No-twos subgroup temperaments: Difference between revisions
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This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 2. These are all [[nonoctave]] scales using a period of a [[tritave]] rather than an octave. | This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 2. These are all [[nonoctave]] scales using a period of a [[tritave]] rather than an octave. | ||
== Izar == | |||
[[Subgroup]]: 3.5.7 | |||
[[Comma list]]: 13841287201/13839609375 | |||
{{Mapping|legend=2|1 7 5|0 -12 -7}} | |||
Sval mapping generators: ~3, ~16807/10125 | |||
[[Optimal tuning]] (CTE): ~3 = 1\1edt, ~16807/10125 = 877.280 | |||
[[Support]]ing [[ET]]s: {{EDs|b13, b11cd, b193, b15cd, b180, b24c, b167, b37c, b154, 141, b50c, b28cd, b128, b63c|equave=t}} | |||
== BPS == | == BPS == | ||
[[Subgroup]]: 3.5.7 | [[Subgroup]]: 3.5.7 | ||
| Line 15: | Line 27: | ||
[[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]] | ||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||
[[Category:Tritave]] | [[Category:Tritave]] | ||
Revision as of 07:45, 6 July 2023
(WIP, catalog of 3.5.7 subgroup rank two temperaments will eventually be redirected here)
This is a collection of subgroup temperaments which omit the prime harmonic of 2. These are all nonoctave scales using a period of a tritave rather than an octave.
Izar
Subgroup: 3.5.7
Comma list: 13841287201/13839609375
Subgroup-val mapping: [⟨1 7 5], ⟨0 -12 -7]]
Sval mapping generators: ~3, ~16807/10125
Optimal tuning (CTE): ~3 = 1\1edt, ~16807/10125 = 877.280
Supporting ETs: b13, b11cd, b193, b15cd, b180, b24c, b167, b37c, b154, 141, b50c, b28cd, b128, b63c
BPS
Subgroup: 3.5.7
Comma list: 245/243
Sval mapping: [⟨1 1 2], ⟨0 -2 1]]
Sval mapping generators: ~3, ~9/7
Optimal tuning (POTE): ~3 = 1\1edt, ~9/7 = 440.4881