The Quartercache: Difference between revisions

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[[Comma list]]: 117440512/117406179

~~[[Sval]] [[mapping]]: [~~{{~~val~~| 1 0 1 5 ~~}}, {{val~~| 0 1 1 -1 ~~}}, {{val~~| 0 0 5 1 }}]

: mapping generators: ~2, ~3, ~33/32

[[~~POTE generator~~]]s: ~3/2 = 701.~~9826~~, ~33/32 = 53.~~3748~~

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9875{{c}}, ~3/2 = 701.9753{{c}}, ~33/32 = 53.3743{{c}}

: [[error map]]: {{val| -0.012 +0.008 -0.004 +0.031 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9802{{c}}, ~33/32 = 53.3730{{c}}

: error map: {{val| 0.000 +0.025 +0.019 +0.075 }}

{{Optimal ET sequence|legend=1| 21, 22, 24, 43, 46, 89, 135, 359, 494, 629, 742, 877, 1012, 1506, 2248, 2383, 2518, 7419, 8431e, 10949e, 13467e }}

[[Badness]] (Sintel): 0.416

The following rank-2 [[mos scale]]s of quartismic have been found:

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== Direct quartismic ==

Instead of 11-limit, defined directly in the 2.33/2.~~7/6~~ subgroup, as the quartisma itself was discovered via a representation where the generator is 33/32 and five of them stack to 7/6. [[45edo]] is an excellent tuning.

Instead of 11-limit, direct quartismic is defined directly in the 2.7/3.33 subgroup, as the quartisma itself was discovered via a representation where the generator is 33/32 and five of them stack to 7/6. [[45edo]] is an excellent tuning. It was named by [[Eliora]] in 2023.

[[Subgroup]]: 2.33/32.~~7/6~~

[[Subgroup]]: 2.7/3.33

[[Comma list]]: 117440512/117406179

: mapping generators: ~2, ~33/32

[[Optimal tuning]]s:

* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.9875{{c}}, ~33/32 = 53.3743{{c}}

: [[error map]]: {{val| -0.012 -0.012 +0.039 }}

* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~33/32 = 53.3730{{c}}

: error map: {{val| 0.000 -0.006 +0.100 }}

{{Optimal ET sequence|legend=1| 21, 22, 45, 337, 382, 427, 472, 517, 562, 607, 652, 1911, 2563, 3215, 5778, 8993* }}

<nowiki/>* wart for 33

== Altierran ==

@@ Line 12: / Line 12: @@
 [[Comma list]]: 117440512/117406179
-[[Sval]] [[mapping]]: [{{val| 1 0 1 5 }}, {{val| 0 1 1 -1 }}, {{val| 0 0 5 1 }}]
+{{Mapping|legend=1| 1 0 1 5 | 0 1 1 -1 | 0 0 5 1 }}
+: mapping generators: ~2, ~3, ~33/32
-[[POTE generator]]s: ~3/2 = 701.9826, ~33/32 = 53.3748
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9875{{c}}, ~3/2 = 701.9753{{c}}, ~33/32 = 53.3743{{c}}
+: [[error map]]: {{val| -0.012 +0.008 -0.004 +0.031 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9802{{c}}, ~33/32 = 53.3730{{c}}
+: error map: {{val| 0.000 +0.025 +0.019 +0.075 }}
 {{Optimal ET sequence|legend=1| 21, 22, 24, 43, 46, 89, 135, 359, 494, 629, 742, 877, 1012, 1506, 2248, 2383, 2518, 7419, 8431e, 10949e, 13467e }}
+[[Badness]] (Sintel): 0.416
 The following rank-2 [[mos scale]]s of quartismic have been found:
@@ Line 23: / Line 30: @@
 == Direct quartismic ==
-Instead of 11-limit, defined directly in the 2.33/2.7/6 subgroup, as the quartisma itself was discovered via a representation where the generator is 33/32 and five of them stack to 7/6. [[45edo]] is an excellent tuning.
+Instead of 11-limit, direct quartismic is defined directly in the 2.7/3.33 subgroup, as the quartisma itself was discovered via a representation where the generator is 33/32 and five of them stack to 7/6. [[45edo]] is an excellent tuning. It was named by [[Eliora]] in 2023.
-[[Subgroup]]: 2.33/32.7/6
+[[Subgroup]]: 2.7/3.33
 [[Comma list]]: 117440512/117406179
-{{Mapping|legend=2| 1 0 0 | 0 1 5 }}
+{{Mapping|legend=2| 1 1 5 | 0 5 1 }}
 : mapping generators: ~2, ~33/32
+[[Optimal tuning]]s:
+* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.9875{{c}}, ~33/32 = 53.3743{{c}}
+: [[error map]]: {{val| -0.012 -0.012 +0.039 }}
+* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~33/32 = 53.3730{{c}}
+: error map: {{val| 0.000 -0.006 +0.100 }}
+{{Optimal ET sequence|legend=1| 21, 22, 45, 337, 382, 427, 472, 517, 562, 607, 652, 1911, 2563, 3215, 5778, 8993* }}
+<nowiki/>* wart for 33
 == Altierran ==