648/625

The interval 648/625 is known as the diminished comma or major diesis, and is the amount by which four 6/5 minor thirds exceed an octave, in other words (6/5)⁴ / 2. Tempering it out leads to 5-limit diminished temperament. This is approximately one step of 19edo, which is the amount by which four 19edo minor thirds exceed an octave.

Interval information

Ratio	648/625
Factorization	23 × 34 × 5-4
Monzo	[3 4 -4⟩
Size in cents	62.56515¢
Names	diminished comma, major diesis
FJS name	[math]\displaystyle{ \text{d2}_{5,5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	18.6276
Weil norm (log2 max(n, d))	18.6797
Wilson norm (sopfr(nd))	38
[sound info]
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