256/243: Difference between revisions

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The '''Pythagorean limma''', or '''Pythagorean diatonic semitone''', is the interval of size 256/243 = 2<sup>8</sup>/3<sup>5</sup> (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.
The '''Pythagorean limma''', or '''Pythagorean diatonic semitone''', is the interval of size 256/243 = 2<sup>8</sup>/3<sup>5</sup> (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.
When this interval is treated as a comma to be tempered out, [[blackwood]] temperament is the result.


== See also ==
== See also ==

Revision as of 19:56, 20 January 2021

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]
Open this interval in xen-calc

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.

When this interval is treated as a comma to be tempered out, blackwood temperament is the result.

See also