Music and Group Theory

Math­e­mat­ics and music are deeply in­ter­twined, as both are struc­tured by pat­terns, rep­e­ti­tion, and sym­me­try. Group theory pro­vides the math­e­mat­i­cal lan­guage to de­scribe mu­si­cal trans­for­ma­tions—such as trans­po­si­tions, in­ver­sions, and rhythms.

By ex­plor­ing how groups act on sets of mu­si­cal notes or rhythms, one can see the har­mo­ny be­tween math­e­mat­i­cal struc­ture and au­di­to­ry beauty. The study of mu­si­cal scales, chord pro­gres­sions, and per­mu­ta­tions of themes all reveal the pres­ence of group-the­o­ret­ic con­cepts, of­fer­ing a new per­spec­tive on the uni­ver­sal­i­ty of sym­me­try and pat­tern.