2187/2048

Interval information

Ratio	2187/2048
Factorization	2-11 × 37
Monzo	[-11 7⟩
Size in cents	113.685¢
Names	Apotome, Pythagorean chromatic semitone
FJS name	[math]\displaystyle{ \text{A1} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	22.0947
Weil norm (log2 max(n, d))	22.1895
Wilson norm (sopfr(nd))	43
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The apotome, also known as the Pythagorean chromatic semitone or the Pythagorean major semitone, is the interval 3⁷/2¹¹ = 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 also

• Gallery of Just Intervals
• Large commas