2197/2187

Interval information

Ratio	2197/2187
Factorization	3-7 × 133
Monzo	[0 -7 0 0 0 3⟩
Size in cents	7.897979¢
Name	threedie
FJS name	[math]\displaystyle{ \text{dd2}^{13,13,13} }[/math]
Special properties	reduced
Tenney height (log2 nd)	22.1961
Weil height (log2 max(n, d))	22.2026
Wilson height (sopfr(nd))	60
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The threedie, 2197/2187, is a 3.13 analog of the 2.5 diesis. 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.