Magic comma

Interval information

Ratio	3125/3072
Factorization	2-10 × 3-1 × 55
Monzo	[-10 -1 5⟩
Size in cents	29.61357¢
Names	magic comma, small diesis
FJS name	[math]\displaystyle{ \text{dd}{-2}^{5,5,5,5,5} }[/math]
Special properties	reduced
Tenney height (log2 nd)	23.1946
Weil height (log2 max(n, d))	23.2193
Wilson height (sopfr(nd))	48
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The magic comma or small diesis is the interval 3125/3072. It is the amount by which five major thirds (5/4) exceeds the twelfth, or “tritave”; in other words (5/4)⁵/3. Tempering it out leads to 5-limit magic temperament.