256/243

From Xenharmonic Wiki
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,
reduced subharmonic
Tenney height (log2 nd) 15.9248
Weil height (log2 max(n, d)) 16
Wilson height (sopfr(nd)) 31
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math]) 		~4.30829 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.

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, named after Easley Blackwood Jr. 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.

Notation

In musical notations that employ the diatonic chain-of-fifths, such as the ups and downs notation, the limma is represented by the distances between B and C, as well as between E and F.

The scale is structured with the following step pattern:

This pattern highlights the placement of the limma intervals between the note pairs above, distinguishing them from the whole tone that occur between the other note pairs.

See also

Retrieved from "https://en.xen.wiki/index.php?title=256/243&oldid=167137"