Undim comma: Difference between revisions

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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.
{{stub}}


[[Category:Undim]]
[[Category:Commas with unknown etymology]]
[[Category:Commas with unknown etymology]]

Revision as of 18:19, 12 November 2024

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

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.

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 schismas. See Undim family for the family of temperament where it is tempered out.