Sensamagic family: Difference between revisions
+ intro to certain entries |
m Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| " |
||
| (10 intermediate revisions by 3 users not shown) | |||
| Line 7: | Line 7: | ||
{{Main| Sensamagic }} | {{Main| Sensamagic }} | ||
Sensamagic is generated by a perfect fifth and a wide supermajor third of ~[[9/7]], two of which make ~[[5/3]]. | Sensamagic is generated by a perfect fifth and a wide supermajor third of ~[[9/7]], two of which make ~[[5/3]]. Among the good edo tunings are [[87edo]] and [[128edo]], as well as the [[optimal patent val]] [[283edo]]. | ||
Another notable tuning is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 703.7424{{c}}, 440.9020{{c}} with pure octaves since prime 2 is not involved in the comma to begin with, though its difference from [[CWE]] is practically unnoticeable. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 54: | Line 54: | ||
=== Overview to extensions === | === Overview to extensions === | ||
Temperaments discussed elsewhere include [[supernatural]] (→ [[Keemic family #Supernatural|Keemic family]]). | The second comma in the comma list defines which [[11-limit]] family member we are looking at. Undecimal sensamagic adds [[385/384]], sensawer adds [[441/440]], octarod adds [[100/99]], shrusus adds [[176/175]]. These temperaments use the same generators as sensamagic. Bisector adds [[121/120]] with a half-octave period. | ||
Temperaments discussed elsewhere include [[supernatural]] (→ [[Keemic family #Supernatural|Keemic family]]) and [[sensigh]] (→ [[Sengic family #Sensigh|Sengic family]]). The rest are considered below. | |||
== Undecimal sensamagic == | == Undecimal sensamagic == | ||
| Line 89: | Line 91: | ||
Comma list: 245/243, 352/351, 364/363 | Comma list: 245/243, 352/351, 364/363 | ||
{{Mapping|legend=0| 1 0 0 0 7 12 | 0 1 1 2 -2 -5 | 0 0 2 -1 -1 -1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 121: | Line 123: | ||
Comma list: 196/195, 245/243, 352/351 | Comma list: 196/195, 245/243, 352/351 | ||
{{Mapping|legend=0| 1 0 0 0 -3 2 | 0 1 1 2 5 2 | 0 0 2 -1 -4 -4 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 132: | Line 134: | ||
== Octarod == | == Octarod == | ||
Octarod tempers out 100/99 and the interval class of [[11/1|11]] is found as a stack of four ~9/7's. The name ''octarod'' | Octarod tempers out [[100/99]] and the interval class of [[11/1|11]] is found as a stack of four ~9/7's. The name ''octarod'' was the former name of the sensamagic comma before being reused for this 11-limit extension, and comes from [[octacot]] and [[rodan]]; it should be noted however that rodan does not temper out 100/99 and therefore does not support this temperament. | ||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
| Line 146: | Line 148: | ||
: error map: {{val| 0.000 +2.570 -3.230 +0.944 +5.801 }} | : error map: {{val| 0.000 +2.570 -3.230 +0.944 +5.801 }} | ||
{{Optimal ET sequence|legend=1| 14c, 19, 22, 27e, 41, 90e, 131e }} * | {{Optimal ET sequence|legend=1| 14c, 19, 22, 27e, 41, 90e, 131e}}* | ||
<nowiki/>[[ | <nowiki/>*[[Optimal patent val]]: [[104edo|104]] | ||
[[Badness]] (Sintel): 0.698 | [[Badness]] (Sintel): 0.698 | ||
| Line 176: | Line 178: | ||
Comma list: 91/90, 176/175, 245/243 | Comma list: 91/90, 176/175, 245/243 | ||
{{Mapping|legend=0| 1 0 0 0 -4 1 | 0 1 1 2 4 1 | 0 0 2 -1 3 3 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 204: | Line 206: | ||
[[Badness]] (Sintel): 1.31 | [[Badness]] (Sintel): 1.31 | ||
[[Category:Sensamagic family| ]] <!-- main article --> | |||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category: | [[Category:Catalogs of rank-3 temperaments]] | ||