Sensipent: Difference between revisions
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* [[Sensipent family#Sendai]] for the 2.3.5.23.29.31-subgroup version, and | * [[Sensipent family#Sendai]] for the 2.3.5.23.29.31-subgroup version, and | ||
* [[Sensipent family#Sensible]] for the 2.3.5.11.17.23.31-subgroup version. | * [[Sensipent family#Sensible]] for the 2.3.5.11.17.23.31-subgroup version. | ||
=== Sensipent interval table === | |||
Amazingly, in the 2.3.5.31-subgroup-limited 155-odd-limit, every interval of every number of generators up to 23 is given at least one interpretation, so that the 27-note MOS ([[19L 8s]]) is surprisingly well-supplied with harmony. The main "holes" are at 24 and 26 gens (as 25 is [[~]][[75/64]]) and that these interpretations tend to be rather complex, requiring a good tuning and a context to justify them. For these reasons, the extensions [[sensible]] and [[sendai]] are likely to be preferred in practice, whose interval tables are thus also documented here, being alternative but higher-accuracy extensions to 2.3.5.31 sensipent. | |||
{| class="wikitable" | |||
! Gens | |||
! Cents | |||
! Ratios | |||
|- | |||
| 1 | |||
| 443.05 | |||
| [[40/31]], [[31/24]], [[162/125]] | |||
|- | |||
| 2 | |||
| 886.1 | |||
| [[5/3]] | |||
|- | |||
| 3 | |||
| 129.15 | |||
| [[100/93]], [[155/144]], [[27/25]] | |||
|- | |||
| 4 | |||
| 572.2 | |||
| [[25/18]], [[216/155]] | |||
|- | |||
| 5 | |||
| 1015.25 | |||
| [[9/5]] | |||
|- | |||
| 6 | |||
| 258.3 | |||
| [[125/108]], [[36/31]], [[93/80]] | |||
|- | |||
| 7 | |||
| 701.35 | |||
| '''[[3/2]]''' | |||
|- | |||
| 8 | |||
| 1144.4 | |||
| [[60/31]], '''[[31/16]]''' | |||
|- | |||
| 9 | |||
| 387.45 | |||
| '''[[5/4]]''' | |||
|- | |||
| 10 | |||
| 830.5 | |||
| [[50/31]], [[155/96]], [[81/50]] | |||
|- | |||
| 11 | |||
| 73.55 | |||
| [[25/24]], [[162/155]] | |||
|- | |||
| 12 | |||
| 516.6 | |||
| [[125/93]], [[27/20]] | |||
|- | |||
| 13 | |||
| 959.65 | |||
| [[125/72]], [[54/31]] | |||
|- | |||
| 14 | |||
| 202.7 | |||
| '''[[9/8]]''' | |||
|- | |||
| 15 | |||
| 645.75 | |||
| [[45/31]], '''[[93/64]]''' | |||
|- | |||
| 16 | |||
| 1088.8 | |||
| '''[[15/8]]''' | |||
|- | |||
| 17 | |||
| 331.85 | |||
| [[75/62]], '''[[155/128]]''' | |||
|- | |||
| 18 | |||
| 774.9 | |||
| '''[[25/16]]''' | |||
|- | |||
| 19 | |||
| 17.95 | |||
| [[125/124]], [[81/80]] | |||
|- | |||
| 20 | |||
| 461.0 | |||
| [[125/96]], [[81/62]] | |||
|- | |||
| 21 | |||
| 904.05 | |||
| '''[[27/16]]''' | |||
|- | |||
| 22 | |||
| 147.1 | |||
| [[135/124]] | |||
|- | |||
| 23 | |||
| 590.15 | |||
| '''[[45/32]]''' | |||
|} | |||
=== Sendai interval table === | === Sendai interval table === | ||