4761/4760

4761/4760, the demiquartervicema or demiquartervice comma is a 23-limit superparticular comma of about 0.36 cents. It is the difference between 69/68 and 70/69. By tempering it out is defined the demiquartervice temperament, which enables the demiquartervice chords.

Interval information

Ratio	4761/4760
Factorization	2-3 × 32 × 5-1 × 7-1 × 17-1 × 232
Monzo	[-3 2 -1 -1 0 0 -1 0 2⟩
Size in cents	0.3636664¢
Names	demiquartervice comma, demiquartervicema
Color name	23oo17urg1, bitwetho-asurugu 1sn, Bitwetho-asurugu comma
FJS name	[math]\displaystyle{ \text{dd}{-3}^{23,23}_{5,7,17} }[/math]
Special properties	square superparticular, reduced
Tenney norm (log2 nd)	24.4338
Weil norm (log2 max(n, d))	24.4341
Wilson norm (sopfr(nd))	87
Comma size	unnoticeable
S-expression	S69
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Etymology

The words demiquartervice and demiquartervicema were introduced by Xenllium in 2023. Both were so named for the following reason – rational intervals 69/68 and 70/69 are mapped to 1/48 of an octave (25¢, demi-quartertone, halfway between both ratios) in some EDOs of the 48n-edo family (such as 48edo and 240edo).

See also

• Unnoticeable comma
• List of superparticular intervals