Quarter-comma Meantone - Greater and Lesser Semitones

Greater and Lesser Semitones

As discussed above, in the quarter-comma meantone temperament,

• the ratio of a semitone is
• the ratio of a tone is

The tones in the diatonic scale can be divided into pairs of semitones. However, since S2 is not equal to T, each tone must be composed of a pair of unequal semitones, S, and X:

Hence,

Notice that S is 117.1 cents, and X is 76.0 cents. Thus, S is the greater semitone, and X is the lesser one. S is commonly called the diatonic semitone (or minor second), while X is called the chromatic semitone (or augmented unison).

The sizes of S and X can be compared to the just intonated ratio 18/17 which is 99.0 cents. S deviates from it by +18.2 cents, and X by −22.9 cents. These two deviations are comparable to the syntonic comma (21.5 cents), which this system is designed to tune out from the Pythagorean major third. However, since even the just intonated ratio 18/17 sounds markedly dissonant, these deviations are considered acceptable in a semitone.