| Title: | Internal Symmetries in Musical 12-Tone Rows |
| Speaker: | Anil Venkatesh Assistant Professor of Mathematics Mathematics Ferris State University Big Rapids, MI |
| Abstract: | In music, a 12-tone row is any of the 12! possible orderings of notes in the Western chromatic scale. The musical notes of a 12-tone composition must always arise in the same order, cycling repeatedly through a predetermined "row" of twelve notes. The repetitive structure of 12-tone music lends itself to mathematical study. In 2003, Hunter and von Hippel investigated symmetry in 12-tone rows, using group theory to enumerate equivalence classes of rows under a group of music-theoretic symmetries. They found that highly symmetric rows constitute just 0.13% of the 12! possibilities, and yet these rows arise in 10% of actual compositions. This result provided strong evidence that composers favor symmetric rows, but leaves us wondering about the remaining 90% of compositions. In this talk, we introduce a way to measure the occurrence of short repetitions and symmetries that go undetected in the analysis of Hunter and von Hippel. We present a new hierarchy of symmetry for 12-tone rows, and offer evidence that composers favor symmetric substructures in their work. |
| Location: | Palenske 227 |
| Date: | 3/21/2019 |
| Time: | 3:30 PM |
@abstract{MCS:Colloquium:AnilVenkatesh:2019:3:21,
author = "{Anil Venkatesh}",
title = "{Internal Symmetries in Musical 12-Tone Rows}",
address = "{Albion College Mathematics and Computer Science Colloquium}",
month = "{21 March}",
year = "{2019}"
}