256/243: Difference between revisions

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'''256/243'''
{{Infobox Interval
|8 -5>
| Ratio = 256/243
| Monzo = 8 -5
| Cents = 90.225
| Name = Pythagorean limma, <br>Pythagorean diatonic semitone
| Sound = jid_256_243_pluck_adu_dr220.mp3
| FJS name = m2
}}


90.225 cents
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.


[[File:jid_256_243_pluck_adu_dr220.mp3]] [[:File:jid_256_243_pluck_adu_dr220.mp3|sound sample]]
== See also ==
 
* [[Gallery of Just Intervals]]
The Pythagorean limma, or Pythagorean semitone, is the interval of size 256/243 = 2^8/3^5 (about 90.2¢), which is the diatonic semitone in Pythagorean tuning. It can be generated by stacking five [[4/3|4/3]] just perfect fourths and octave-reducing the resulting interval.
* [[Medium commas]]
 
* [[5edo]], [[10edo]], [[15edo]], [[20edo]], [[25edo]] and [[30edo]], which temper it out.
See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]], [[Comma|comma]]
 
[[5edo|5edo]], [[10edo|10edo]], [[15edo|15edo]], [[20edo|20edo]], [[25edo|25edo]] and [[30edo|30edo]] temper it out.

Revision as of 05:41, 17 August 2020

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.

See also

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