User:Hotcrystal0/31-tone commas

There are three notable 31-tone circular commas involving octave-reduced harmonics. These are tempered out in miscellaneous 31st-octave temperaments.

31-comma

Interval information

Factorization	2-49 × 331
Monzo	[-49 31⟩
Size in cents	160.605¢
Name	31-comma
FJS name	[math]\displaystyle{ \text{dddd}{-3} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	98.1338
Weil norm (log2 max(n, d))	98.2677
Wilson norm (sopfr(nd))	191
Comma size	large
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The 31-comma is the amount by which 31 3/2 perfect fifths exceed 18 octaves.

31-5-comma

Interval information

Factorization	272 × 5-31
Monzo	[72 0 -31⟩
Size in cents	24.27487¢
Name	31-5-comma
FJS name	[math]\displaystyle{ \text{17d9}_{5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	143.98
Weil norm (log2 max(n, d))	144
Wilson norm (sopfr(nd))	299
Comma size	small
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The 31-5-comma is the amount by which 31 5/4 classical major thirds fall short of 10 octaves.

31-7-comma

Interval information

Factorization	2-87 × 731
Monzo	[-87 0 0 31⟩
Size in cents	33.6031¢
Name	31-7-comma
FJS name	[math]\displaystyle{ \text{9d12}^{7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	174.028
Weil norm (log2 max(n, d))	174.056
Wilson norm (sopfr(nd))	391
Comma size	medium
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The 31-7-comma is the amount by which 31 7/4 harmonic sevenths exceed 25 octaves.