Superpyth: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 13: / Line 13: @@
 [[MOS scale]]s of superpyth have cardinalities of 5, 7, 12, 17, or 22.
-== Temperament data ==
+For more technical data, see [[Archytas clan #Superpyth]].
-{{Main| Archytas clan #Superpyth }}
 == Interval chains ==
@@ Line 208: / Line 207: @@
 The boundary of propriety is [[17edo]].
-== Tuning spectrum ==
+== Tunings ==
+=== Prime-optimized tunings ===
+{| class="wikitable mw-collapsible mw-collapsed"
+|+style=white-space:nowrap | 2.3.7 Prime-Optimized Tunings
+|-
+! Weight-skew\Order !! Euclidean
+|-
+| Tenney || CTE<br>~3/2 = 709.5948¢
+|-
+| Tenney-Weil || CTWE<br>~3/2 = 709.3901¢
+|-
+| Frobenius || CFE<br>~3/2 = 712.8606¢<br>Eigenmonzo basis: 2.49/3 (2/5-comma tuning)
+|-
+| Frobenius-Weil || CFWE<br>~3/2 = 711.9997¢<br>Eigenmonzo basis: 2.823543/243 (7/19-comma tuning)
+|-
+| Benedetti || CBE<br>~3/2 = 707.7286¢<br>Eigenmonzo basis: 2.{{monzo| 0 -49 0 18 }} (18/85-comma tuning)
+|-
+| Benedetti-Weil || CBWE<br>~3/2 = 707.9869¢<br>Eigenmonzo basis: 2.{{monzo| 0 -63 25 }} (25/113-comma tuning)
+|}
+{| class="wikitable mw-collapsible mw-collapsed"
+|+style=white-space:nowrap | 7-limit Prime-Optimized Tunings
+|-
+! Weight-skew\Order !! Euclidean
+|-
+| Tenney || CTE<br>~3/2 = 709.5907¢
+|-
+| Tenney-Weil || CTWE<br>~3/2 = 710.1193¢
+|-
+| Frobenius || CFE<br>~3/2 = 709.7805¢<br>Eigenmonzo basis: 2.5859375/49
+|-
+| Frobenius-Weil || CFWE<br>~3/2 = 710.2428¢<br>Eigenmonzo basis: 2.{{monzo| 0 3 -37 18 }}
+|-
+| Benedetti || CBE<br>~3/2 = 709.4859¢<br>Eigenmonzo basis: 2.{{monzo| 0 -1225 -3969 450 }}
+|-
+| Benedetti-Weil || CBWE<br>~3/2 = 710.0321¢<br>Eigenmonzo basis: 2.{{monzo| 0 665 -15771 5160 }}
+|}
+=== Tuning spectrum ===
 {| class="wikitable center-all left-4"
 ! ET<br>Generator
@@ Line 298: / Line 335: @@
 | 49/48
 | 712.861
-| 2/5 comma
+| 2/5 comma, 2.3.7 CFE tuning
 |-
 |