256/243
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Ratio | 256/243 |
Factorization | 2^{8} × 3^{-5} |
Monzo | [8 -5⟩ |
Size in cents | 90.224996¢ |
Names | Pythagorean limma, Pythagorean diatonic semitone, blackwood comma |
Color name | sw2, sawa 2nd |
FJS name | [math]\text{m2}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 15.9248 |
Weil height (log_{2} max(n, d)) | 16 |
Wilson height (sopfr (nd)) | 31 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.66139 bits |
Comma size | medium |
S-expression | S7 * S8^{2} |
[sound info] | |
open this interval in xen-calc |
English Wikipedia has an article on:
The interval 256/243, the Pythagorean limma, or Pythagorean diatonic semitone factors as 2^{8}/3^{5}, is about 90.2 cents in size, and is the diatonic semitone in Pythagorean tuning. It can be generated by stacking five 4/3 just perfect fourths and octave-reducing the resulting interval.
Approximation
This interval is well approximated by any tuning generated with accurate octaves and fifths. For example, 4\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 blackwood temperament, and it may be called the blackwood comma. Edos tempering it out include 5edo, 10edo, 15edo, 20edo, 25edo and 30edo. See limmic temperaments for a number of other temperaments where it is tempered out.
See also
- 243/128 – its octave complement
- 729/512 – its fifth complement
- 16/15 – the classic (5-limit) diatonic semitone
- Gallery of just intervals
- Medium comma
- Pythagorean tuning