Sensamagic family: Difference between revisions
m →13-limit: Fix subgroup value |
+overview to extensions; misc cleanup |
||
| Line 1: | Line 1: | ||
The '''sensamagic family''' of rank-3 | The '''sensamagic family''' of [[rank-3 temperament]]s tempers out [[245/243]]. For a list of rank-2 temperaments, see [[Sensamagic clan]]. | ||
== Sensamagic | == Sensamagic == | ||
{{Main| Sensamagic }} | {{Main| Sensamagic }} | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 245/243 | [[Comma list]]: 245/243 | ||
| Line 18: | Line 18: | ||
: Angle (3/2, 9/7) = 86.5288° | : Angle (3/2, 9/7) = 86.5288° | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~3/2 = 703.7424, ~9/7 = 440.9020 | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
| Line 42: | Line 42: | ||
* 24: 64/63, 15059072/14348907 | * 24: 64/63, 15059072/14348907 | ||
}} | }} | ||
=== Overview to extensions === | |||
Temperaments discussed elsewhere include [[supernatural]] (→ [[Keemic family #Supernatural|Keemic family]]). Considered below are undecimal sensamagic, sensawer, octarod, shrusus, bisector and sensigh. | |||
== Undecimal sensamagic == | == Undecimal sensamagic == | ||
Subgroup: 2.3.5.7.11 | {{Main| Sensamagic }} | ||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 245/243, 385/384 | [[Comma list]]: 245/243, 385/384 | ||
| Line 50: | Line 55: | ||
[[Mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 1 2 -2 }}, {{val| 0 0 2 -1 -1 }}] | [[Mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 1 2 -2 }}, {{val| 0 0 2 -1 -1 }}] | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~3/2 = 703.8004, ~9/7 = 440.9178 | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
| Line 76: | Line 81: | ||
== Sensawer == | == Sensawer == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 245/243, 441/440 | [[Comma list]]: 245/243, 441/440 | ||
| Line 82: | Line 87: | ||
[[Mapping]]: [{{val| 1 0 0 0 -3 }}, {{val| 0 1 1 2 5 }}, {{val| 0 0 2 -1 -4 }}] | [[Mapping]]: [{{val| 1 0 0 0 -3 }}, {{val| 0 1 1 2 5 }}, {{val| 0 0 2 -1 -4 }}] | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~3/2 = 703.1900, ~9/7 = 441.1359 | ||
{{Val list|legend=1| 14c, 19e, 27e, 41, 60e, 87, 302d, 389d, 476bd }} | {{Val list|legend=1| 14c, 19e, 27e, 41, 60e, 87, 302d, 389d, 476bd }} | ||
| Line 100: | Line 105: | ||
== Octarod == | == Octarod == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 100/99, 245/243 | [[Comma list]]: 100/99, 245/243 | ||
| Line 106: | Line 111: | ||
[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 1 2 0 }}, {{val| 0 0 2 -1 4 }}] | [[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 1 2 0 }}, {{val| 0 0 2 -1 4 }}] | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~3/2 = 705.0464, ~9/7 = 439.5050 | ||
{{Val list|legend=1| 8d, 14c, 19, 22, 27e, 41, 104, 131e }} | {{Val list|legend=1| 8d, 14c, 19, 22, 27e, 41, 104, 131e }} | ||
| Line 115: | Line 120: | ||
== Shrusus == | == Shrusus == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 176/175, 245/243 | [[Comma list]]: 176/175, 245/243 | ||
| Line 121: | Line 126: | ||
[[Mapping]]: [{{val| 1 0 0 0 -4 }}, {{val| 0 1 1 2 4 }}, {{val| 0 0 2 -1 3 }}] | [[Mapping]]: [{{val| 1 0 0 0 -4 }}, {{val| 0 1 1 2 4 }}, {{val| 0 0 2 -1 3 }}] | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~3/2 = 706.3702, ~9/7 = 442.1147 | ||
{{Val list|legend=1| 22, 46, 68, 95, 141bc, 163bc, 209bc, 350bc }} | {{Val list|legend=1| 22, 46, 68, 95, 141bc, 163bc, 209bc, 350bc }} | ||
| Line 139: | Line 144: | ||
== Bisector == | == Bisector == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 121/120, 245/243 | [[Comma list]]: 121/120, 245/243 | ||
| Line 147: | Line 152: | ||
Mapping generators: ~77/54, ~3, ~9/7 | Mapping generators: ~77/54, ~3, ~9/7 | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~3/2 = 703.0884, ~9/7 = 441.1060 | ||
{{Val list|legend=1| 22, 46, 68, 82e, 106de, 114, 128e }} | {{Val list|legend=1| 22, 46, 68, 82e, 106de, 114, 128e }} | ||
| Line 167: | Line 172: | ||
=== 17-limit === | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||