936/935: Difference between revisions
m it's the ''major'' minthma |
m Cleanup |
||
| Line 4: | Line 4: | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''936/935''', the '''ainisma''' or '''ainic comma''', is | '''936/935''', the '''ainisma''' or '''ainic comma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] [[comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272|tannisma (273/272)]] from the [[385/384|keenanisma (385/384)]], and the [[256/255|septendecimal kleisma (256/255)]] from the [[352/351|major minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. See [[#Commatic relations]] for more. | ||
== Commatic relations == | == Commatic relations == | ||
| Line 30: | Line 30: | ||
== Temperaments == | == Temperaments == | ||
When tempered out in the full 17-limit, the resulting rank-6 temperament is called the '''ainismic | When tempered out in the full 17-limit, the resulting rank-6 temperament is called the '''ainismic''' temperament, or in the 2.3.5.11.13.17 subgroup, the rank-5 '''ainic''' temperament. Both are characterized by the presence of [[essentially tempered chord]]s called [[ainismic chords]]. | ||
=== Ainic === | === Ainic === | ||
[[Subgroup]]: 2.3.5.11.13.17 | [[Subgroup]]: 2.3.5.11.13.17 | ||
[[ | [[Subgroup val|Subgroup-val]] [[mapping]]:<br> | ||
{| class="right-all" | {| class="right-all" | ||
|- | |- | ||
| Line 50: | Line 48: | ||
| ⟨ || 0 || 0 || 0 || 0 || 1 || 1 || ]] | | ⟨ || 0 || 0 || 0 || 0 || 1 || 1 || ]] | ||
|} | |} | ||
: | : mapping generators: ~2, ~3, ~5, ~11, ~13 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7942{{c}}, ~5/4 = 386.4863{{c}}, ~11/8 = 551.7011{{c}}, ~13/8 = 840.0893{{c}} | ||
* [[CWE]]: ~2 = | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8763{{c}}, ~5/4 = 386.5772{{c}}, ~11/8 = 551.8274{{c}}, ~13/8 = 840.2857{{c}} | ||
{{Optimal ET sequence|legend=1| 22, 24, 31, 34, 46, 53, 58, 65, 72, 87, 111, 137, 183, 304, 320, 354, 400, 407, 441, 537, 552g, 624 }} | {{Optimal ET sequence|legend=1| 22, 24, 31, 34, 46, 53, 58, 65, 72, 87, 111, 137, 183, 304, 320, 354, 400, 407, 441, 537, 552g, 624 }} | ||
| Line 60: | Line 58: | ||
=== Ainismic === | === Ainismic === | ||
[[Subgroup]]: 2.3.5.7.11.13.17 | [[Subgroup]]: 2.3.5.7.11.13.17 | ||
[[Mapping]]:<br> | [[Mapping]]:<br> | ||
| Line 81: | Line 77: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7942{{c}}, ~5/4 = 386.4863{{c}}, ~7/4 = 968.8259{{c}}, ~11/8 = 551.7011{{c}}, ~13/8 = 840.0893{{c}} | ||
* [[CWE]]: ~2 = | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8763{{c}}, ~5/4 = 386.5773{{c}}, ~7/4 = 968.9509{{c}}, ~11/8 = 551.8275{{c}}, ~13/8 = 840.2857{{c}} | ||
{{Optimal ET sequence|legend=1| 22, 26, 31, 38df, 41, 46, 58, 72, 103, 111, 121, 149, 159, 171, 183, 217, 224, 270, 354, 400, 441, 552g, 624, 1393ceegg, 1576cdegg }} | {{Optimal ET sequence|legend=1| 22, 26, 31, 38df, 41, 46, 58, 72, 103, 111, 121, 149, 159, 171, 183, 217, 224, 270, 354, 400, 441, 552g, 624, 1393ceegg, 1576cdegg }} | ||
| Line 90: | Line 86: | ||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Ainismic]] | [[Category:Ainismic]] | ||
[[Category:Commas named by translating something into another language]] | [[Category:Commas named by translating something into another language]] | ||