Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited


limma, leimma


    (Greek: "remnant", plural: leimmata, limmata)

  • 1. The Pythagorean diatonic semitone, the interval left after subtracting two Whole Tones from the Perfect Fourth. It has a ratio of 256/243 and 90 cents.

    . . . . . . . . . . . . . . . . . . . .

  • 2. The term used by W. S. B. Woolhouse (in his Essay on Musical Intervals, Harmonics, and Temperament) to refer 16/15 [= ~ 111.731 cents], the ratio of the 5-limit diatonic semitone.

    As this interval resembles another Pythagorean semitone much more closely, the apotome, Woolhouse perhaps should have used that name instead. Apparently he based his terminology on the function of this semitone, as the apotome was the Pythagorean chromatic semitone and the limma was the Pythagorean diatonic semitone.


(to download a zip file of the entire Dictionary, click here)

  • For many more diagrams and explanations of historical tunings, see my book.
  • If you don't understand my theory or the terms I've used, start here
  • I welcome feedback about this webpage:
    corrections, improvements, good links.
    Let me know if you don't understand something.


    return to the Microtonal Dictionary index
    return to my home page
    return to the Sonic Arts home page