Musical Set Theory
In musical set theory inversion may be usefully thought of as the compound operation transpositional inversion, which is the same sense of inversion as in the Inverted melodies section above, with transposition carried out after inversion. Pitch inversion by an ordered pitch interval may be defined as:
which equals
First invert the pitch or pitches, x = −x, then transpose, −x + n.
Pitch class inversion by a pitch class interval may be defined as:
Inversion about a pitch axis is a compound operation much like set theory's transpositional inversion, however in pitch axis inversion the transposition may be chromatic or diatonic transposition.
Read more about this topic: Inversion (music)
Famous quotes containing the words musical, set and/or theory:
“Creative force, like a musical composer, goes on unweariedly repeating a simple air or theme, now high, now low, in solo, in chorus, ten thousand times reverberated, till it fills earth and heaven with the chant.”
—Ralph Waldo Emerson (1803–1882)
“Men would never be superstitious, if they could govern all their circumstances by set rules, or if they were always favoured by fortune: but being frequently driven into straits where rules are useless, and being often kept fluctuating pitiably between hope and fear by the uncertainty of fortune’s greedily coveted favours, they are consequently for the most part, very prone to credulity.”
—Baruch (Benedict)
“The weakness of the man who, when his theory works out into a flagrant contradiction of the facts, concludes “So much the worse for the facts: let them be altered,” instead of “So much the worse for my theory.””
—George Bernard Shaw (1856–1950)