相关论文: Algebraic Structures in Microtonal Music
Musical pieces can be modeled as complex networks. This fosters innovative ways to categorize music, paving the way towards novel applications in multimedia domains, such as music didactics, multimedia entertainment and digital music…
Music is a repetition of patterns and rhythms. It can be composed by repeating a certain number of bars in a structured way. In this paper, the objective is to generate a loop of 8 bars that can be used as a building block of music. Even…
Modern keyboards allow a musician to play multiple instruments at the same time by assigning zones -- fixed pitch ranges of the keyboard -- to different instruments. In this paper, we aim to further extend this idea and examine the…
Even though chord roots constitute a fundamental concept in music theory, existing models do not explain and determine them to full satisfaction. We present a new method which takes sequential context into account to resolve ambiguities and…
After briefly revising the concepts of consonance/dissonance, a respective mathematic-computational model is described, based on Helmholtz's consonance theory and also considering the partials intensity. It is then applied to characterize…
Transformational musical theory has so far mainly focused on the study of groups acting on musical chords, one of the most famous example being the action of the dihedral group D24 on the set of major and minor chords. Comparatively less…
In this contribution, we consider MUltiple SIgnal Classification (MUSIC)-type algorithm for a non-iterative microwave imaging of small and arbitrary shaped extended anomalies located in a homogeneous media from scattering matrix whose…
We develop a model of musical rhythm and meter based on optimizing the trade-off between human psychological preferences for perceiving repeated patterns in time with a desire for variety and complexity. By mapping these competing…
Inferring music time structures has a broad range of applications in music production, processing and analysis. Scholars have proposed various methods to analyze different aspects of time structures, such as beat, downbeat, tempo and meter.…
We show that the number of numerical semigroups with multiplicity three, four or five and fixed genus is increasing as a function in the genus. To this end we use the Kunz polytope for these multiplicities. Counting numerical semigroups…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
We propose a novel approach for the generation of polyphonic music based on LSTMs. We generate music in two steps. First, a chord LSTM predicts a chord progression based on a chord embedding. A second LSTM then generates polyphonic music…
This paper introduces a novel recurrent model for music composition that is tailored to the structure of polyphonic music. We propose an efficient new conditional probabilistic factorization of musical scores, viewing a score as a…
We endow the category of bialgebras over a pair of operads in distribution with a cofibrantly generated model category structure. We work in the category of chain complexes over a field of characteristic zero. We split our construction in…
Digital advances have transformed the face of automatic music generation since its beginnings at the dawn of computing. Despite the many breakthroughs, issues such as the musical tasks targeted by different machines and the degree to which…
This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…
After our book---Mathematics and Music: Composition, Perception, and Performance, 2nd edition, CRC Press, 2020---was published, we found a striking example of the importance of the Tonnetz for analyzing the harmonic structure of The…
The presence of skew quadrupole fields will linearly couple the x and y motions. The x and y motions can then be written as the sum of two normal modes >. This paper presents analytical perturbation theory results for the tunes of the…
We study mass-deformed N=2 gauge theories from various points of view. Their partition functions can be computed via three dual approaches: firstly, (p,q)-brane webs in type II string theory using Nekrasov's instanton calculus, secondly,…
We describe the construction of the genus-zero parts of conformal field theories in the sense of G. Segal from representations of vertex operator algebras satisfying certain conditions. The construction is divided into four steps and each…