4 papers
Some Patterns of Research in Mathematics
Octavio A. Agustín-Aquino
We partially update Grossman's 2005 survey of patterns in mathematical research using a sample of 401 profiles from MathSciNet. The mathematical landscape has changed substantially…
Blues for Alice: The Interplay of Neo-Riemannian and Cadential Viewpoints
Octavio A. Agustín-Aquino
We extend a property of Mazzola's theory of cadential sets in relation to the modulation between minor and major tonalities from triadic to tetradic harmony, using the PLRQ group o…
An Algebraic-Symmetric Analysis of Counterpoint and Modulation in the Music of Claudio Monteverdi
Octavio A. Agustín-Aquino, Brandon J. Curiel-López
We address certain structural innovations in the music of Claudio Monteverdi, which defined the pivotal transition from the Renaissance prima pratica to the Baroque seconda pratica…
Melody and Variation Generation Through KAM Theory
Octavio A. Agustín-Aquino, Alicia Santiago-Santos
We use the Newton iteration of KAM theory for diffeomorphisms of the circle as a source for melody generation and its variations