The Limma or Leimma ( Greek λεῖμμα , remnant ') denotes the Pythagorean semitone in music since Euclid (around 300 BC) . In Euclid's "division of the canon" one finds the following definitions with the "proportions" (= aspect ratios , corresponds to our current frequency ratios ):
- Fourth = octave - fifth:
- Whole tone = fifth - fourth:
- Ditonos = 2 whole tones:
- Limma = fourth - ditonos: cent .
The Limma is the diatonic semitone of the Pythagorean tuning.
As a supplement, the
The apotone (113.7 cents) is a Pythagorean comma (23.5 cents) larger than the limma (90.2 cents).
- When adding or subtracting intervals, the frequency ratios are multiplied or divided.