Subgroup temperaments: Difference between revisions

{{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}

: mapping generators: ~2, ~5/3

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

: [[gencom]]: [2 6/5; 100/99 385/384]

{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}

[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents

{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}

: [[gencom]]: [2 6/5; 126/125]

{{Mapping|legend=3| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }}

: [[gencom]]: [2 11/10; 121/120 126/125]

{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131* }}

[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents

{{Mapping|legend=3| 1 -3/7 4/7 11/7 4 -6/7 | 0 0 -1 -3 -2 2 }}

: [[gencom]]: [2 6/5; 56/55 91/90 100/99]

{{Mapping|legend=3| 1 0 0 0 0 0 | 0 -8/3 1/3 7/3 -1/2 1/2 }}

: [[gencom]]: [2 13/11; 275/273 847/845]

{{Optimal ET sequence|legend=1| 29, 33, 37, 41, 45, 49, 78, 94, 143* }}

[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents

{{Mapping|legend=3| 1 -1/2 -1/2 -1/2 3/2 | 0 -15/4 9/4 25/4 -19/4 }}

: [[gencom]]: [2 12/11; 3025/3024 3125/3087]

{{Optimal ET sequence|legend=1| 8, 33, 41, 49, 204*^† }}

[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents

{{Mapping|legend=3| 1 -3 0 2 0 1 | 0 24/5 -6/5 -26/5 9/5 -1/5 }}

: [[gencom]]: [2 13/10; 121/120 169/168 275/273]

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

: [[gencom]]: [2 9/7; 245/243]

{{Optimal ET sequence|legend=1| 8, 11, 19, 30, 41, 49, 52, 145*, 166^†, 197*^†, 215^†, 264*^† }}

[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents

{{Mapping|legend=3| 1 -1/6 5/6 0 0 -1/3 | 0 -1/2 -3/2 0 0 1 }}

: [[gencom]]: [2 6/5; 325/324]

{{Mapping|legend=2| 1 0 2 -2 | 0 3 -1 5 }}

: mapping generators: ~2, ~12/7

{{Mapping|legend=3| 1 -4/3 3 -1/3 5/3 | 0 4/3 -3 7/3 -11/3 }}

: [[gencom]]: [2 7/6; 176/175 540/539]

{{Optimal ET sequence|legend=1| 9, 22, 31, 40, 191c*, 231c*, 271c*, 311c* }}

[[Tp tuning #T2 tuning|RMS error]]: 0.6028 cents

{{Mapping|legend=3| 1 -5/4 3 -1/4 7/4 -1/4 | 0 -1/4 -3 3/4 -21/4 19/4 }}

: [[gencom]]: [2 7/6; 144/143 176/175 196/195]

{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 156c*†, 205c*† }}

[[Tp tuning #T2 tuning|RMS error]]: 0.8790 cents

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

: mapping generators: ~2, ~13/12

{{Mapping|legend=3| 1 -5/4 2 -1/4 3/4 3/4 | 0 -1/2 3 3/2 -3/2 1/2 }}

: [[gencom]]: [2 13/12; 56/55 78/77 91/90]

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

: mapping generators: ~2, ~21/20

{{Mapping|legend=3| 1 1/10 -4/5 11/10 1/5 | 0 -3/2 -1 3/2 1 }}

: [[gencom]]: [2 21/20; 100/99 245/242]

{{Mapping|legend=2| 1 0 1 | 0 1 2 }}

: mapping generators: ~2, ~7/3

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

: [[gencom]]: [2 7/6; 99/98]

{{Mapping|legend=2| 1 0 5 | 0 1 -2 }}

: mapping generators: ~2, ~5

{{Mapping|legend=3| 1 2 0 -1 | 0 -4/5 1 2/5 }}

: [[gencom]]: [2 5; 225/224]

{{Optimal ET sequence|legend=1| 3, 13, 16, 19, 22, 25, 72, 97, 122, 269c* }}

[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents

{{Mapping|legend=2| 1 0 10 17 22 | 0 1 -6 -10 -13 }}

: mapping generators: ~2, ~3

{{Mapping|legend=3| 1 1 -5 -1 2 4 | 0 1 29/4 5/4 -11/4 -23/4 }}

: [[gencom]]: [2 3/2; 196/195, 352/351, 364/363]

{{Mapping|legend=3| 1 2 -3/4 -11/4 9/4 5/4 | 0 -2 0 12 -9 -3 }}

: [[gencom]]: [2 15/13; 352/351 676/675 847/845]

{{Mapping|legend=3| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }}

: [[gencom]]: [63/50 10/9; 250047/250000]

{{Mapping|legend=3| 1 0 -3/4 5/4 -3/4 1/4 | 0 0 0 -4 3 1 }}

: [[gencom]]: [2 13/10; 847/845 1001/1000]

{{Mapping|legend=3| 1 0 -3/4 5/4 -3/4 1/4 1/4 | 0 0 0 -4 3 1 2 }}

: [[gencom]]: [2 13/10; 170/169 221/220 847/845]

{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 95^t, 124^t }}

[[Tp tuning #T2 tuning|RMS error]]: 0.7521 cents

{{Mapping|legend=3| 1 0 -1/3 0 -1/3 2/3 | 0 0 -4/3 0 5/3 -1/3 }}

: [[gencom]]: [2 13/10; 2200/2197]

{{Mapping|legend=3| 1 2 -5/3 0 4/3 1/3 | 0 -2 4 0 -5 1 }}

: [[gencom]]: [2 15/13; 352/351 676/675]

=== Hypnosis ===

[[Subgroup]]: 2.3.7.11/5.13

{{Mapping|legend=3| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }}

: [[gencom]]: [2 3/2; 352/351 364/363]

{{Optimal ET sequence|legend=1| 5, 7, 12f, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595b*^† }}

[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents

{{Mapping|legend=3| 2 4 -2 0 9 2 | 0 -2 3/2 0 -5 -3/2 }}

: [[gencom]]: [55/39 15/13; 243/242 676/675]

{{Optimal ET sequence|legend=1| 10, 14, 24, 106, 130, 154, 178*, 202* }}

=== Oceanfront ===

[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~49/40 = 350.966

[[Tp tuning #T2 tuning|RMS error]]: ?

== 3/2.5/2… subgroups ==

{{Mapping|legend=2| 1 3 4 | 0 -4 -5 }}

: sval mapping generators: ~3/2, ~15/14

Supporting ETs: *5, *6, *7[+5/2, +7/2], *9[-5/2, --7/2], *11, *16, *17[+5/2], *23[+5/2, +7/2], *21[-7/2], *27, *28[+5/2], *38, *43[-7/2], *49

==== 3/2.5/2.7/2.11/2 ====

{{Mapping|legend=2| 1 3 4 4 | 0 -4 -5 1 }}

: sval mapping generators: ~3/2, ~15/14

[[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2], *21[-7/2], *38[-11/2], *43[-7/2, -11/2], *59[-7/2, -11/2], *70[-7/2, -11/2], *75[--7/2, -11/2]

==== 3/2.5/2.7/2.11/2.13/2 ====

[[Support]]ing [[ET]]s: *11, *5, *16, *6, *27[-11/2]

=== Semiwolf ===

Supporting ETs: *5, *6[+13], *7[-7, -13], *9, *11[+13], *13, *14, *17[-7, -13], *19[+13], *21[-7, -13], *22[-7], *23[+13], *25[-7, -13], *31[-7]

=== Doubleton ===

Supporting ETs: *6, *10, *16, *14[-13], *8[+7], *22, *18[-13], *26, *24[-13], *28[+7], *20[+7], *36[-13], *12[+7, +13], *34[-13]

== 5/2-equave subgroups ==

Supporting ETs: *5[-7], *8, *19[+7], *21[-7], *27[+7], *29[-7], *35[+7], *43[+7], *37[-7], *51[+7, +11], *45[-7], *59[+7, +11]

= Related temperament collections =