Journal of Mathematics and Music最新文献_第9页

From actantial model to conceptual graph: Thematized action in John Cage's 0′00′(4′33′′No. 2) 从现实模型到概念图:约翰·凯奇的《0’00’(4’33’)》中的主题化行动。2）

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2020-05-29 DOI: 10.1080/17459737.2020.1760953

Michael D. Fowler

引用次数: 1

Musical pitch quantization as an eigenvalue problem 作为特征值问题的音高量化

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2020-05-24 DOI: 10.1080/17459737.2020.1763488

Peter beim Graben, Maria Mannone

引用次数: 7

Homological persistence in time series: an application to music classification 时间序列的同调持久性:在音乐分类中的应用

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2020-05-03 DOI: 10.1080/17459737.2020.1786745

Mattia G. Bergomi, A. Baratè

{"title":"Homological persistence in time series: an application to music classification","authors":"Mattia G. Bergomi, A. Baratè","doi":"10.1080/17459737.2020.1786745","DOIUrl":"https://doi.org/10.1080/17459737.2020.1786745","url":null,"abstract":"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. In the static case, persistent homology allows one to provide a representation of a manifold paired with a continuous function as a collection of multisets of points and lines called persistence diagrams. The idea is to fingerprint the change of a variable-geometry space as a time series of persistence diagrams, and afterwards compare such time series by using dynamic time warping. As an application, we express some music features and their time dependency by updating the values of a function defined on a polyhedral surface, called the Tonnetz. Thereafter, we use this time-based representation to automatically classify three collections of compositions according to their style, and discuss the optimal time-granularity for the analysis of different musical genres.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"6 1","pages":"204 - 221"},"PeriodicalIF":1.1,"publicationDate":"2020-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91326696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

Why topology? 为什么拓扑?

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2020-05-03 DOI: 10.1080/17459737.2020.1799563

Dmitri Tymoczko

引用次数: 6

Mathematical approaches to defining the semitone in antiquity 古代定义半音的数学方法

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2020-04-30 DOI: 10.1080/17459737.2020.1753122

Caleb Mutch

{"title":"Mathematical approaches to defining the semitone in antiquity","authors":"Caleb Mutch","doi":"10.1080/17459737.2020.1753122","DOIUrl":"https://doi.org/10.1080/17459737.2020.1753122","url":null,"abstract":"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 element – the number series 16, 17, 18 – to serve different ends. The number 17 provides the simplest way to divide the 9:8 whole tone into two parts, but the status of those two parts was debated, as was their relationship to the standard 256:243 semitone of Greek theory. I account for this diversity by appealing to the contexts in which the authors wrote – music treatises vs. commentaries on Plato's Timaeus – and to the importance placed on mathematics in Neoplatonist curricula. The article concludes by examining how confusion regarding the 16, 17, 18 series lingered even in the medieval period due to ambiguities in Boethius's De institutione musica, and how medieval authors eventually superseded the debate through a Euclid-inspired geometric division of the 9:8 ratio.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"19 1","pages":"292 - 306"},"PeriodicalIF":1.1,"publicationDate":"2020-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79120564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Symbolic structures in music theory and composition, binary keyboards, and the Thue–Morse shift 音乐理论与作曲中的符号结构，二进制键盘，以及休-莫尔斯变换

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2020-03-17 DOI: 10.1080/17459737.2020.1732490

R. Gómez, L. Nasser

引用次数: 3

An alternative approach to generalized Pythagorean scales. Generation and properties derived in the frequency domain 广义毕达哥拉斯尺度的另一种方法。在频域的产生和性质推导

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2020-03-05 DOI: 10.1080/17459737.2020.1726690

R. Cubarsi

引用次数: 1

Generalized Tonnetze and Zeitnetze, and the topology of music concepts 广义的韵律和韵律，以及音乐概念的拓扑结构

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2020-03-02 DOI: 10.1080/17459737.2020.1725667

Jason Yust

{"title":"Generalized Tonnetze and Zeitnetze, and the topology of music concepts","authors":"Jason Yust","doi":"10.1080/17459737.2020.1725667","DOIUrl":"https://doi.org/10.1080/17459737.2020.1725667","url":null,"abstract":"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 to important musical concepts. Two kinds of music-theoretical geometry have been proposed that can house Tonnetze: geometrical duals of voice-leading spaces and Fourier phase spaces. Fourier phase spaces are particularly appropriate for Tonnetze in that their objects are pitch-class distributions (real-valued weightings of the 12 pitch classes) and proximity in these space relates to shared pitch-class content. They admit of a particularly general method of constructing a geometrical Tonnetz that allows for interval and chord duplications in a toroidal geometry. This article examines how these duplications can relate to important musical concepts such as key or pitch height, and details a method of removing such redundancies and the resulting changes to the homology of the space. The method also transfers to the rhythmic domain, defining Zeitnetze for cyclic rhythms. A number of possible Tonnetze are illustrated: on triads, seventh chords, ninth chords, scalar tetrachords, scales, etc., as well as Zeitnetze on common cyclic rhythms or timelines. Their different topologies – whether orientable, bounded, manifold, etc. – reveal some of the topological character of musical concepts.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"36 1","pages":"170 - 203"},"PeriodicalIF":1.1,"publicationDate":"2020-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76161633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6

Some remarks on hypergestural homology of spaces and its relation to classical homology 空间的超手势同调及其与经典同调的关系

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2020-02-27 DOI: 10.1080/17459737.2020.1722269

J. Arias-Valero, E. Lluis-Puebla

{"title":"Some remarks on hypergestural homology of spaces and its relation to classical homology","authors":"J. Arias-Valero, E. Lluis-Puebla","doi":"10.1080/17459737.2020.1722269","DOIUrl":"https://doi.org/10.1080/17459737.2020.1722269","url":null,"abstract":"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 hypergestures playing the role of singular simplices and singular cubes. In this article, we locate Mazzola's hypergestural homology as a special kind of abstract cubical homology and propose two variations of Mazzola's construction, corresponding to simple geometric and physical interpretations of boundaries of hypergestures. Moreover, we discuss the relationship between hypergestural homology and classical cubical homology and prove that in many cases, one of our hypergestural homologies is invariant under homotopy equivalence of spaces, which is the main result of the article. Also, based on some examples, several structural improvements of hypergestural homology are suggested. However, one of these examples suggests that hypergestural homology could provide combinatorial information about a topological space beyond classical homology. Our computations are based on an explicit presentation of hypergestures, not included in previous works on gesture theory. This article has an Online Supplement, in which we expose some technical details, including the proof of the main result.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"14 1","pages":"245 - 265"},"PeriodicalIF":1.1,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86854379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

On the topological characterization of gestures in a convenient category of spaces 方便范畴空间中手势的拓扑表征

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2020-02-13 DOI: 10.1080/17459737.2020.1716403

Timothy L. Clark

引用次数: 4