Würschmidt comma

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Interval information
Ratio 393216/390625
Monzo [17 1 -8
Size in cents 11.445
Name(s) Würschmidt comma

The Würschmidt comma, 393216/390625 = [17 1 -8, is a 5-limit comma of 11.4 cents.

It is the amount by which eight major thirds fall short of a perfect fifth, octave-reduced: ((5/4)8 × 393216/390625) / 4 = 3/2.

Therefore, it is also the amount by which seven major thirds fall short of 24/5 (i.e. 6/5 plus two octaves). In other words, ((5/4)7 × 393216/390625) / 4 = 6/5.

Tempering it out leads to würschmidt temperament. As in meantone, it implies that 3/2 will be tempered flat and/or 5/4 will be tempered sharp, and therefore 6/5 will be tempered flat.

See also