1296/1295: Difference between revisions

Interval information
Ratio	1296/1295
Subgroup monzo	2.3.5.7.37 [4 4 -1 -1 -1⟩
Size in cents	1.336344¢
Name	meancubic comma
FJS name	[math]\displaystyle{ \text{P1}_{5,7,37} }[/math]
Special properties	square superparticular,; reduced
Tenney norm (log2 nd)	20.6786
Weil norm (log2 max(n, d))	20.6797
Wilson norm (sopfr(nd))	69
Comma size	unnoticeable
S-expression	S36
	Open this interval in xen-calc

Revision as of 18:18, 24 July 2025

1296/1295, the meancubic comma is a 37-limit or 2.3.5.7.37-subgroup comma of about 1.336 cents. This is also a square-particular interval.

This comma is the difference between 37/36 and 36/35, etc.

By tempering it out is defined the meancube temperament.

Subgroup: 2.3.5.7.37

Mapping: [⟨1 1 2 2 4], ⟨0 1 0 0 4], ⟨0 0 1 0 -1], ⟨0 0 0 1 -1]]

Edos: 19, 53, 5, 31, 22, 27, 46, 12[-37], 7, 41, 8[+7], 9[-37], 26, 50, 15[+37], 58

Edo join: 72 & 53 & 99 & 31

WE tuning: ~2 = 1199.945, ~3/2 = 701.871, ~5/4 = 386.499, ~7/4 = 969.046

CWE tuning: ~2 = 1200.000, ~3/2 = 701.851, ~5/4 = 386.465, ~7/4 = 969.029

@@ Line 12: / Line 12: @@
 ===meancube===
 [[Rank]]: 4
+[[Subgroup]]: 2.3.5.7.37
+[[Mapping]]: {{mapping| 1 1 2 2 4 | 0 1 0 0 4 | 0 0 1 0 -1 | 0 0 0 1 -1}}
 [[Edo]]s: 19, 53, 5, 31, 22, 27, 46, 12[-37], 7, 41, 8[+7], 9[-37], 26, 50, 15[+37], 58
-[[Subgroup]]: 2.3.5.7.37
 [[Edo join]]: 72 & 53 & 99 & 31
-[[Mapping]]: {{mapping| 1 1 2 2 4 | 0 1 0 0 4 | 0 0 1 0 -1 | 0 0 0 1 -1}}
 [[WE tuning]]: ~2 = 1199.945, ~3/2 = 701.871, ~5/4 = 386.499, ~7/4 = 969.046