56edo: Difference between revisions

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 <nowiki>*</nowiki> The following table assumes the [[patent val]] {{val| 56 89 130 157 194 207 }}. Other approaches are possible. Inconsistent intervals are marked ''italic''.
-== Commas ==
+== Regular temperament properties ==
-* 5-limit commas: 2048/2025, {{monzo| -5 -10 9 }};
+{| class="wikitable center-4 center-5 center-6"
-* 7-limit commas: 686/675, 875/864, 1029/1024
+! rowspan="2" | [[Subgroup]]
-* 11-limit commas: 100/99, 245/242, 385/384, 686/675
+! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Mapping]]
+! rowspan="2" | Optimal<br>8ve Stretch (¢)
+! colspan="2" | Tuning Error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
+|-
+| 2.3
+| {{monzo| 89 -56 }}
+| [{{val| 56 89 }}]
+| -1.64
+| 1.63
+| 7.64
+|-
+| 2.3.5
+| 2048/2025, 1953125/1889568
+| [{{val| 56 89 130 }}]
+| -1.01
+| 1.61
+| 7.50
+|-
+| 2.3.5.7
+| 686/675, 875/864, 1029/1024
+| [{{val| 56 89 130 157 }}]
+| -0.352
+| 1.80
+| 8.38
+|-
+| 2.3.5.7.11
+| 100/99, 245/242, 385/384, 686/675
+| [{{val| 56 89 130 157 194 }}]
+| -0.618
+| 1.69
+| 7.90
+|-
+| 2.3.5.7.11.13
+| 91/90, 100/99, 169/168, 245/242, 385/384
+| [{{val| 56 89 130 157 194 207 }}]
+| -0.299
+| 1.70
+| 7.95
+|}
+=== Rank-2 temperaments ===
+{| class="wikitable center-all left-5"
+|+ Table of rank-2 temperaments by generator
+|-
+! Periods<br>per 8ve
+! Generator<br>(Reduced)
+! Cents<br>(Reduced)
+! Associated Ratio<br>(Reduced)
+! Temperament
+|-
+| 1
+| 3\56
+| 64.29
+| 25/24
+| [[Sycamore]]
+|-
+| 1
+| 9\56
+| 192.86
+| 28/25
+| [[Hemithirds]]
+|-
+| 1
+| 11\56
+| 235.71
+| 8/7
+| [[Slendric]]
+|-
+| 1
+| 15\56
+| 321.43
+| 6/5
+| [[Superkleismic]]
+|-
+| 1
+| 25\56
+| 535.71
+| 15/11
+| [[Maquila]] (56d) / [[maquiloid]] (56)
+|-
+| 2
+| 11\56
+| 235.71
+| 8/7
+| [[Echidnic]]
+|-
+| 2
+| 23\56<br>(5\56)
+| 492.86<br>(107.14)
+| 4/3<br>(17/16)
+| [[Keen]] / keenic
+|-
+| 4
+| 23\56<br>(5\56)
+| 492.86<br>(107.14)
+| 4/3<br>(17/16)
+| [[Bidia]] (7-limit)
+|-
+| 7
+| 23\56<br>(1\56)
+| 492.86<br>(21.43)
+| 4/3<br>(?)
+| [[Sevond]]
+|}
 == Scales ==