Rin comma

Interval information

Ratio	1977326743/1953125000
Factorization	2-3 × 5-12 × 711
Monzo	[-3 0 -12 11⟩
Size in cents	21.3204¢
Name	rin comma
Color name	11za12g8, lezo-aquadtrigu octave
FJS name	[math]\displaystyle{ \text{10d8}^{7,7,7,7,7,7,7,7,7,7,7}_{5,5,5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	61.744
Weil norm (log2 max(n, d))	61.7618
Wilson norm (sopfr(nd))	143
Comma size	small
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The rin comma, 1977326743/1953125000 = [-3 0 -12 11⟩, is a 2.5.7 subgroup comma measuring about 21.32 cents. It is the comma which a stack of eleven 7/5s exceeds a stack of five octaves and a 5/4.

Etymology

It was named by Kaisei in 2026 from the Japanese reading of the Chinese character 隣, "rin", meaning “neighboring” or “adjacent”, since it was found while investigating approximations of 5/4 generated by stacks of adjacent-prime ratios (e.g. 7/5 and 11/7).