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:
“A pregnant woman and her spouse dream of three babies—the perfect four-month-old who rewards them with smiles and musical cooing, the impaired baby, who changes each day, and the mysterious real baby whose presence is beginning to be evident in the motions of the fetus.”
—T. Berry Brazelton (20th century)
“1st Witch. When shall we three meet again?
In thunder, lightning, or in rain?
2nd Witch. When the hurly-burly’s done,
When the battle’s lost and won.
3rd Witch. That will be ere set of sun.
1st Witch. Where the place?
2nd Witch. Upon the heath.
3rd Witch. There to meet with Macbeth.”
—William Shakespeare (1564–1616)
“A theory if you hold it hard enough
And long enough gets rated as a creed....”
—Robert Frost (1874–1963)