Dimcomp comma

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Interval information
Ratio 390625/388962
Factorization 2-1 × 3-4 × 58 × 7-4
Monzo [-1 -4 8 -4
Size in cents 7.3860816¢
Name dimcomp comma
Color name quadruyoyo comma
FJS name [math]\text{5d}{-4}^{5,5,5,5,5,5,5,5}_{7,7,7,7}[/math]
Special properties reduced
Tenney height (log2 n⋅d) 37.1447
Weil height (max(n, d)) 390625
Benedetti height (n⋅d) 151938281250
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.62633 bits
Comma size small
open this interval in xen-calc

The dimcomp comma is a 7-limit small comma measuring about 7.4 cents. It is the amount by which a stack of four quasi-tempered minor thirds (25/21) exceeds an octave.

Temperaments

Tempering out this comma in the 7-limit leads to the dimcomp temperament, with the effect of splitting the octave into four equal parts, and edos that are not multiples of 4 cannot be tempering it out. Rank-2 temperaments tempering it out include diminished, compton, bidia, quadritikleismic, octoid, etc.

See dimcomp family for a number of rank-3 temperaments where it is tempered out.

See also