5 citations
4 papers
Pairwise Well-Formed Modes and Transformations
David Clampitt, Thomas Noll
One of the most significant attitudinal shifts in the history of music occurred in the Renaissance, when an emerging triadic consciousness moved musicians towards a new scalar form…
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…
Morphisms of Generalized Interval Systems and PR-Groups
Thomas M. Fiore, Thomas Noll, Ramon Satyendra
We begin the development of a categorical perspective on the theory of generalized interval systems (GIS's). Morphisms of GIS's allow the analyst to move between multiple interval…
Commuting Groups and the Topos of Triads
Thomas M. Fiore, Thomas Noll
The goal of this article is to clarify the relationship between the topos of triads and the neo-Riemannian PLR-group. To do this, we first develop some theory of generalized interv…