Misty comma: Difference between revisions

Interval information
Ratio	67108864/66430125
Factorization	226 × 3-12 × 5-3
Monzo	[26 -12 -3⟩
Size in cents	17.59885¢
Name	misty comma
FJS name	[math]\displaystyle{ \text{ddd3}_{5,5,5} }[/math]
Special properties	reduced,; reduced subharmonic
Tenney norm (log2 nd)	51.9853
Weil norm (log2 max(n, d))	52
Wilson norm (sopfr(nd))	103
Comma size	small
	Open this interval in xen-calc

Revision as of 16:10, 27 October 2022

The misty comma, 67108864/66430125 = [26 -12 -3⟩, is an interval of 17.599 cents, that can be written as (81/80)/(32805/32768)², (2048/2025)/(32805/32768), (128/125)/(531441/524288). Since these are commas of 12edo, so is the misty comma. It factors into simpler commas as (393216/390625)(1600000/1594323). However, the misty temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of 87edo and 99edo. This temperament is notably in the schismic-Pythagorean equivalence continuum, with n = 3.

@@ Line 1: / Line 1: @@
+{{Infobox Interval
+| Ratio = 67108864/66430125
+| Name = misty comma
+| Comma = yes
+}}
 The '''misty comma''', '''67108864/66430125''' = {{monzo|26 -12 -3}}, is an interval of 17.599 cents, that can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[schismic-Pythagorean equivalence continuum]], with ''n'' = 3.
-[[Category:5-limit]]
-[[Category:Small commas]]
 [[Category:Misty]]