Articles

All-(Generalized-)Interval(-System)Chords
MusMat (2016) Vol. 1, No. 1, pp. 44-57

We survey the all-interval chords of small order and the interval systems in which they are situated. We begin with an examination of traditional all-interval chords in chromatic pitch-class spaces, and extend the notion of their structure to their counterparts ...

A GAP Tutorial for Transformational Music Theory
Music Theory Online (2011) Vol. 17, pp. np

GAP (an acronym for Groups, Algorithms, and Programming) is a system of computational discrete algebra that may function as an application for experimentation in transformational music theory. In particular, it offers tools to music theorists that are not readily available ...

Wreath Products in Transformational Music Theory
Perspectives of New Music (2009) Vol. 47, No. 1, pp. 193-210

 

Klein-Bottle "Tonnetze"
Music Theory Online (2003) Vol. 9, pp. np

Departing from the toroidal Tonnetz of neo-Riemannian theory, we construct a generalized Klein-bottle Tonnetz. Further, we examine associated transformational graphs and analytical contexts, using operators from the cyclic T group, the dihedral T/I group, and a generalized quaternion T/M subgroup. ...