29 citations · 94 across the 18 of their papers we have counts for
19 papers
Transformations of Triads and Seventh Chords: Group Extensions and Duality
Thomas M. Fiore, Thomas Noll, Ethan Bonnell +5
Transformational music theory, pioneered by David Lewin, uses simply transitive group actions to analyze music. In this paper, we construct a simply transitive group action on a di…
Voicing Transformations and a Linear Representation of Uniform Triadic Transformations
Thomas M. Fiore, Thomas Noll
Motivated by analytical methods in mathematical music theory, we determine the structure of the subgroup J of GL(3,Z12) generated by the three voicing reflections. As applications…
Hexatonic Systems and Dual Groups in Mathematical Music Theory
Cameron Berry, Thomas M. Fiore
Motivated by the music-theoretical work of Richard Cohn and David Clampitt on late-nineteenth century harmony, we mathematically prove that the PL-group of a hexatonic cycle is dua…
Approximation in K-theory for Waldhausen Quasicategories
Thomas M. Fiore
We prove a series of Approximation Theorems in the setting of Waldhausen quasicategories. These theorems, inspired by Waldhausen's 1985 Approximation Theorem, give sufficient condi…
Incorporating Voice Permutations into the Theory of Neo-Riemannian Groups and Lewinian Duality
Thomas M. Fiore, Thomas Noll, Ramon Satyendra
A familiar problem in neo-Riemannian theory is that the P, L, and R operations defined as contextual inversions on pitch-class segments do not produce parsimonious voice leading. W…
Waldhausen Additivity: Classical and Quasicategorical
Thomas M. Fiore, Malte Pieper
We use a simplicial product version of Quillen's Theorem A to prove classical Waldhausen Additivity of wS., which says that the "subobject" and "quotient" functors of cofiber seque…