2187/2048

Interval information

Ratio	2187/2048
Factorization	2-11 × 37
Monzo	[-11 7⟩
Size in cents	113.685¢
Names	apotome, Pythagorean chroma, Pythagorean chromatic semitone, whitewood comma
Color name	Lw1, lawa unison
FJS name	[math]\displaystyle{ \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
Comma size	large
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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.

English Wikipedia has an article on:

Semitone#Pythagorean tuning

Approximation

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

Temperaments

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

• 4096/2187 – its octave complement
• Gallery of just intervals
• Large comma
• 25/24 – classic chromatic semitone