Sensipent family: Difference between revisions

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=== 2.3.5.31 ===

Fascinatingly, essentially the only extension that preserves the occurrence of sensi's 5-limit structure in such large edos as [[539edo|539]] is the one to prime 31 by interpreting the generator accurately as [[40/31]]~[[31/24]] by tempering [[961/960|S31 = 961/960]], so that the large [[31-limit]] quarter-tones [[32/31]] and [[31/30]] are equated. For a less sparse subgroup present in smaller edo tunings like [[111edo]] at the cost of slight accuracy, see the extension to the 2.3.5.11.17.31 subgroup [[#Sensible]].

Fascinatingly, essentially the only simple and accurate extension that preserves the occurrence of sensi's 5-limit structure in such large edos as [[539edo|539]] is the one to prime 31 by interpreting the generator accurately as [[40/31]]~[[31/24]] by tempering [[961/960|S31 = 961/960]], so that the large [[31-limit]] quarter-tones [[32/31]] and [[31/30]] are equated. For a less sparse subgroup present in smaller edo tunings like [[111edo]] at the cost of slight accuracy, see the extension to the 2.3.5.11.17.31 subgroup [[#Sensible]].

[[Subgroup]]: 2.3.5.31

[[Comma list]]: 78732/78125, 961/960

{{Optimal ET sequence|legend=1| 8, 11c, 19, 46, 65, 344, 409, 474, 539, 604c }}

[[Optimal tuning]] ([[CTE]]): 2 = 1\1, ~31/28 = 443.050

Badness (Dirichlet): 0.243

=== Sensible ===

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 === 2.3.5.31 ===
-Fascinatingly, essentially the only extension that preserves the occurrence of sensi's 5-limit structure in such large edos as [[539edo|539]] is the one to prime 31 by interpreting the generator accurately as [[40/31]]~[[31/24]] by tempering [[961/960|S31 = 961/960]], so that the large [[31-limit]] quarter-tones [[32/31]] and [[31/30]] are equated. For a less sparse subgroup present in smaller edo tunings like [[111edo]] at the cost of slight accuracy, see the extension to the 2.3.5.11.17.31 subgroup [[#Sensible]].
+Fascinatingly, essentially the only simple and accurate extension that preserves the occurrence of sensi's 5-limit structure in such large edos as [[539edo|539]] is the one to prime 31 by interpreting the generator accurately as [[40/31]]~[[31/24]] by tempering [[961/960|S31 = 961/960]], so that the large [[31-limit]] quarter-tones [[32/31]] and [[31/30]] are equated. For a less sparse subgroup present in smaller edo tunings like [[111edo]] at the cost of slight accuracy, see the extension to the 2.3.5.11.17.31 subgroup [[#Sensible]].
 [[Subgroup]]: 2.3.5.31
 [[Comma list]]: 78732/78125, 961/960
+{{Mapping|legend=1| 1 6 8 10 | 0 -7 -9 -8}}
+{{Optimal ET sequence|legend=1| 8, 11c, 19, 46, 65, 344, 409, 474, 539, 604c }}
+[[Optimal tuning]] ([[CTE]]): 2 = 1\1, ~31/28 = 443.050
+Badness (Dirichlet): 0.243
 === Sensible ===