Wizma

Interval information

Ratio	420175/419904
Factorization	2-6 × 3-8 × 52 × 75
Monzo	[-6 -8 2 5⟩
Size in cents	1.116953¢
Name	wizma
Color name	z5yy3, quinzo-ayoyo 3rd
FJS name	[math]\text{d3}^{5,5,7,7,7,7,7}[/math]
Special properties	reduced
Tenney height (log2 nd)	37.3603
Weil height (log2 max(n, d))	37.3613
Wilson height (sopfr(nd))	81
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.21075 bits
Comma size	unnoticeable
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The wizma (monzo: [-6 -8 2 5⟩, ratio: 420175/419904) is an unnoticeable 7-limit comma measuring about 1.12 ¢. In terms of other commas, it is the difference between 245/243 and 1728/1715, and it is the sum of 2401/2400 and 4375/4374, the two smallest 7-limit superparticular commas.

Temperaments

Tempering out this comma alone in the 7-limit leads to the rank-3 wizmic temperament, where the septimal comma (64/63) is split into two equal parts, each for 245/243~1728/1715.

See Wizmic microtemperaments for a collection of rank-2 temperaments where it is tempered out.