94edo: Difference between revisions

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@@ Line 21: / Line 21: @@
 == Regular temperament properties ==
+{| class="wikitable center-4 center-5 center-6"
-{| class="wikitable center-all"
+! rowspan="2" | Subgroup
-! colspan="2" |
+! rowspan="2" | [[Comma list]]
-! 3-limit
+! rowspan="2" | [[Mapping]]
-! 5-limit
+! rowspan="2" | Optimal<br>8ve stretch (¢)
-! 7-limit
+! colspan="2" | Tuning error
-! 11-limit
+|-
-! 13-limit
+! [[TE error|Absolute]] (¢)
-! 17-limit
+! [[TE simple badness|Relative]] (%)
-! 19-limit
-! 23-limit
-! 29-limit
-! 31-limit
 |-
-! colspan="2" |Octave stretch (¢)
+| 2.3
+| {{monzo| 149 -94 }}
+| [{{val| 94 149 }}]
 | -0.054
+| 0.054
+| 0.43
+|-
+| 2.3.5
+| 32805/32768, 9765625/9565938
+| [{{val| 94 149 218 }}]
 | +0.442
+| 0.704
+| 5.52
+|-
+| 2.3.5.7
+| 225/224, 3125/3087, 118098/117649
+| [{{val| 94 149 218 264 }}]
 | +0.208
+| 0.732
+| 5.74
+|-
+| 2.3.5.7.11
+| 225/224, 385/384, 1331/1323, 2200/2187
+| [{{val| 94 149 218 264 325 }}]
 | +0.304
+| 0.683
+| 5.35
+|-
+| 2.3.5.7.11.13
+| 225/224, 275/273, 325/324, 385/384, 1331/1323
+| [{{val| 94 149 218 264 325 348 }}]
 | +0.162
+| 0.699
+| 5.48
+|-
+| 2.3.5.7.11.13.17
+| 170/169, 225/224, 275/273, 289/288, 325/324, 385/384
+| [{{val| 94 149 218 264 325 348 384 }}]
 | +0.238
+| 0.674
+| 5.28
+|-
+| 2.3.5.7.11.13.17.19
+| 170/169, 190/189, 225/224, 275/273, 289/288, 325/324, 385/384
+| [{{val| 94 149 218 264 325 348 384 399 }}]
 | +0.323
+| 0.669
+| 5.24
+|-
+| 2.3.5.7.11.13.17.19.23
+| 170/169, 190/189, 209/208, 225/224, 275/273, 289/288, 300/299, 323/322
+| [{{val| 94 149 218 264 325 348 384 399 425 }}]
 | +0.354
-| +0.227
-| +0.134
-|-
-! rowspan="2" |Error
-! [[TE error|absolute]] (¢)
-| 0.054
-| 0.704
-| 0.732
-| 0.683
-| 0.699
-| 0.674
-| 0.669
 | 0.637
-| 0.715
-| 0.741
-|-
-! [[TE simple badness|relative]] (%)
-| 0.43
-| 5.52
-| 5.74
-| 5.35
-| 5.48
-| 5.28
-| 5.24
 | 4.99
-| 5.60
-| 5.81
 |}
-et has a lower relative error than any previous ETs in the 23-limit. The next ET that does better in this subgroup is 193.
+et is lower in relative error than any previous equalt temperaments in the 23-limit, and the next ET that does better in this subgroup is 193.
 === Rank-2 temperaments ===
@@ Line 98: / Line 114: @@
 | 11\94
 | 140.426
-| 243/224 <br> 13/12
+| 243/224
-| [[Tsaharuk]] <br> [[Quanic]]
+| [[Tsaharuk]] / [[quanic]]
 |-
 | 1
@@ Line 111: / Line 127: @@
 | 497.872
 | 4/3
-| [[Schismatic]] / [[Garibaldi]]
+| [[Helmholtz]] / [[garibaldi]] / [[cassandra]]
 |-
 | 2
@@ Line 150: / Line 166: @@
 * 53&amp;94 {{multival| 1 -8 -14 23 20 -46 -3 -35 … }} (one garibaldi)
 * 41&amp;94 {{multival| 1 -8 -14 23 20 48 -3 -35 … }} (another garibaldi, only differing in the mappings of 17 and 23)
-* 135&amp;94 {{multival| 1 -8 -14 23 20 48 -3 59 … }}(another garibaldi)
+* 135&amp;94 {{multival| 1 -8 -14 23 20 48 -3 59 … }} (another garibaldi)
 * 130&amp;94 {{multival| 6 -48 10 -50 26 6 -18 -22 … }} (a pogo extension)
 * 58&amp;94 {{multival| 6 46 10 44 26 6 -18 -22 … }} (a supers extension)