No-twos subgroup temperaments: Difference between revisions
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* Mintaka does not include the 5th harmonic, and has an ~11/7 generator, two of which give the ~27/11, and three of which give the ~27/7 (9/7 and a tritave). | * Mintaka does not include the 5th harmonic, and has an ~11/7 generator, two of which give the ~27/11, and three of which give the ~27/7 (9/7 and a tritave). | ||
== Arcturus == | == 3.5.7 subgroup temperaments == | ||
=== Arcturus === | |||
''see [[Arcturus]], [[Arcturus clan]]'' | ''see [[Arcturus]], [[Arcturus clan]]'' | ||
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[[Optimal ET sequence]]: [[2edt|b2]], [[11edt|b11]], [[13edt|b13]] | [[Optimal ET sequence]]: [[2edt|b2]], [[11edt|b11]], [[13edt|b13]] | ||
== | === BPS === | ||
''see [[Bohlen-Pierce-Stearns]]'' | ''see [[Bohlen-Pierce-Stearns]]'' | ||
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[[Optimal ET sequence]]: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]] | [[Optimal ET sequence]]: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]] | ||
==Canopus== | === Canopus === | ||
''see [[Canopus]]'' | |||
[[Subgroup]]: 3.5.7 | [[Subgroup]]: 3.5.7 | ||
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[[Support]]ing [[ET]]s: {{EDs|b13, b10, b75, b62, b23, b49, b36, b16, b7cd, 29, b42c, b19cd, b33cd, b55c|equave=t}} | [[Support]]ing [[ET]]s: {{EDs|b13, b10, b75, b62, b23, b49, b36, b16, b7cd, 29, b42c, b19cd, b33cd, b55c|equave=t}} | ||
== Izar == | === Izar === | ||
[[Subgroup]]: 3.5.7 | [[Subgroup]]: 3.5.7 | ||
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[[Support]]ing [[ET]]s: {{EDs|b13, b11cd, b193, b15cd, b180, b24c, b167, b37c, b154, 141, b50c, b28cd, b128, b63c|equave=t}} | [[Support]]ing [[ET]]s: {{EDs|b13, b11cd, b193, b15cd, b180, b24c, b167, b37c, b154, 141, b50c, b28cd, b128, b63c|equave=t}} | ||
== Mintaka == | == 3.5.11 subgroup temperaments == | ||
=== Polaris === | |||
''Main article: [[Polaris]]'' | |||
Polaris tempers out the comma 177147/171875, and thus equates 7 5/3's with 15/11, or equivalently 7 9/5's with 11/9. | |||
[[Subgroup]]: 3.5.11 | |||
[[Comma list]]: 177147/171875 | |||
[[Gencom]]: [3/1 5/3; 177147/171875] | |||
[[Mapping]]: [{{{val|1 2 1}}, {{val|0 1 -6}}]] | |||
[[POTE generator]]: ~5/3 = 892.6 | |||
[[EDT]]s: 17, 15, 32, 49, 13[+11], 47, 19, 11[+11], 81, 66, 79[+11], 62[+11], 28[+11], 21[-11] | |||
=== Deneb === | |||
''Main article: [[Deneb]]'' | |||
[[Subgroup]]: 3.5.11 | |||
[[Comma list]]: 6655/6561 | |||
[[Gencom]]: [3/1 11/9; 6655/6561] | |||
[[Mapping]]: [{{val|1 2 2}}, {{val|0 -3 1}}] | |||
[[POTE generator]]: ~[[11/9]] = 340.242 | |||
[[EDT]]s: 28, 11, 17, 6, 39, 5, 67, 45, 50, 16, 23, 73, 61, 62 | |||
=== Alnilam === | |||
Effectively a [[microtemperament]], Alnilam takes a generator of an 81/55 flat fifth and equates 9 of them with [[11/9]]. The name was given by [[User:CompactStar|CompactStar]] to continue with the theme of naming no-twos temperaments after proper star names, but also to indirectly reference [[mavila]]. | |||
[[Subgroup]]: 3.5.11 | |||
[[Comma list]]: {{monzo|0 -35 9 0 10}} | |||
[[Gencom]]: [3/1 81/55; {{monzo|0 -35 9 0 10}}] | |||
[[Mapping]]: [[{{val|1 5 -1}}, {{val|0 -10 9}}] | |||
[[CTE tuning|CTE generator]]: ~81/55 = 672.410 | |||
[[EDT]]s: 99, 17, 82, 116, 181, 65, 14[-5], 280, 48, 215, 31, 133, 314, 263 | |||
== Other tritave-based subgroups == | |||
=== Aldebaran === | |||
''see [[Aldebaran]]'' | |||
[[Subgroup]]: 3.5.13 | |||
[[Comma list]]: 3159/3125 | |||
[[Mapping]]: [{{val|1 0 5}}, {{val|0 1 -2}}] | |||
[[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 | |||
=== Mintaka === | |||
''see [[Mintaka]]'' | ''see [[Mintaka]]'' | ||
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[[Support]]ing [[ET]]s: {{EDs|b22, b5, b17, b39, b12, b61, b27, b7, b83, b49, b56, b32, b29, b100|equave=t}} | [[Support]]ing [[ET]]s: {{EDs|b22, b5, b17, b39, b12, b61, b27, b7, b83, b49, b56, b32, b29, b100|equave=t}} | ||
== No-twos-or-threes subgroup temperaments == | == No-twos-or-threes subgroup temperaments == | ||