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  • On the use of relational presheaves in transformational music theory
    J. Math. Music (IF 0.467) Pub Date : 2020-10-14
    Alexandre Popoff

    Traditional transformational music theory describes transformations between musical elements as functions between sets and studies their subsequent algebraic properties and their use for music analysis. This is formalized from a categorical point of view by the use of functors C → S e t s where C is a category, often a group or a monoid. At the same time, binary relations have also been used in mathematical

    更新日期:2020-10-16
  • Introduction
    J. Math. Music (IF 0.467) Pub Date : 2020-10-12
    Moreno Andreatta; Emmanuel Amiot; Jason Yust

    (2020). Introduction. Journal of Mathematics and Music: Vol. 14, Geometry and Topology in Music; Guest Editors: Moreno Andreatta, Emmanuel Amiot, and Jason Yust, pp. 107-113.

    更新日期:2020-10-12
  • Why topology?
    J. Math. Music (IF 0.467) Pub Date : 2020-09-24
    Dmitri Tymoczko

    Music theorists have modeled voice leadings as paths through higher-dimensional configuration spaces. This paper uses topological techniques to construct two-dimensional diagrams capturing these spaces’ most important features. The goal is to enrich set theory’s contrapuntal power by simplifying the description of its geometry. Along the way, I connect homotopy theory to “transformational theory,”

    更新日期:2020-10-12
  • Ombak and octave stretching in Balinese gamelan
    J. Math. Music (IF 0.467) Pub Date : 2020-09-20
    William A. Sethares; Wayne Vitale

    A primary esthetic in the performance practice of Balinese gamelan is the ombak (Indonesian for wave), which is manifest in musical form, performance, and tuning. The ombak arises in a paired tuning system in which corresponding unisons of two instruments (or instrumental groups) are tuned to slightly different frequencies, one higher and one lower, to produce beats. Pitch classes are not necessarily

    更新日期:2020-09-21
  • A 5-dimensional Tonnetz for nearly symmetric hexachords
    J. Math. Music (IF 0.467) Pub Date : 2020-08-20
    Vaibhav Mohanty

    The standard 2-dimensional Tonnetz describes parsimonious voice leading connections between major and minor triads as the 3-dimensional Tonnetz does for dominant seventh and half-diminished seventh chords. In this paper, a 5-dimensional Tonnetz is introduced, providing a geometric framework for parsimonious voice leading among nearly symmetric hexachords of the mystic-Wozzeck genus. Cartesian coordinates

    更新日期:2020-08-21
  • A detailed list and a periodic table of set classes
    J. Math. Music (IF 0.467) Pub Date : 2020-07-17
    Luis Nuño

    In this paper, pitch-class sets are analyzed in terms of their intervallic structures and those related by transposition are called a set type. Then, non-inversionally-symmetrical set classes are split into two set types related by inversion. As a higher version of the interval-class vector, I introduce the trichord-type vector, whose elements are the number of times each trichord type is contained

    更新日期:2020-07-17
  • Beneath (or beyond) the surface: Discovering voice-leading patterns with skip-grams
    J. Math. Music (IF 0.467) Pub Date : 2020-07-14
    David R. W. Sears; Gerhard Widmer

    Recurrent voice-leading patterns like the Mi-Re-Do compound cadence (MRDCC) rarely appear on the musical surface in complex polyphonic textures, so finding these patterns using computational methods remains a tremendous challenge. The present study extends the canonical n-gram approach by using skip-grams, which include sub-sequences in an n-gram list if their constituent members occur within a certain

    更新日期:2020-07-15
  • Homological persistence in time series: an application to music classification
    J. Math. Music (IF 0.467) Pub Date : 2020-07-14
    Mattia G. Bergomi; Adriano Baratè

    Meaningful low-dimensional representations of dynamical processes are essential to better understand the mechanisms underlying complex systems, from music composition to learning in both biological and artificial intelligence. We suggest to describe time-varying systems by considering the evolution of their geometrical and topological properties in time, by using a method based on persistent homology

    更新日期:2020-07-14
  • Entropy of Fourier coefficients of periodic musical objects
    J. Math. Music (IF 0.467) Pub Date : 2020-07-01
    Emmanuel Amiot

    There are many ways to define and measure organization, or complexity, in music, most using the notion of informational entropy, as the opposite of organization. Some researchers prompted me to study whether it could be done from the magnitudes of Fourier coefficients of musical objects (pc-sets or rhythms) instead of addressing their atomic elements (pitches, rhythmic onsets). Indeed I found that

    更新日期:2020-07-01
  • From actantial model to conceptual graph: Thematized action in John Cage's 0′00′(4′33′′No. 2)
    J. Math. Music (IF 0.467) Pub Date : 2020-05-29
    Michael D. Fowler

    In this article, I build an actantial model, M, of John Cage's 1962 indeterminate work 0′00′′ (4 ′33 ′′ No. 2). To further investigate Greimas' actantial axes of desire, knowledge and power, I generate an ontology, O, that records the facts of the model through hierarchies of relations and concepts. This allows for a conceptual graph (CG), C, that describes the score's instructions and its actants

    更新日期:2020-05-29
  • Musical pitch quantization as an eigenvalue problem
    J. Math. Music (IF 0.467) Pub Date : 2020-05-24
    Peter beim Graben; Maria Mannone

    How can discrete pitches and chords emerge from the continuum of sound? Using a quantum cognition model of tonal music, we prove that the associated Schrödinger equation in Fourier space is invariant under continuous pitch transpositions. However, this symmetry is broken in the case of transpositions of chords, entailing a discrete cyclic group as transposition symmetry. Our research relates quantum

    更新日期:2020-05-24
  • Mathematical approaches to defining the semitone in antiquity
    J. Math. Music (IF 0.467) Pub Date : 2020-04-30
    Caleb Mutch

    Connections between mathematics and music have been recognized since the days of Ancient Greece. The Pythagoreans' association of musical intervals with integer ratios is so well known that it occludes the great variety of approaches to the music-mathematical relationship in Ancient Greece and Rome. The present article uncovers this diversity by examining how authors from Antiquity used one mathematical

    更新日期:2020-04-30
  • Symbolic structures in music theory and composition, binary keyboards, and the Thue–Morse shift
    J. Math. Music (IF 0.467) Pub Date : 2020-03-17
    Ricardo Gómez; Luis Nasser

    We address the broad idea of using mathematical models to inform music theory and composition by implementing them directly in the process of music creation. The mathematical model we will use is the Thue–Morse dynamical system. We briefly survey previously published works that were similarly motivated, and then discuss a new piece of music we composed, inspired by this symbolic dynamical system. In

    更新日期:2020-03-17
  • Quantum GestART: identifying and applying correlations between mathematics, art, and perceptual organization
    J. Math. Music (IF 0.467) Pub Date : 2020-03-11
    Maria Mannone; Federico Favali; Balandino Di Donato; Luca Turchet

    Mathematics can help analyze the arts and inspire new artwork. Mathematics can also help make transformations from one artistic medium to another, considering exceptions and choices, as well as artists' individual and unique contributions. We propose a method based on diagrammatic thinking and quantum formalism. We exploit decompositions of complex forms into a set of simple shapes, discretization

    更新日期:2020-03-11
  • An alternative approach to generalized Pythagorean scales. Generation and properties derived in the frequency domain
    J. Math. Music (IF 0.467) Pub Date : 2020-03-05
    Rafael Cubarsi

    Abstract scales are formalized as a cyclic group of classes of projection functions related to iterations of the scale generator. Their representatives in the frequency domain are used to built cyclic sequences of tone iterates satisfying the closure condition. The refinement of cyclic sequences with regard to the best closure provides a constructive algorithm that allows to determine cyclic scales

    更新日期:2020-03-05
  • Generalized Tonnetze and Zeitnetze, and the topology of music concepts
    J. Math. Music (IF 0.467) Pub Date : 2020-03-02
    Jason Yust

    The music-theoretic idea of a Tonnetz can be generalized at different levels: as a network of chords relating by maximal intersection, a simplicial complex in which vertices represent notes and simplices represent chords, and as a triangulation of a manifold or other geometrical space. The geometrical construct is of particular interest, in that allows us to represent inherently topological aspects

    更新日期:2020-03-02
  • Some remarks on hypergestural homology of spaces and its relation to classical homology
    J. Math. Music (IF 0.467) Pub Date : 2020-02-27
    Juan Sebastián Arias-Valero; Emilio Lluis-Puebla

    Classical homology of a topological space provides invariants of the space by means of triangulation or squaring made up from singular simplices (simplicial homology) or singular cubes (cubical homology) in the space. In much the same way, Mazzola's hypergestural homology intends to associate invariants to topological categories and, in particular, topological spaces by means of approximation with

    更新日期:2020-02-27
  • Gauge models of musical forces
    J. Math. Music (IF 0.467) Pub Date : 2020-02-17
    Reinhard Blutner; Peter beim Graben

    Metaphors involving motion and forces are a source of inspiration for understanding tonal music and tonal harmonies since ancient times. Starting with the rise of quantum cognition, the modern interactional conception of forces as developed in gauge theory has recently entered the field of theoretical musicology. We develop a gauge model of tonal attraction based on SU(2) symmetry. This model comprises

    更新日期:2020-02-17
  • On the topological characterization of gestures in a convenient category of spaces
    J. Math. Music (IF 0.467) Pub Date : 2020-02-13
    Timothy L. Clark

    In this paper, we reconsider the topological characterization of gestures in a convenient category of spaces mentioned by Mazzola in 2009, recovering Arias's 2018 result that the relevant equivalence is a homeomorphism. We also show the topological characterization of gestures extends to an adjunction between the category of gestures and the category of continuous maps whose domain is a one-dimensional

    更新日期:2020-02-13
  • Difference tones in “ non-Pythagorean” scales based on logarithms
    J. Math. Music (IF 0.467) Pub Date : 2020-01-21
    Thomas Morrill

    In order to explore tonality outside of the “Pythagorean” paradigm of integer ratios, Robert Schneider introduced a musical scale based on the logarithm function. We seek to refine Schneider's scale so that the difference tones generated by different degrees of the scale are themselves octave equivalents of notes in the scale. In doing so, we prove that a scale which contains all its difference tones

    更新日期:2020-01-21
  • Axiomatic scale theory
    J. Math. Music (IF 0.467) Pub Date : 2020-01-10
    Daniel Harasim; Stefan E. Schmidt; Martin Rohrmeier

    Scales are a fundamental concept of musical practice around the world. They commonly exhibit symmetry properties that are formally studied using cyclic groups in the field of mathematical scale theory. This paper proposes an axiomatic framework for mathematical scale theory, embeds previous research, and presents the theory of maximally even scales and well-formed scales in a uniform and compact manner

    更新日期:2020-01-10
  • Functorial semiotics for creativity
    J. Math. Music (IF 0.467) Pub Date : 2019-11-27
    Guerino Mazzola

    In this paper, we develop a mathematically conceived semiotic theory. This project seems essential for a future computational creativity science since the outcome of the process of creativity must add new signs to given semiotic contexts. The mathematical framework is built upon categories of functors, in particular linearized categories deduced from path categories of digraphs and the Gabriel–Zisman

    更新日期:2019-11-27
  • Modulation in tetradic harmony and its role in jazz
    J. Math. Music (IF 0.467) Pub Date : 2019-09-05
    Octavio A. Agustín-Aquino; Guerino Mazzola

    After a quick exposition of Mazzola's quantum modulation model for the so-called triadic interpretation of the major scale within the equal temperament, we study the model for the tetradic interpretation of the same scale. It is known that tetrads are fundamental for jazz music, and some classical objects for this kind of music are recovered.

    更新日期:2019-09-05
  • An analysis of pitch-class segmentation in John Cage's Ryoanji for oboe using morphological image analysis and formal concept analysis
    J. Math. Music (IF 0.467) Pub Date : 2019-09-05
    Michael D. Fowler

    In 1983, John Cage used the traditional stone garden, or karesansui at the Zen temple, Ryōan-ji in Kyoto as a model to generate a series of visual and musical works that utilized tracings of a collection of his own rocks. In this article, I analyze the first of the musical works, Ryoanji for oboe, using mixed methods drawn from morphological image analysis and formal concept analysis (FCA). I introduce

    更新日期:2019-09-05
  • Encoding musical procedures by sequential transducers
    J. Math. Music (IF 0.467) Pub Date : 2019-07-30
    Marianthi Bozapalidou

    The aim of this paper is to establish the interconnection between musical functions and sequential transducers, thus enabling to transform musical properties into machine structural properties. Simply transitive left group actions deriving from generalized interval systems as well as musical metre partitioning and group preference rules GPR2, GPR3 are investigated in the proposed setup.

    更新日期:2019-07-30
  • Note from the new co-editors-in-chief
    J. Math. Music (IF 0.467) Pub Date : 2019-07-17
    Jason Yust, Emmanuel Amiot

    (2019). Note from the new co-editors-in-chief. Journal of Mathematics and Music: Vol. 13, No. 1, pp. 1-3.

    更新日期:2019-07-17
  • Correction
    J. Math. Music (IF 0.467) Pub Date : 2019-07-15

    (2019). Correction. Journal of Mathematics and Music: Vol. 13, No. 1, pp. 107-107.

    更新日期:2019-07-15
  • Pseudo-distances between chords of different cardinality on generalized voice-leading spaces
    J. Math. Music (IF 0.467) Pub Date : 2019-07-05
    Grégoire Genuys

    In this paper, we study the possibility of defining pseudo-distances between musical chords of different cardinality, from the distance defined on the generalized voice-leading space by Callender, Quinn, and Tymoczko [“Generalized Voice-Leading Spaces.” Science 320 (5874): 346–348]. This latter distance measures the size of the minimal voice leading between two chords. A pseudo-distance is a weaker

    更新日期:2019-07-05
  • Classification of Turkish makam music: a topological approach
    J. Math. Music (IF 0.467) Pub Date : 2019-06-20
    Mehmet Emin Aktas, Esra Akbas, Jason Papayik, Yunus Kovankaya

    In this paper, we study Turkish makam music, a system of varied melodies and chords, computationally. Our main goal is to classify the makams using their notes. For this reason, we utilize the topology of complex networks. We first represent songs with weighted networks where vertices and edges correspond to musical notes and their co-occurrences respectively. We then define the diffusion Fréchet function

    更新日期:2019-06-20
  • Mapping k-combinations and Dih4 in John Cage's Variations I as utilities for determinate and indeterminate realization strategies
    J. Math. Music (IF 0.467) Pub Date : 2019-06-20
    Michael D. Fowler

    This article analyses the 1958 graphic score, Variations I, by John Cage (1912–1992). I firstly trace the resistance that the work has established towards traditional analysis, given its meta-score qualities, and the “distance metric problem,” which arises from the necessity to generate musical parameter data from the measurement of perpendiculars between points and lines printed on six transparent

    更新日期:2019-06-20
  • Optimal tuning of multi-rank keyboards
    J. Math. Music (IF 0.467) Pub Date : 2019-06-05
    Aricca Bannerman, James Emington, Anil Venkatesh

    The Helmholtzian theory of sensory consonance by spectral matching has been used by many scholars to evaluate equal temperaments. This approach highlights certain temperaments, such as the 12-, 19-, and 31-note tunings, for their fit of popular just intervals. We study the spectral matching of linear temperaments, which are generated by the octave plus a second independent interval. Our project further

    更新日期:2019-06-05
  • Music and combinatorics on words: a historical survey
    J. Math. Music (IF 0.467) Pub Date : 2019-05-23
    Srečko Brlek, Marc Chemillier, Christophe Reutenauer

    (2018). Music and combinatorics on words: a historical survey. Journal of Mathematics and Music: Vol. 12, Music and Combinatorics on Words, pp. 125-133.

    更新日期:2019-05-23
  • An algorithmic approach to South Indian classical music
    J. Math. Music (IF 0.467) Pub Date : 2019-05-21
    Shayan Srinivasa Garani, Harish Seshadri

    (2019). An algorithmic approach to South Indian classical music. Journal of Mathematics and Music: Vol. 13, No. 2, pp. 107-134.

    更新日期:2019-05-21
  • Modelling melodic variation and extracting melodic templates from flamenco singing performances
    J. Math. Music (IF 0.467) Pub Date : 2019-05-17
    Nadine Kroher, José-Miguel Díaz-Báñez

    A key concept in flamenco singing is the constant re-interpretation of orally transmitted melodic templates, which undergo variation and ornamentation during spontaneous performances. We propose a novel framework which allows us to model a set of interpretations of the same melody and analyse differences among them. We apply a multiple progressive sequence alignment technique to obtain a graphical

    更新日期:2019-05-17
  • On features of fugue subjects. A comparison of J.S. Bach and later composers
    J. Math. Music (IF 0.467) Pub Date : 2019-05-17
    Jesper Rydén

    The musical form fugue has inspired many composers, in particular writing for the organ. By quantifying a fugue subject, comparisons can be made on a statistical basis between J.S. Bach and composers from later epochs, a priori dividing works into three categories. The quantification is made by studying the following features: length, expressed in number of notes written; range (in semitones); number

    更新日期:2019-05-17
  • Kaleidoscope substitutions and pairwise well-formed modes: major-minor duality transformationally revisited
    J. Math. Music (IF 0.467) Pub Date : 2019-05-16
    Thomas Noll, David Clampitt

    Pairwise well-formed modes are investigated as substitutions on words over a three-letter alphabet. Motivating examples are the major and minor modes, here described in terms of the substitutions a↦ac,b↦ba,c↦cab and a↦ab,b↦ca,c↦bac. Pairwise well-formedness is investigated through the inspection of the two-letter-mergings of a substiution, namely concatenations with letter insertions from the right

    更新日期:2019-05-16
  • Dual lattice-path transformations and the dynamics of the major and minor exo-modes
    J. Math. Music (IF 0.467) Pub Date : 2019-05-15
    Thomas Noll

    The article investigates an extension of the theory of well-formed modes and proposes a model of the major and minor modes in harmonic tonality. The established theory of well-formed modes is well adapted to the description of the medieval diatonic modes. Its core is the conversion of the circle-of-fifths encoding into the circle-of-steps encoding of the seven generic scale degrees. This conversion

    更新日期:2019-05-15
  • John Cage's Silent Piece and the Japanese gardening technique of shakkei: Formalizing Whittington's conjecture through conceptual graphs
    J. Math. Music (IF 0.467) Pub Date : 2019-05-15
    Michael D. Fowler

    This article examines John Cage's Silent Piece (commonly known as 4′33′′). I analyze the work through formalizing the frame conjecture of Stephen Whittington [2013. “Digging In John Cage's Garden: Cage and Ryōanji.” Malaysian Music Journal 2 (2): 12–21], which suggests that the work's spatial conditions are akin to those found in the Japanese gardening technique of shakkei, or borrowed scenery. By

    更新日期:2019-05-15
  • Harmonic distance in intervals and chords
    J. Math. Music (IF 0.467) Pub Date : 2019-05-15
    Rafael Cubarsi

    The harmonic distance between two pure tones, in the sense used by Tenney, is generalised to chords whose pitches are harmonic fractions. In the tonal graph generated by the harmonics involved in a chord, which for n-TET systems has its equivalent in the Tonnetz, the melodic distance between the lowest common ancestor and the lowest common harmonic of the pitches composing the chord is a measure of

    更新日期:2019-05-15
  • 2:3:4 Harmony within the tritave
    J. Math. Music (IF 0.467) Pub Date : 2019-05-15
    Markus Schmidmeier

    In the Pythagorean tuning system, the fifth is used to generate a scale of 12 notes per octave. In this paper, we use the octave to generate a scale of 19 notes per tritave; one can play this scale on a traditional piano. In this system, the octave becomes a proper interval and the 2:3:4 chord a proper chord. We study harmonic properties obtained from the 2:3:4 chord, in particular composition elements

    更新日期:2019-05-15
  • Variety and multiplicity for partitioned factors in Christoffel and Sturmian words
    J. Math. Music (IF 0.467) Pub Date : 2019-05-14
    Norman Carey, David Clampitt

    The fundamental results in mathematical music theory due to Clough and Myerson, Cardinality equals Variety (CV) and Structure yields Multiplicity (SM), correspond to statements about Christoffel words. These results may be stated and proved in a purely word-theoretic environment by means of the concept of a partitioned factor. In this setting, the generalized circle of fifths of Clough and Myerson

    更新日期:2019-05-14
  • Creating improvisations on chord progressions using suffix trees
    J. Math. Music (IF 0.467) Pub Date : 2019-05-14
    Lorraine A.K. Ayad, Marc Chemillier, Solon P. Pissis

    Technology nowadays takes an increasing part of “creativity” in live music software such as the OMax-ImproteK-Djazz improvisation environment. Specifically, Djazz implements techniques for indexing and creating improvisations using a given chord progression. It relies on a database that we call a dictionary, storing musical sequences (audio or MIDI) associated with known chord changes. We define an

    更新日期:2019-05-14
  • Naming and ordering the modes, in light of combinatorics on words
    J. Math. Music (IF 0.467) Pub Date : 2019-05-08
    David Clampitt, Thomas Noll

    One of the most telling features of the application of combinatorics on words in mathematical music theory is the extent to which aspects of the history of theory are captured by the word theory model. Well-formed modes, including the usual diatonic modes, are modeled by Christoffel words and their conjugates. A class of Sturmian morphisms produces words representing the Glarean modes, and gives rise

    更新日期:2019-05-08
  • MetricSplit: an automated notation of rhythm aligned with metric structure
    J. Math. Music (IF 0.467) Pub Date : 2019-05-08
    Markus Lepper, Baltasar Trancón y Widemann

    For any musical rhythm given by a sequence of duration values as rational numbers, traditional common western notation (CWN) provides infinite possibilities for its notation, using the standard devices: note symbols, prolongation dots, ties, and proportional brackets. But given additionally a musical meter, which in CWN is some hierarchical organization of time points, repeated with every measure,

    更新日期:2019-05-08
  • Combinatorics of words and morphisms in some pieces of Tom Johnson
    J. Math. Music (IF 0.467) Pub Date : 2019-05-03
    Jean-Paul Allouche, Tom Johnson

    We survey several occurrences of combinatorics of words and morphisms in the pieces of Tom Johnson, showing in particular that some of the sequences of notes that he used intuitively can be interpreted or constructed through combinatorial objects such as morphisms. Furthermore some of these sequences have an independent interest in number theory and theoretical computer science.

    更新日期:2019-05-03
  • Marcel Frémiot, determinism versus chaos, and the tower of Hanoi
    J. Math. Music (IF 0.467) Pub Date : 2019-05-03
    Jean-Paul Allouche

    Marcel Frémiot composed Messe pour orgue à l'usage des paroisses by using the tower of Hanoi puzzle. We give some context around this piece, describing in particular the Hanoi puzzle, its links with automatic sequences, and discussions with Marcel about ordered versus chaotic sequences.

    更新日期:2019-05-03
  • Effects of weighting the ends of a tubular bell on modular frequencies
    J. Math. Music (IF 0.467) Pub Date : 2019-04-03
    D.L. Oliver, A. Arsie

    This paper presents a mathematical analysis of a modified tubular bell. Tubular bells are often modeled as a vibrating beam with free boundary conditions. However, most orchestral tubular bells contain a single cap attached to one end of the tube. This cap affects both the strike note as well as the relative frequencies of the overtones. However, the literature contains little information regarding

    更新日期:2019-04-03
  • Consonance based interval systems and their matrices: Leibniz's harmonic equations
    J. Math. Music (IF 0.467) Pub Date : 2019-04-03
    Walter Bühler

    The article aims to draw attention to the diatonic algorithm, a simple numerical algorithm, by which musical scales and intervals can be described, if they fit to the staff notation of the European tradition. The essential concept for this non-Pythagorean algorithm was developed by Gottfried Wilhelm Leibniz (1646–1716) in his manuscripts and in his correspondence with Conrad Henfling (1648–1716) under

    更新日期:2019-04-03
  • Designing inharmonic strings
    J. Math. Music (IF 0.467) Pub Date : 2018-09-06
    William A. Sethares, Kevin Hobby

    Uniform strings have a harmonic sound; non-uniform strings have an inharmonic sound. Given a precise description of a non-uniform string, its inharmonic spectrum can be calculated using standard techniques. This paper addresses the inverse problem: given a desired/specified spectrum, how can string parameters be chosen so as to achieve that specification? The design method casts the inverse problem

    更新日期:2018-09-06
  • Spaces of gestures are function spaces
    J. Math. Music (IF 0.467) Pub Date : 2018-08-30
    Juan Sebastián Arias

    From the point of view of musical performance, gestures are the movements of the body of the performer when playing an instrument. This vague idea can be modeled mathematically, by mixing category theory and topology, giving rise to the definition of a topological gesture with a given skeleton and body in a topological space. The skeleton represents the abstract configuration of the body's limbs and

    更新日期:2018-08-30
  • Introduction to gestural similarity in music. An application of category theory to the orchestra
    J. Math. Music (IF 0.467) Pub Date : 2018-08-22
    Maria Mannone

    Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional structures and strategies. Mathematics can also be applied to the entire making of music, from the score to the performance, connecting compositional structures to the

    更新日期:2018-08-22
  • Expanded interval cycles
    J. Math. Music (IF 0.467) Pub Date : 2018-08-09
    Adam H. Berliner, David Castro, Justin Merritt, Christopher Southard

    Pitch space is commonly represented using the face of a clock, in which the 12 pitch-classes are mapped onto the elements of Z12. Combining this form of representation with modular arithmetic results in the emergence of significant rotationally symmetric patterns, which can be used to generate pitch content and to effect a modulation between closely related collections within a composition. We generalize

    更新日期:2018-08-09
  • Relational poly-Klumpenhouwer networks for transformational and voice-leading analysis
    J. Math. Music (IF 0.467) Pub Date : 2018-08-06
    Alexandre Popoff, Moreno Andreatta, Andrée Ehresmann

    In the field of transformational music theory, which emphasizes the possible transformations between musical objects, Klumpenhouwer networks (K-nets) constitute a useful framework with connections in both group theory and graph theory. Recent attempts at formalizing K-nets in their most general form have evidenced a deeper connection with category theory. These formalizations use diagrams in sets,

    更新日期:2018-08-06
  • Quirinus van Blankenburg's Transporteur
    J. Math. Music (IF 0.467) Pub Date : 2018-08-03
    Franck Jedrzejewski

    (2018). Quirinus van Blankenburg's Transporteur. Journal of Mathematics and Music: Vol. 12, No. 2, pp. 123-124.

    更新日期:2018-08-03
  • Introduction to the special issue on perfect balance and the discrete Fourier transform
    J. Math. Music (IF 0.467) Pub Date : 2018-07-26
    Thomas M. Fiore

    (2017). Introduction to the special issue on perfect balance and the discrete Fourier transform. Journal of Mathematics and Music: Vol. 11, Perfect Balance and the Discrete Fourier Transform, pp. 65-66.

    更新日期:2018-07-26
  • Perfect balance and circularly rich words
    J. Math. Music (IF 0.467) Pub Date : 2018-07-26
    Norman Carey

    A recent article [Milne, Andrew J., David Bulger, and Steffan A. Herff. 2017. “Exploring the Space of Perfectly Balanced Rhythms and Scales.” Journal of Mathematics and Music 11 (2):101--133] posits the notion of balance and contrasts it with evenness, which may be associated with the patterns of step intervals in either maximally even sets or well-formed scales. Scales defined as “perfectly balanced”

    更新日期:2018-07-26
  • Corrigendum
    J. Math. Music (IF 0.467) Pub Date : 2018-07-26

    (2017). Corrigendum. Journal of Mathematics and Music: Vol. 11, Perfect Balance and the Discrete Fourier Transform, pp. 174-174.

    更新日期:2018-07-26
  • Exploring the space of perfectly balanced rhythms and scales
    J. Math. Music (IF 0.467) Pub Date : 2018-07-16
    Andrew J. Milne, David Bulger, Steffen A. Herff

    Periodic scales and meters typically embody “organizational principles” – their pitches and onset times are not randomly distributed, but structured by rules or constraints. Identifying such principles is useful for understanding existing music and for generating novel music. In this article, we identify and discuss a novel organizational principle for scales and rhythms that we feel is of both theoretical

    更新日期:2018-07-16
  • The discrete Fourier transform of distributions
    J. Math. Music (IF 0.467) Pub Date : 2018-07-06
    Emmanuel Amiot

    This article (being the first chapter of the book Music Through Fourier Space published by Springer International Publishing Switzerland in 2016 and reprinted here in the Journal of Mathematics and Music with the kind permission of Springer International Publishing Switzerland) gives the basic definitions and tools for the discrete Fourier transform (DFT) of subsets of a cyclic group, which can model

    更新日期:2018-07-06
  • Decompositions of nil sums of roots of unity. An adaptation of “Sommes nulles de racines de l'unité”
    J. Math. Music (IF 0.467) Pub Date : 2018-06-22
    Emmanuel Amiot

    Sets of roots of unity that sum to zero have interesting musical and mathematical relevance. It seems natural to conjecture that these sets are disjoint unions of the simplest such, i.e. regular polygons, but this is not true.

    更新日期:2018-06-22
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