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 greater part of what my neighbors call good I believe in my soul to be bad, and if I repent of anything, it is very likely to be my good behavior. What demon possessed me that I behaved so well? You may say the wisest thing you can, old man,you who have lived seventy years, not without honor of a kind,I hear an irresistible voice which invites me away from all that.”
—Henry David Thoreau (18171862)
“For one moment seek
a lesser beauty
and a lesser grace,
but you will find
no peace in the end
save in her presence.”
—Hilda Doolittle (18861961)