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.
Read more about this topic: Quarter-comma Meantone
Famous quotes containing the words greater and/or lesser:
“The axioms of physics translate the laws of ethics. Thus, “the whole is greater than its part;” “reaction is equal to action;” “the smallest weight may be made to lift the greatest, the difference of weight being compensated by time;” and many the like propositions, which have an ethical as well as physical sense. These propositions have a much more extensive and universal sense when applied to human life, than when confined to technical use.”
—Ralph Waldo Emerson (1803–1882)
“Constantly choosing the lesser of two evils is still choosing evil.”
—Jerry Garcia (1942–1995)