相关论文: Algebraic Structures in Microtonal Music
Mathematics is a far reaching discipline and its tools appear in many applications. In this paper we discuss its role in music and signal processing by revisiting the use of mathematics in algorithms that can extract chord information from…
This paper studies the homotopy theory of the Grothendieck construction using model categories and semi-model categories, provides a unifying framework for the homotopy theory of operads and their algebras and modules, and uses this…
Arranging music for a different set of instruments that it was originally written for is traditionally a tedious and time-consuming process, performed by experts with intricate knowledge of the specific instruments and involving significant…
Equal temperament, in which semitones are tuned in the irrational ratio of $2^{1/12} : 1$, is best seen as a serviceable compromise, sacrificing purity for flexibility. Just intonation, in which intervals are given by products of powers of…
This paper constructs a tree structure for the music rhythm using the L-system. It models the structure as an automata and derives its complexity. It also solves the complexity for the L-system. This complexity can resolve the similarity…
A set of basic notes, or `scale', forms the basis of music. Scales are specific to specific genre of music. In this second article of the series we explore the development of various scales associated with western classical music, arguably…
We study a numerical semigroup ring as an algebra over another numerical semigroup ring. The complete intersection property of numerical semigroup algebras is investigated using factorizations of monomials into minimal ones. The goal is to…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
In this paper, we analyze web-downloaded data on people sharing their music library. By attributing to each music group usual music genres (Rock, Pop...), and analysing correlations between music groups of different genres with…
Music is increasingly being used as a therapeutic tool in the field of rehabilitation medicine and psychophysiology. One of the main key components of music is its temporal organization. The characteristics of neurocognitive processes…
Computational models of music, while providing good descriptions of melodic development, still cannot fully grasp the general structure comprised of repetitions, transpositions, and reuse of melodic material. We present a corpus of strongly…
In this paper we propose the Music Note Ontology, an ontology for modelling music notes and their realisation. The ontology addresses the relation between a note represented in a symbolic representation system, and its realisation, i.e. a…
In this article, a novel method to compute all discrete polyharmonic functions in the quarter plane for models with small steps, zero drift and a finite group is proposed. A similar method is then introduced for continuous polyharmonic…
The past year has seen enormous progress in string theory. It has become clear that all of the different string theories are different limits of a single theory. Moreover, in certain limits, one obtains a new, eleven-dimensional structure…
Modern-day Optical Music Recognition (OMR) is a fairly fragmented field. Most OMR approaches use datasets that are independent and incompatible between each other, making it difficult to both combine them and compare recognition systems…
In this paper, we consider the MUltiple SIgnal Classification (MUSIC) algorithm for identifying the locations of small electromagnetic inhomogeneities surrounded by random scatterers. For this purpose, we rigorously analyze the structure of…
Artistic style has been studied for centuries, and recent advances in machine learning create new possibilities for understanding it computationally. However, ensuring that machine-learning models produce insights aligned with the interests…
Symbolic music generation has attracted increasing attention, while most methods focus on generating short piece (mostly less than 8 bars, and up to 32 bars). Generating long music calls for effective expression of the coherent music…
The aim is to explore new opportunities of the pitch organization of the musical scale. Specifically, a numerical comparison of the different musical temperaments among themselves in the degree of approximation of the Pythagorean scale is…
The Pythagorean school attributed consonance in music to simplicity of frequency ratios between musical tones. In the last two centuries, the consonance curves developed by Helmholtz, Plompt and Levelt shifted focus to psycho-acoustic…