Undim comma

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 height (log2 nd)	81.987
Weil height (log2 max(n, d))	82
Wilson height (sopfr(nd))	162
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~3.07975 bits
Comma size	small
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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.

Etymology

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