256/243

Interval information

Ratio	256/243
Factorization	28 × 3-5
Monzo	[8 -5⟩
Size in cents	90.225¢
Names	Pythagorean limma, Pythagorean diatonic semitone
FJS name	[math]\displaystyle{ \text{m2} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	15.9248
Weil norm (log2 max(n, d))	16
Wilson norm (sopfr(nd))	31
[sound info]
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English Wikipedia has an article on:

Semitone#Pythagorean tuning

The Pythagorean limma, or Pythagorean diatonic semitone, is the interval of size 256/243 = 2⁸/3⁵ (about 90.2¢), which 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

4\53 is a very good approximation of the interval.

Temperament

When this ratio is taken as a comma to be tempered (and the starting JI subgroup is the 5-limit), it produces blackwood temperament. Edos tempering it out include 5edo, 10edo, 15edo, 20edo, 25edo and 30edo.

See also

• 243/128 – its octave complement
• 729/512 – its fifth complement
• 16/15 - the classic (5-limit) diatonic semitone
• Gallery of just intervals
• Limma family, where it is tempered out
• Medium comma
• Pythagorean tuning