3136/3125

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Interval information
Ratio 3136/3125
Factorization 26 × 5-5 × 72
Monzo [6 0 -5 2
Size in cents 6.0832436¢
Names hemimean comma,
didacus comma
FJS name [math]\text{ddd3}^{7,7}_{5,5,5,5,5}[/math]
Special properties reduced
Tenney height (log2 n⋅d) 23.2244
Weil height (max(n, d)) 3136
Benedetti height (n⋅d) 9800000
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.55514 bits
Comma size small
open this interval in xen-calc

3136/3125, the hemimean comma or didacus comma, is a 7-limit small comma measuring about 6.1 ¢. It is the difference between five classic major thirds (5/4) and two subminor sevenths (7/4); it is also the difference between the septimal semicomma (126/125) and the septimal kleisma (225/224).

Temperaments

In the 2.5.7 subgroup, tempering out the comma leads to the rank-2 2.5.7 subgroup temperament didacus (a variant of hemithirds without a mapping for 3) with a generator of 28/25. In the full 7-limit (2.3.5.7), tempering it out leads to the rank-3 hemimean family of temperaments, which splits the syntonic comma into two equal parts, each representing 126/125~225/224. It also splits 5/4 into two equal parts, each representing 28/25. Typical edos tempering out the comma include 68, 80, 87, 99, 111, 118 and 130, and all of them tune both 126/125 and 225/224 to a single step. Smaller edos that temper out the comma are 19, 25, 31, 37, which temper out both 126/125 and 225/224, thus also 81/80, on the 2.9.5.7 subgroup.

See also