Zobrazeno 1 - 10
of 179
pro vyhledávání: '"00a65"'
Autor:
Sills, Andrew V.
In 1986, composer Wendy Carlos introduced three unusual musical scales she called alpha, beta and gamma, equal temperament-inspired scales that de-emphasize the octave as the primary interval in favor of the major and minor thirds and the perfect fif
Externí odkaz:
http://arxiv.org/abs/2408.14551
Autor:
Cañadas, Agustín Moreno, Espinosa, Pedro Fernando Fernández, Nieto, José Gregorio Rodríguez, Mendez, Odette M., Arteaga-Bastidas, Ricardo Hugo
Since their introduction, Brauer configuration algebras (BCAs) and their specialized messages have helped research in several fields of mathematics and sciences. This paper deals with a new perspective on using such algebras as a theoretical framewor
Externí odkaz:
http://arxiv.org/abs/2404.07240
Autor:
Rietsch, Konstanze
We give a definition of a what we call a `tonnetz' on a triangulated surface, generalising the famous tonnetz of Euler from 1739. In Euler's tonnetz the vertices of a regular `$A_2$ triangulation' of the plane are labelled with notes, or pitch-classe
Externí odkaz:
http://arxiv.org/abs/2401.15692
Autor:
Borner, Harald, Lorenz, Falko
We realize the Pauli group $P$ as Galois group of polynomials over the rational numbers. It is shown by construction that each pure polynomial in the infinite family of the form $X^8+k^2$ for $k\neq \lambda^2, 2\lambda^2; k,\lambda \in \mathbb{Q}^*$
Externí odkaz:
http://arxiv.org/abs/2401.07338
Autor:
Alons, Caleb Scott
Mathematical music theory has assumed without proof that musical notes can be associated with the equivalence classes of $\mathbb{Z}_n$. We contest the triviality of this assertion, which we call the Pitch-class Integer Theorem (PCIT). Since the exis
Externí odkaz:
http://arxiv.org/abs/2401.03325
Autor:
Rempe, Lasse
"Phase-locking" is a fundamental phenomenon in which coupled or periodically forced oscillators synchronise. The Arnold family of circle maps, which describes a forced oscillator, is the simplest mathematical model of phase-locking and has been studi
Externí odkaz:
http://arxiv.org/abs/2309.06595
Autor:
O'Dorney, Evan M.
By a "scheme" of a musical canon, we mean the time and pitch displacement of each entering voice. When the time displacements are unequal, achieving consonant sonorities is especially challenging. Using a first-species theoretical model, we quantify
Externí odkaz:
http://arxiv.org/abs/2302.14160
There has been an everlasting discussion around the concept of form in music. This work is motivated by such debate by using a complex systems framework in which we study the form as an emergent property of rhythm. Such a framework corresponds with t
Externí odkaz:
http://arxiv.org/abs/2207.03602
Topological data analysis has been recently applied to investigate stylistic signatures and trends in musical compositions. A useful tool in this area is Persistent Homology. In this paper, we develop a novel method to represent a weighted directed g
Externí odkaz:
http://arxiv.org/abs/2204.11139
The `colored Cube Dance' is an extension of Douthett's and Steinbach's Cube Dance graph, related to a monoid of binary relations defined on the set of major, minor, and augmented triads. This contribution explores the automorphism group of this monoi
Externí odkaz:
http://arxiv.org/abs/2204.03022