Pythagorean comma: Difference between revisions
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{{Wikipedia| Pythagorean comma }} | {{Wikipedia| Pythagorean comma }} | ||
The '''Pythagorean comma''' or '''ditonic comma''' is the interval with the ratio '''531441/524288''' ([[monzo]]: {{monzo| -19 12 }}). It is the amount by which twelve fifths exceed seven octaves, or in other words (3/2)<sup>12</sup>/2<sup>7</sup>. It also can be written as the ratio between the apotome and limma, ([[2187/2048]])/([[256/243]]), and as the ratio between the Pythagorean augmented fourth and the Pythagorean diminished fifth, ([[729/512]])/([[1024/729]]). In addition, it is also the difference | The '''Pythagorean comma''' or '''ditonic comma''' is the interval with the ratio '''531441/524288''' ([[monzo]]: {{monzo| -19 12 }}). It is the amount by which twelve fifths exceed seven octaves, or in other words (3/2)<sup>12</sup>/2<sup>7</sup>. It also can be written as the ratio between the apotome and limma, ([[2187/2048]])/([[256/243]]), and as the ratio between the Pythagorean augmented fourth and the Pythagorean diminished fifth, ([[729/512]])/([[1024/729]]). In addition, it is also the difference between six [[9/8]] major seconds and an octave. | ||
In [[pythagorean tuning]], this interval is an ''inverse'' diminished second, even though it has a positive size. | In [[pythagorean tuning]], this interval is an ''inverse'' diminished second, even though it has a positive size. | ||