37edo: Difference between revisions

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@@ Line 574: / Line 574: @@
 |}
-== Just approximation ==
+== Regular temperament properties ==
+{| class="wikitable center-4 center-5 center-6"
-=== Temperament measures ===
+! rowspan="2" | Subgroup
-The following table shows [[TE temperament measures]] (RMS normalized by the rank) of 37EDO.
+! rowspan="2" | [[Comma list]]
-{| class="wikitable center-all"
+! rowspan="2" | [[Mapping]]
-! colspan="2" |
+! rowspan="2" | Optimal<br>8ve stretch (¢)
-! 3-limit
+! colspan="2" | Tuning error
-! 5-limit
+|-
-! 7-limit
+! [[TE error|Absolute]] (¢)
-! 11-limit
+! [[TE simple badness|Relative]] (%)
-! 13-limit
+|-
-! no-3 11-limit
+| 2.5
-! no-3 13-limit
+| {{monzo| 86 -37 }}
-! no-3 17-limit
+| [{{val| 37 86 }}]
-! no-3 19-limit
+| -0.619
-! no-3 23-limit
+| 0.619
+| 1.91
+|-
+| 2.5.7
+| 3136/3125, 4194304/4117715
+| [{{val| 37 86 104 }}]
+| -0.905
+| 0.647
+| 2.00
 |-
-! colspan="2" |Octave stretch (¢)
+| 2.5.7.11
-| -3.65
+| 176/175, 1375/1372, 65536/65219
-| -2.85
+| [{{val| 37 86 104 128 }}]
-| -2.50
-| -2.00
-| -1.79
 | -0.681
+| 0.681
+| 2.10
+|-
+| 2.5.7.11.13
+| 176/175, 640/637, 847/845, 1375/1372
+| [{{val| 37 86 104 128 137 }}]
 | -0.692
-| -0.265
-| -0.0386
-| +0.299
-|-
-! rowspan="2" |Error
-! [[TE error|absolute]] (¢)
-| 3.64
-| 3.18
-| 2.82
-| 2.71
-| 2.52
-| 0.681
 | 0.610
-| 1.11
-| 1.17
-| 1.41
-|-
-! [[TE simple badness|relative]] (%)
-| 11.24
-| 9.82
-| 8.70
-| 8.37
-| 7.78
-| 2.10
 | 1.88
-| 3.41
-| 3.59
-| 4.35
 |}
-* 37EDO is most prominent in the no-3 11-, 13-, 17-, 19- and 23-limit subgroups. The next EDO that does better in these subgroups is 109, 581, 103, 124 and 93, respectively.
+* 37et is most prominent in the no-3 11-, 13-, 17-, 19- and 23-limit subgroups. The next ETs doing better in these subgroups are 109, 581, 103, 124 and 93, respectively.
-== Scales ==
+=== Rank-2 temperaments ===
-* [[MOS_Scales_of_37edo|MOS Scales of 37edo]]
-* [[roulette6]]
-* [[roulette7]]
-* [[roulette13]]
-* [[roulette19]]
-* [[Chromatic_pairs#Shoe|Shoe]]
-* [[37ED4]]
-* [[square_root_of_13_over_10|The Square Root of 13/10]]
-== Linear temperaments ==
 * [[List of 37et rank two temperaments by badness]]
@@ Line 721: / Line 696: @@
 |
 |}
+== Scales ==
+* [[MOS Scales of 37edo]]
+* [[roulette6]]
+* [[roulette7]]
+* [[roulette13]]
+* [[roulette19]]
+* [[Chromatic pairs #Shoe|Shoe]]
+* [[37ED4]]
+* [[square_root_of_13_over_10|The Square Root of 13/10]]
 == Music ==