80-17-comma

Interval information

Subgroup monzo	2.17 [327 -80⟩
Size in cents	3.56724¢
Name	80-17-comma
Color name	s1117u80-32, lesa-quinquadquadsu negative 32nd
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	653.997
Weil height (log2 max(n, d))	654
Wilson height (sopfr(nd))	2014
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.31715 bits
Comma size	small
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80-17-comma is an interval which represents the difference between a circle of 80 17/16s and 7 octaves. For EDOs upwards to the several thousands, it is tempered out if and only if 80 divides N.

Theory

80-17-comma serves as an identity in the rank-two temperaments octogintic and mercury, where it maps 17/16 to 7 periods. Other notable temperaments tempering it out are 5040edo, which is a highly composite edo, and 4320edo.