Sensipent family: Difference between revisions

Line 97:

Badness (Dirichlet): 0.639

==== 2.3.5.11.17.31 ====

==== 2.3.5.11.17.23 ====

~~Sensible uses the accurate mapping of prime 31 in sensipent, so that the sensible generator serves many roles in subgroup harmony without the need for interpreting it as high-damage ~~~[[~~9/7~~]] ~~or ~[[13/10]] intervals~~. Its S-expression-based comma list is {([[256/255|S16]],) [[8019/8000|S9/S10]], [[961/960|S31]], [[1024/1023|S32]], [[1089/1088|S33]]} implying also tempering [[496/495]] = S31 * S32 and [[528/527]] = S32 * S33 as well as [[16337/16335]] = S31/S33 = ([[17/15|34/30]])/([[33/31]])2 = ([[17~~/15]])/([[33/31]])2. A notable [[patent val]] tuning not appearing in the optimal ET sequence is [[157edo]]~~.

[[Subgroup]]: 2.3.5.11.17.23

[[~~Subgroup~~]]: ~~2.3.5.11.17.31~~

[[Comma list]]: [[8019/8000]], [[16384/16335]], [[256/255]], [[576/575]]

~~[[Comma list]]: [[8019/8000]], [[16384/16335]], [[256/255]], [[961/960]]~~

{{Optimal ET sequence|legend=1| 19, 46, 65, 111, 176g~~, 287cg~~ }}

[[Optimal tuning]] ([[CTE]]): 2 = 1\1, ~31/24 = 443.185

Badness (Dirichlet): 0.555

==== 2.3.5.11.17.23.31 ====

Sensible uses the accurate mapping of prime 31 in sensipent, so that the sensible generator serves many roles in subgroup harmony without the need for interpreting it as high-damage [[~]][[9/7]] or [[~]][[13/10]] intervals. Its S-expression-based comma list is {([[256/255|S16]],) [[8019/8000|S9/S10]], [[576/575|S24]], [[961/960|S31]], [[1024/1023|S32]], [[1089/1088|S33]]} implying also tempering [[496/495]] = S31 * S32 and [[528/527]] = S32 * S33 as well as [[16337/16335]] = S31/S33 = ([[17/15|34/30]])/([[33/31]])2 = ([[17/15]])/([[33/31]])2. A notable [[patent val]] tuning not appearing in the optimal ET sequence is [[157edo]].

[[Subgroup]]: 2.3.5.11.17.23.31

[[Comma list]]: [[8019/8000]], [[16384/16335]], [[256/255]], [[576/575]], [[961/960]]

[[Optimal tuning]] ([[CTE]]): 2 = 1\1, ~31/24 = 443.~~185~~

[[Optimal tuning]] ([[CTE]]): 2 = 1\1, ~31/24 = 443.183

Badness (Dirichlet): 0.~~519~~

Badness (Dirichlet): 0.490

== Sensi ==

@@ Line 97: / Line 97: @@
 Badness (Dirichlet): 0.639
-==== 2.3.5.11.17.31 ====
+==== 2.3.5.11.17.23 ====
-Sensible uses the accurate mapping of prime 31 in sensipent, so that the sensible generator serves many roles in subgroup harmony without the need for interpreting it as high-damage ~[[9/7]] or ~[[13/10]] intervals. Its S-expression-based comma list is {([[256/255|S16]],) [[8019/8000|S9/S10]], [[961/960|S31]], [[1024/1023|S32]], [[1089/1088|S33]]} implying also tempering [[496/495]] = S31 * S32 and [[528/527]] = S32 * S33 as well as [[16337/16335]] = S31/S33 = ([[17/15|34/30]])/([[33/31]])<sup>2</sup> = ([[17/15]])/([[33/31]])<sup>2</sup>. A notable [[patent val]] tuning not appearing in the optimal ET sequence is [[157edo]].
+[[Subgroup]]: 2.3.5.11.17.23
-[[Subgroup]]: 2.3.5.11.17.31
+[[Comma list]]: [[8019/8000]], [[16384/16335]], [[256/255]], [[576/575]]
-[[Comma list]]: [[8019/8000]], [[16384/16335]], [[256/255]], [[961/960]]
+{{Mapping|legend=1| 1 6 8 -6 -6 2 | 0 -7 -9 15 16 4 }}
-{{Mapping|legend=1| 1 6 8 -6 -6 10 | 0 -7 -9 15 16 -8 }}
+{{Optimal ET sequence|legend=1| 19, 46, 65, 111, 176g }}
-{{Optimal ET sequence|legend=1| 19, 46, 65, 111, 176g, 287cg }}
+[[Optimal tuning]] ([[CTE]]): 2 = 1\1, ~31/24 = 443.185
+Badness (Dirichlet): 0.555
+==== 2.3.5.11.17.23.31 ====
+Sensible uses the accurate mapping of prime 31 in sensipent, so that the sensible generator serves many roles in subgroup harmony without the need for interpreting it as high-damage [[~]][[9/7]] or [[~]][[13/10]] intervals. Its S-expression-based comma list is {([[256/255|S16]],) [[8019/8000|S9/S10]], [[576/575|S24]], [[961/960|S31]], [[1024/1023|S32]], [[1089/1088|S33]]} implying also tempering [[496/495]] = S31 * S32 and [[528/527]] = S32 * S33 as well as [[16337/16335]] = S31/S33 = ([[17/15|34/30]])/([[33/31]])<sup>2</sup> = ([[17/15]])/([[33/31]])<sup>2</sup>. A notable [[patent val]] tuning not appearing in the optimal ET sequence is [[157edo]].
+[[Subgroup]]: 2.3.5.11.17.23.31
+[[Comma list]]: [[8019/8000]], [[16384/16335]], [[256/255]], [[576/575]], [[961/960]]
+{{Mapping|legend=1| 1 6 8 -6 -6 2 10 | 0 -7 -9 15 16 4 -8 }}
+{{Optimal ET sequence|legend=1| 19, 46, 65, 111, 176g }}
-[[Optimal tuning]] ([[CTE]]): 2 = 1\1, ~31/24 = 443.185
+[[Optimal tuning]] ([[CTE]]): 2 = 1\1, ~31/24 = 443.183
-Badness (Dirichlet): 0.519
+Badness (Dirichlet): 0.490
 == Sensi ==