Würschmidt comma: Difference between revisions
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Jdfreivald (talk | contribs) m Related the comma to 3/2. |
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The Würschmidt comma | The Würschmidt comma is 393216/390625 = |17 1 -8>, an interval of 11.445 cents. | ||
It is the amount by which eight major thirds falls 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 falls 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|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. | |||
Revision as of 13:49, 12 June 2020
The Würschmidt comma is 393216/390625 = |17 1 -8>, an interval of 11.445 cents.
It is the amount by which eight major thirds falls 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 falls 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.