2187/2048
Ratio | 2187/2048 |
Factorization | 2^{-11} × 3^{7} |
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 (log_{2} nd) | 22.0947 |
Weil height (log_{2} 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 |
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): 3^{7}/2^{11} = 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.
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