3


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* PEWE (Pure-Equaves WE): ~3 = 1\1ed3, ~[[7/3]] = 1480.661
* [[POTE]]: ~3 = 1901.955{{c}}, ~7/3 = 1480.661{{c}}
* [[CWE]]: ~3 = 1\1ed3, ~[[7/3]] = 1479.487
* [[CWE]]: ~3 = 1901.955{{c}}, ~7/3 = 1479.487{{c}}


[[Support]]ing [[ET]]s: {{EDs|b9, b5, b14, b13, b23, b22, b32, b6f, b31, b19f, b17f, b41, b7ff, b40|equave=t}}
[[Support]]ing [[ET]]s: {{EDs| b9, b5, b14, b13, b23, b22, b32, b6f, b31, b19f, b17f, b41, b7ff, b40 |equave=t}}


== Sadalmelik ==
== Sadalmelik ==
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[[Comma list]]: 85293/83521
[[Comma list]]: 85293/83521


[[Sval]] [[mapping]]: [{{val| 1 0 2 }}, {{val| 0 4 1 }}]
{{Mapping|legend=2| 1 0 2 | 0 4 1 }}
 
: mapping generators: ~3, ~17/9
Sval mapping generators: ~3, ~17/9


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~3 = 1\1ed3, ~[[17/9]] = 1109.689
* [[CTE]]: ~3 = 1901.955{{c}}, ~17/9 = 1109.689{{c}}
* [[CWE]]: ~3 = 1\1ed3, ~[[17/9]] = 1110.376
* [[CWE]]: ~3 = 1901.955{{c}}, ~17/9 = 1110.376{{c}}


[[Support]]ing [[ET]]s: {{EDs|b12, b5, b7, b17, b29, b19, b41, b53, b31, b65, b22f, b9ff, b77, b43|equave=t}}
[[Support]]ing [[ET]]s: {{EDs| b12, b5, b7, b17, b29, b19, b41, b53, b31, b65, b22f, b9ff, b77, b43 |equave=t}}


= No-twos-or-threes subgroup temperaments =
= No-twos-or-threes subgroup temperaments =
== Antipyth ==
== Antipyth ==
{{main|Antipyth}}
{{Main| Antipyth }}


[[Subgroup]]: 5.7.11
[[Subgroup]]: 5.7.11
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{{Mapping|legend=2| 1 2 7 | 0 1 7 }}
{{Mapping|legend=2| 1 2 7 | 0 1 7 }}
: mapping generators: ~5, ~7/25


Mapping generators: ~5, ~7/25
[[Optimal tuning]]s ([[CTE]]): ~5 = 2786.314{{c}}, ~7/5 = 592.728{{c}}


[[Optimal tuning]] ([[CTE]]): ~5 = 1\1ed5, ~[[7/5]] = 592.728
[[Support]]ing [[ET]]s: {{EDs| c14, c5, c19, c33, c47, c9e, c61, c75, c23e, c24e, c52e, c80e, c89e, c37e |equave=5}}
 
[[Support]]ing [[ET]]s: {{EDs|c14, c5, c19, c33, c47, c9e, c61, c75, c23e, c24e, c52e, c80e, c89e, c37e|equave=5}}


== Juggernaut ==
== Juggernaut ==
{{main|Juggernaut}}
{{Main| Juggernaut }}


[[Subgroup]]: 5.7.11
[[Subgroup]]: 5.7.11
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{{Mapping|legend=2| 2 4 3 | 0 1 0 }}
{{Mapping|legend=2| 2 4 3 | 0 1 0 }}
: mapping generators: ~11/5, ~7/25


Mapping generators: ~11/5, ~7/25
[[Optimal tuning]] ([[CTE]]): ~11/5 = 1393.157{{c}}, ~[[7/5]] = 582.512{{c}}


[[Optimal tuning]] ([[CTE]]): ~11/5 = 1\2ed5, ~[[7/5]] = 582.512
[[Support]]ing [[ET]]s: {{EDs| c14, c10, c6, c18, c24, c22, c32, c16, c38, c8d, c34, c26d, c46, c52e |equave=5}}
 
[[Support]]ing [[ET]]s: {{EDs|c14, c10, c6, c18, c24, c22, c32, c16, c38, c8d, c34, c26d, c46, c52e|equave=5}}


=== Tridecimal juggernaut ===
=== Tridecimal juggernaut ===
[[Subgroup]]: 5.7.11.13
Subgroup: 5.7.11.13


[[Comma list]]: 125/121, 637/625
Comma list: 125/121, 637/625


{{Mapping|legend=2| 2 4 3 0 | 0 1 0 -2 }}
{{Mapping|legend=2| 2 4 3 0 | 0 1 0 -2 }}


Mapping generators: ~11/5, ~7/25
[[Optimal tuning]] ([[CTE]]): ~11/5 = 1393.157{{c}}, ~[[7/5]] = 582.512{{c}}
 
[[Optimal tuning]] ([[CTE]]): ~11/5 = 1\2ed5, ~[[7/5]] = 582.512


[[Support]]ing [[ET]]s: {{EDs|c10, c14, c6, c24, c34, c16f, c44, c18f, c38, c26f, c54, c64|equave=5}}
[[Support]]ing [[ET]]s: {{EDs| c10, c14, c6, c24, c34, c16f, c44, c18f, c38, c26f, c54, c64 |equave=5}}


= Graphs =
= Graphs =
See: [[Catalog of 3.5.7 subgroup rank two temperaments#Graphs]]
See: [[Catalog of 3.5.7 subgroup rank two temperaments #Graphs]]


== Projective tuning space diagrams ==
== Projective tuning space diagrams ==
See: [[Catalog of 3.5.7 subgroup rank two temperaments#Projective tuning space diagrams]]
See: [[Catalog of 3.5.7 subgroup rank two temperaments #Projective tuning space diagrams]]


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Non-octave temperaments]]
[[Category:Non-octave temperaments]]
[[Category:Catalogs of rank-2 temperaments]]
[[Category:Catalogs of rank-2 temperaments]]