Definitions of tuning terms
© 1998 by Joseph L. Monzo
All definitions by Joe Monzo unless otherwise cited
(Greek: "remnant", plural: leimmata, limmata)
[from John Chalmers, Divisions of the Tetrachord]
In prime
factor notation
this interval is written
2^{8}3^{5}.
The limma can be calculated thus by regular fractional math:
4 81 4 64 256  ÷  =  *  =  3 64 3 81 243
or by vector addition:
2 3 [ 2 1] 4/3  [6 4] ÷ 81/64  =  [ 8 5] 256/243
Below is a diagram illustrating this description, on an approximate logarithmic scale:
ratio vector 2 3 A 1/1 + [ 0 0]  \  \  \ G 9/8 + [3 2] 81/64 [6 4] = ditone  /  /  / F 81/64 + [6 4] \  256/243 [ 8 5] = limma E 4/3 + [ 2 1] /
A more accurate logarithmic value for it is ~90.22499567 cents.
As the size of this 16/15 interval resembles another Pythagorean semitone  the apotome  much more closely, Woolhouse perhaps should have used that name instead. Apparently he based his terminology on the function of this semitone, for the apotome is the Pythagorean chromatic semitone while the limma is the Pythagorean diatonic semitone.
[from Joe Monzo, JustMusic: A New Harmony]
see also
apotome,
anomaly,
diesis,
comma,
kleisma,
skhisma,
5limit intervals, 100 cents and under
Tutorial on ancient Greek tetrachordtheory
updated:
2002.09.12
2002.01.05
(to download a zip file of the entire Dictionary, click here) 

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