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Interval information
Ratio 2187/2048
Factorization 2-11 × 37
Monzo [-11 7
Size in cents 113.68501¢
Names apotome,
Pythagorean chroma,
Pythagorean chromatic semitone,
whitewood comma
Color name Lw1, lawa unison
FJS name [math]\text{A1}[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 nd) 22.0947
Weil height (log2 max(n, d)) 22.1895
Wilson height (sopfr (nd)) 43
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~4.62809 bits
Comma size large

[sound info]
open this interval in xen-calc
English Wikipedia has an article on:

2187/2048, the apotome, also known as the Pythagorean chromatic semitone or the Pythagorean chroma, is the chromatic semitone in the Pythagorean tuning. It is the 3-limit interval between seven perfect just fifths (3/2) and four octaves (2/1): 37/211 = 2187/2048, and measures about 113.7¢. 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.


This interval is well approximated by any tuning generated with accurate octaves and fifths. For example, 5\53 is a very good approximation.


When this ratio is taken as a comma to be tempered in the 5-limit, it produces the whitewood temperament, and it may be called the whitewood comma. See apotome family for extensions thereof.

See also