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Pythagorean comma
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==Size== [[File:Pythagorean_tuning_geometric.svg|thumb|300px|The Pythagorean comma shown as the gap (on the right side) which causes a 12-pointed star to fail to close, which star represents the Pythagorean scale; each line representing a just perfect fifth. That gap has a central angle of 7.038 degrees, which is 23.46% of 30 degrees.]] The size of a Pythagorean comma, measured in [[Cent (music)|cents]], is :<math>\hbox{apotome} - \hbox{limma} \approx 113.69 - 90.23 \approx 23.46 ~\hbox{cents} \!</math> or more exactly, in terms of [[Interval ratio|frequency ratios]]: :<math>\frac{\hbox{apotome}}{\hbox{limma}} =\frac{3^7/2^{11}}{2^8/3^5} = \frac{3^{12}}{2^{19}} = \frac{531441}{524288} = 1.0136432647705078125 \!</math> {{-}}
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