Connections To Abstract Algebra
Expanding on the methods of musical set theory, some theorists have used abstract algebra to analyze music. For example, the notes in an equal temperament octave form an abelian group with 12 elements. It is possible to describe just intonation in terms of a free abelian group.
Transformational theory is a branch of music theory developed by David Lewin. The theory allows for great generality because it emphasizes transformations between musical objects, rather than the musical objects themselves.
Theorists have also proposed musical applications of more sophisticated algebraic concepts. Mathematician Guerino Mazzola has applied topos theory to music, though the result has been controversial.
The chromatic scale has a free and transitive action of the cyclic group, with the action being defined via transposition of notes. So the chromatic scale can be thought of as a torsor for the group .
Read more about this topic: Music And Mathematics
Famous quotes containing the words connections, abstract and/or algebra:
“Our business being to colonize the country, there was only one way to do it—by spreading over it all the associations and connections of family life.”
—Henry Parkes (1815–1896)
“But it thought no bed too narrow—it stood with lips askew
And shook its great head sadly like the abstract Jew.”
—Robert Penn Warren (1905–1989)
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)