2197/2187

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Interval information
Ratio 2197/2187
Factorization 3-7 × 133
Monzo [0 -7 0 0 0 3
Size in cents 7.8979793¢
Name threedie
Color name s3o32, satritho 2nd,
Satritho comma
FJS name [math]\text{dd2}^{13,13,13}[/math]
Special properties reduced
Tenney height (log2 n⋅d) 22.1961
Weil height (max(n, d)) 2197
Benedetti height (n⋅d) 4804839
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.65837 bits
Comma size small
S-expression S25 * S262
open this interval in xen-calc

The threedie, 2197/2187, is a 3.13-subgroup analog of the 2.5-subgroup diesis. Measuring about 7.9 ¢, it is a small comma. Analogously to tempering the diesis, which divides the octave into three sharp 5/4s, tempering the threedie divides the tritave into three slightly flat 13/9s, since (13/9)3/3 = 2197/2187. Furthermore, tempering out the threedie divides 9/8 into three instances of 27/26. 596edo provides the optimal patent val for the corresponding rank-5 temperament.