No-threes subgroup temperaments: Difference between revisions
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This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 3. | This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 3. | ||
== Overview by mapping of 5 == | |||
Classified by focusing on the mapping of 5th harmonic, similar to [[Rank-2 temperaments by mapping of 3]]. | |||
* French decimal and Trader are with ~2/1 period and ~5/4 generator. There is one-to-one correspondence between 2.5 subgroup and mapped intervals. | |||
* Didacus is with a ~28/25 generator, two of which give the ~5/4. | |||
* Ostara, Movila and Vengeance are with variety expressed generator, three of which give the ~5/2. | |||
* Insect is with a ~55/32 generator, three of which give the ~5/1. | |||
* Frostburn is with a ~28/25 generator, four of which give the ~8/5. | |||
Others are more far. | |||
Temperaments discussed elsewhere include | |||
* Jubilic → [[Jubilismic clan]] | |||
* Berylic → [[4th-octave temperaments]] | |||
* etc. | |||
== Llywelyn aka shoe == | == Llywelyn aka shoe == | ||
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{{Optimal ET sequence|legend=1|7, 18dg, 25, 32, 57, 488, 545, 602, 659, 716, 773, 830, 887, 1717g}} | {{Optimal ET sequence|legend=1|7, 18dg, 25, 32, 57, 488, 545, 602, 659, 716, 773, 830, 887, 1717g}} | ||
== Yer (rank 3) == | === Yer (rank 3) === | ||
[[Subgroup]]: 2.11.13.17.19 | [[Subgroup]]: 2.11.13.17.19 | ||
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{{Optimal ET sequence|legend=1| 11, 13, 24, 33, 37, 46, 57, 70, 127, 197eh }} | {{Optimal ET sequence|legend=1| 11, 13, 24, 33, 37, 46, 57, 70, 127, 197eh }} | ||
== Yamablu == | === Yamablu === | ||
Yamablu, with a generator of ~17/13, is named for its tempering of the yama comma (209/208) and the blume comma (2057/2048), which also implies the blumeyer comma (2432/2431). The [[Kite's Method of Naming Rank-2 Scales using Mode Numbers|13th Yamablu[13]]] scale is a linear-temperament version of [[Gjaeck]]. | Yamablu, with a generator of ~17/13, is named for its tempering of the yama comma (209/208) and the blume comma (2057/2048), which also implies the blumeyer comma (2432/2431). The [[Kite's Method of Naming Rank-2 Scales using Mode Numbers|13th Yamablu[13]]] scale is a linear-temperament version of [[Gjaeck]]. | ||
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[[Tp tuning #T2 tuning|RMS error]]: 0.4898 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.4898 cents | ||
== Mavericks == | === Mavericks === | ||
[[Subgroup]]: 2.13.19 | [[Subgroup]]: 2.13.19 | ||