Undim comma: Difference between revisions

Interval information
Factorization	241 × 3-20 × 5-4
Monzo	[41 -20 -4⟩
Size in cents	15.64513¢
Name	Undim comma
FJS name	[math]\displaystyle{ \text{5d4}_{5,5,5,5} }[/math]
Special properties	reduced,; reduced subharmonic
Tenney norm (log2 nd)	81.987
Weil norm (log2 max(n, d))	82
Wilson norm (sopfr(nd))	162
Comma size	small
	Open this interval in xen-calc

Latest revision as of 16:19, 10 December 2024

The undim comma (monzo: [41 -20 -4⟩, ratio: 2199023255552/2179240250625) is a small 5-limit comma of about 15.645 cents. It is the amount by which a stack of four ptolemaic augmented seconds (1215/1024) falls short of the octave.

Tempering out this comma results in the 5-limit version of the undim temperament. This temperament is notably a member of the schismic–Pythagorean equivalence continuum, with n = 4. In other words, it equates the Pythagorean comma with a stack of four schismas. See Undim family for the family of temperament where it is tempered out.

This comma was named by Petr Pařízek in 2011 in terms of the corresponding temperament, undim^[1].

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-The '''undim comma''' is an interval of about 15.645 cents. It has the monzo [41 -20 -4⟩ and the ratio '''2199023255552 / 2179240250625'''.
+The '''undim comma''' ({{monzo|legend=1| 41 -20 -4 }}, [[ratio]]: 2199023255552/2179240250625) is a [[small comma|small]] [[5-limit]] [[comma]] of about 15.645 [[cent]]s. It is the amount by which a stack of four [[1215/1024|ptolemaic augmented seconds (1215/1024)]] falls short of the [[octave]].
-It equates the [[pythagorean comma]] with a stack of 4 [[schisma]]s.
+== Temperaments ==
+[[Tempering out]] this comma results in the 5-limit version of the [[undim]] temperament. This temperament is notably a member of the [[schismic–Pythagorean equivalence continuum]], with ''n'' = 4. In other words, it equates the [[Pythagorean comma]] with a stack of four [[schisma]]s. See [[Undim family]] for the family of temperament where it is tempered out.
-It defines the [[undim family]] of temperaments.
+== Etymology ==
-{{stub}}
+This comma was named by [[Petr Pařízek]] in 2011 in terms of the corresponding temperament, undim<ref>See [[Undim family]] for sources.</ref>.
+== Notes ==
+[[Category:Undim]]
+[[Category:Commas named for their regular temperament properties]]