Search Results - "Journal of mathematics and music (Society for Mathematics and Computation in Music)"

Towards a mathematical foundation for music theory and composition: a theory of structure by Flieder, Drew

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An algebra of chords for a non-degenerate Tonnetz by Cubarsi, Rafael

“…For an n-TET tuning system, we propose a formalism to study the transformations of k-chords over a generalized non-degenerate Tonnetz generated by a given…”
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Generalizations of Euler's Tonnetz on triangulated surfaces by Rietsch, Konstanze

“…We give a definition of a what we call a "tonnetz" on a triangulated surface, generalizing the famous Tonnetz of Euler (Euler, Leonhard. 1739. Tentamen novae…”
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Music-driven geometric and topologic intuition: a case study with the Klein bottle by Mannone, Maria, Montiel, Mariana, Wilhelmi, Miguel R.

“…The comprehension of mathematical notions can profit from the personal background of a population of students, drawing upon their former knowledge in another…”
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Quantum approach to jam session by Fugiel, Bogusław

“…A quantum mechanical approach to the psychoacoustic effect of Shepard tones has been explored. Melodic intervals are represented by qubits. The phenomenon of…”
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Antisphere: exploring non-Euclidean musical spaces by Howard, Emily

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Quantum-like melody perception by Fugiel, Bogusław

“…I propose a quantum-like approach to the description of melody perception where classic intervals that constitute a melody are replaced by acoustical qubits,…”
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Mathematical foundations of complex tonality by Boland, Jeffrey R., Hughston, Lane P.

“…Equal temperament, in which semitones are tuned in the irrational ratio of $ 2^{1/12} : 1 $ 2 1 / 12 : 1 , is best seen as a serviceable compromise,…”
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Teponazcuauhtla, or "Forest of Resonances" Mesoamerican Plot of Harmony by Pareyon, Gabriel

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Towards a generative syntax of tonal harmony by Rohrmeier, Martin

“…This paper aims to propose a hierarchical, generative account of diatonic harmonic progressions and suggest a set of phrase-structure grammar rules. It argues…”
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Machine composition of Korean music via topological data analysis and artificial neural network by Tran, Mai Lan, Lee, Dongjin, Jung, Jae-Hun

“…Common AI music composition algorithms train a machine by feeding a set of music pieces. This approach is a blackbox optimization, i.e. the underlying…”
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A framework for topological music analysis (TMA) by Alcalá-Alvarez, Alberto, Padilla-Longoria, Pablo

“…In the present article we describe and discuss a framework for applying different topological data analysis (TDA) techniques to a music fragment given as a…”
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Parsimonious sequences of finite sets and their applications to chord progressions and music composition by Bedouelle, Hugues

“…Parsimony is a broad concept with applications in music theory and composition. Two sets A and B of finite cardinality n (n-sets) are in parsimonious relation…”
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Renaissance canons with asymmetric schemes by 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…”
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An integer linear programming model for tilings by Auricchio, Gennaro, Ferrarini, Luca, Lanzarotto, Greta

“…In this paper, we propose an integer linear programming model whose solutions are the aperiodic rhythms tiling with a given rhythm A. We show how it can be…”
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Musical stylistic analysis: a study of intervallic transition graphs via persistent homology by Mijangos, Martín, Bravetti, Alessandro, Padilla-Longoria, Pablo

“…We develop a novel method to represent a weighted directed graph as a finite metric space and then use persistent homology to extract useful features. We apply…”
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Exhaustive chord progressions and their use in music composition by Bedouelle, Hugues

“…A general approach for the design of mild chord progressions from the n-chords (unordered pitch-class sets of cardinal n) of a p-tonic scale was developed…”
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On the divisions of the octave in generalized Pythagorean scales and their bidimensional representation by Cubarsi, Rafael

“…For well-formed generalized Pythagorean scales, it is explained how to fill in a bidimensional table, referred to as a scale keyboard, to represent the scale…”
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Hierarchical set theory by Tymoczko, Dmitri

“…Musicians often operate with a hierarchy of scale-like collections, each embedded within the next, and with transposition and inversion available at every…”
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Iterative method of construction for almost smooth rhythms by Hazama, Fumio

“…The present article introduces the notion of marked rhythm and its almost smoothness through a certain transformation Rep, called repulsion map. A marked…”
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