# 256/243

(Redirected from Pythagorean limma)
 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 $\text{m2}$ Special properties reduced,reduced subharmonic Tenney height (log2 n⋅d) 15.9248 Weil height (max(n, d)) 256 Benedetti height (n⋅d) 62208 Harmonic entropy(Shannon, $\sqrt{n\cdot d}$) ~4.66139 bits Comma size medium S-expression S7 * S82 https://en.xen.wiki/w/File:Jid_256_243_pluck_adu_dr220.mp3[sound info] open this interval in xen-calc
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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.

## 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.