2187/2048
| 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 | |
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.
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