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2187/2048 |-11 7>

113.6850 cents

sound sample

The apotome, also known as the Pythagorean chromatic semitone or the Pythagorean major semitone, is the interval 3^7/2^11 = 2187/2048 which is the chromatic semitone in the Pythagorean (3-limit) version of the diatonic scale. Unlike the situation in meantone tunings, it is larger, not smaller, than the corresponding diatonic semitone, which is the Pythagorean minor second of 256/243. It measures about 113.7¢ and can be generated by stacking seven 3/2 perfect fifths and octave-reducing the resulting interval.

See: Gallery of Just Intervals, comma