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Discrete Mathematics and Combinatorics Commons™
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Full-Text Articles in Discrete Mathematics and Combinatorics
Taking Notes: Generating Twelve-Tone Music With Mathematics, Nathan Molder
Taking Notes: Generating Twelve-Tone Music With Mathematics, Nathan Molder
Electronic Theses and Dissertations
There has often been a connection between music and mathematics. The world of musical composition is full of combinations of orderings of different musical notes, each of which has different sound quality, length, and em phasis. One of the more intricate composition styles is twelve-tone music, where twelve unique notes (up to octave isomorphism) must be used before they can be repeated. In this thesis, we aim to show multiple ways in which mathematics can be used directly to compose twelve-tone musical scores.
On The Non-Existence Of A Projective (75, 4,12, 5) Set In Pg(3, 7), Aaron C.S. Chan, James A. Davis, Jonathan Jedwab
On The Non-Existence Of A Projective (75, 4,12, 5) Set In Pg(3, 7), Aaron C.S. Chan, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
We show by a combination of theoretical argument and computer search that if a projective (75, 4, 12, 5) set in PG(3, 7) exists then its automorphism group must be trivial. This corresponds to the smallest open case of a coding problem posed by H. Ward in 1998, concerning the possible existence of an infinite family of projective two-weight codes meeting the Griesmer bound.