1225/1224: Difference between revisions
mNo edit summary |
Expand with some ways to pump it |
||
| Line 4: | Line 4: | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''1225/1224''', the '''noellisma''', is | '''1225/1224''', the '''noellisma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] (also 2.3.5.7.17-[[subgroup]]) [[comma]] measuring about 1.41 [[cent]]s. It is the amount by which a stack of two [[7/6]] subminor thirds exceeds [[34/25]], and the amount by which a stack of two [[35/24]] subfifths exceeds [[17/8]], one octave above [[17/16]]. It is also the difference between [[35/34]] and [[36/35]], and between [[49/48]] and [[51/50]]. | ||
== Commatic relations == | == Commatic relations == | ||
| Line 25: | Line 25: | ||
== Temperaments == | == Temperaments == | ||
Tempering out this comma in the 17-limit results in the rank-6 '''noellismic | [[Tempering out]] this comma in the 17-limit results in the rank-6 '''noellismic''' temperament, or in the 2.3.5.7.17 subgroup, the rank-4 '''noellic''' temperament. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below. | ||
=== Noellic === | === Noellic === | ||
| Line 31: | Line 31: | ||
{{Mapping|legend=2| 1 0 0 0 -3 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 2 }} | {{Mapping|legend=2| 1 0 0 0 -3 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 2 }} | ||
: mapping generators: ~2, ~3, ~5, ~7 | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.0440{{c}}, ~5/4 = 386.1228{{c}}, ~7/4 = 968.5468{{c}} | |||
[[Optimal tuning]] ([[CTE]]): ~2 = | |||
{{Optimal ET sequence|legend=1| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }} | {{Optimal ET sequence|legend=1| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }} | ||
| Line 56: | Line 55: | ||
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | | ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | ||
|} | |} | ||
: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | : mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.0440{{c}}, ~5/4 = 386.1228{{c}}, ~7/4 = 968.5468{{c}}, ~11/8 = 551.3179{{c}}, ~13/8 = 840.5277{{c}} | ||
{{Optimal ET sequence|legend=1| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }} | {{Optimal ET sequence|legend=1| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }} | ||
| Line 67: | Line 65: | ||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Noellismic]] | [[Category:Noellismic]] | ||
[[Category:Commas referencing a famous use of a number]] | [[Category:Commas referencing a famous use of a number]] | ||