From Xenharmonic Wiki
(Redirected from Pythagorean limma)
Jump to navigation Jump to search
Interval information
Ratio 256/243
Factorization 28 × 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 (log2 nd) 15.9248
Weil height (log2 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 * S82

[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 28/35, 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.


This interval is well approximated by any tuning generated with accurate octaves and fifths. For example, 4\53 is a very good approximation.


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