Würschmidt comma: Difference between revisions
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The '''Würschmidt comma''' ({{monzo| 17 1 -8 }} = '''393216/390625''') is a [[5-limit]] [[comma]] of 11.4 cents. | The '''Würschmidt comma''' ({{monzo| 17 1 -8 }} = '''393216/390625''') 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)<sup>8</sup> × 393216/390625) / 4 = 3/2. | It is the amount by which eight major thirds fall short of a perfect fifth, octave-reduced: ((5/4)<sup>8</sup> × 393216/390625) / 4 = 3/2. It is also equal to the difference between the lesser diesis and the magic comma, ([[128/125]])/([[3125/3072]]). | ||
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)<sup>7</sup> × 393216/390625) / 4 = 6/5. | 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)<sup>7</sup> × 393216/390625) / 4 = 6/5. | ||