Clevelandisma

Interval information

Ratio	2000033/2000000
Factorization	2-7 × 5-6 × 76 × 17
Monzo	[-7 0 -6 6 0 0 1⟩
Size in cents	0.02856513¢
Name	Clevelandisma
FJS name	[math]\text{6d5}^{7,7,7,7,7,7,17}_{5,5,5,5,5,5}[/math]
Special properties	reduced
Tenney height (log2 nd)	41.8632
Weil height (log2 max(n, d))	41.8632
Wilson height (sopfr(nd))	103
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19983 bits
Comma size	unnoticeable
S-expression	S49 / S50
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2000033/2000000, otherwise known as the clevelandisma, is an unnoticeable comma of the 17-limit (and 2.5.7.17 subgroup) with a value of approximately 0.029 cents. It forms the difference by which a stack of three 50/49's (jubilismas) falls short of 17/16, or a stack of six 10/7s falls short of 17/2. It is tempered out in many notable approximations of the 2.5.7 subgroup, including 31 and 68 as well as the 2.5.7 microtemperament 789edo, therefore leading to most strong 2.5.7 systems into the tens of thousands also having a good 17th harmonic.

Etymology

This comma was named by Lériendil in 2024, inspired by the cantonisma (a similar 2.5.7.p ultraparticular comma) sharing the name of a city in Ohio; in addition to this reference, this comma can be thought of as "cleaving" multiple intervals of the 17th harmonic, particularly in that 10 + 7 = 17 and 10/7 is the interval that splits 17/2.

See also

• Unnoticeable comma