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Journal of Mathematics and Music最新文献

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Axiomatic scale theory 公理化尺度理论
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2020-01-10 DOI: 10.1080/17459737.2019.1696899
Daniel Harasim, Stefan E. Schmidt, M. Rohrmeier
{"title":"Axiomatic scale theory","authors":"Daniel Harasim, Stefan E. Schmidt, M. Rohrmeier","doi":"10.1080/17459737.2019.1696899","DOIUrl":"https://doi.org/10.1080/17459737.2019.1696899","url":null,"abstract":"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. All theorems and lemmata are completely proven in a modern and consistent notation. In particular, new simplified proofs of existing theorems such as the equivalence of non-degenerate well-formedness and Myhill's property are presented. This model of musical scales explicitly formalizes and utilizes the cyclic order relation of pitch classes.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"49 1","pages":"223 - 244"},"PeriodicalIF":1.1,"publicationDate":"2020-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77681394","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: 11
An analysis of pitch-class segmentation in John Cage's Ryoanji for oboe using morphological image analysis and formal concept analysis 用形态图像分析和形式概念分析分析约翰·凯奇的双簧管《龙音记》中音高类的分割
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2020-01-02 DOI: 10.1080/17459737.2019.1639082
Michael D. Fowler
{"title":"An analysis of pitch-class segmentation in John Cage's Ryoanji for oboe using morphological image analysis and formal concept analysis","authors":"Michael D. Fowler","doi":"10.1080/17459737.2019.1639082","DOIUrl":"https://doi.org/10.1080/17459737.2019.1639082","url":null,"abstract":"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 the aesthetics of the karesansui and then examine the previous work of van Tonder and Lyons regarding the medial axis transform (MAT) of the garden at Ryōan-ji. This leads to the use of the distance transform, local maxima, and Voronoi diagram in order to decompose the two-dimensional image plane of Cage's Ryoanji for oboe. Finally, using the technique of FCA for constructing a number of formal concept lattices, the pitch-class segmentation of Ryoanji for oboe is investigated in regard to the sound gardens and the classes of Voronoi regions found across sound gardens.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"196 1","pages":"21 - 47"},"PeriodicalIF":1.1,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86171898","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: 4
On features of fugue subjects. A comparison of J.S. Bach and later composers 论赋格主体的特点。巴赫与后来作曲家的比较
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2020-01-02 DOI: 10.1080/17459737.2019.1610193
J. Rydén
{"title":"On features of fugue subjects. A comparison of J.S. Bach and later composers","authors":"J. Rydén","doi":"10.1080/17459737.2019.1610193","DOIUrl":"https://doi.org/10.1080/17459737.2019.1610193","url":null,"abstract":"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 of pitch classes; initial interval (in semitones); number of unique intervals between successive notes; maximum interval between successive notes (in semitones). A data set of subjects from various composers was constructed. An analysis of principal components (PCA) makes possible an interpretation of the variability as well as a visualisation of all cases. Regression models for counts are introduced to investigate differences between composers, taking into account dependence on covariates. Concerning the range of the subject, a statistically significant difference was found between Bach and other composers. Furthermore, regarding the number of unique notes employed, a statistically significant difference was found between all composer categories.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"11 1","pages":"1 - 20"},"PeriodicalIF":1.1,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78588452","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: 4
Functorial semiotics for creativity 创造力的功能符号学
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2020-01-02 DOI: 10.1080/17459737.2019.1675193
G. Mazzola
{"title":"Functorial semiotics for creativity","authors":"G. Mazzola","doi":"10.1080/17459737.2019.1675193","DOIUrl":"https://doi.org/10.1080/17459737.2019.1675193","url":null,"abstract":"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 calculus of fractions. Semantics in this approach is extended to a number of “global” constructions enabled by the Yoneda Lemma, including cohomological constructions. This approach concludes with a short discussion of classes of creativity with respect to the proposed functorial semiotics.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"109 1","pages":"66 - 105"},"PeriodicalIF":1.1,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78073369","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: 1
Geometry and Topology in Music ( Special Issue of the Journal of Mathematics and Music edited by M. Andreatta, E. Amiot et J. Yust, vol. 14, n° 2). 音乐中的几何与拓扑(数学与音乐杂志特刊，M. Andreatta, E. Amiot et J. Yust编辑，卷14,n°2)。
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2020-01-01 DOI: 10.1080/17459737.2020.1793528
M. Andreatta, E. Amiot, Jason Yust
{"title":"Geometry and Topology in Music ( Special Issue of the Journal of Mathematics and Music edited by M. Andreatta, E. Amiot et J. Yust, vol. 14, n° 2).","authors":"M. Andreatta, E. Amiot, Jason Yust","doi":"10.1080/17459737.2020.1793528","DOIUrl":"https://doi.org/10.1080/17459737.2020.1793528","url":null,"abstract":"","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"226 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78454628","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
Quantum GestART: identifying and applying correlations between mathematics, art, and perceptual organization 量子GestART:识别和应用数学、艺术和感知组织之间的相关性
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2019-12-16 DOI: 10.1080/17459737.2020.1726691
Maria Mannone, Federico Favali, Balandino Di Donato, L. Turchet
{"title":"Quantum GestART: identifying and applying correlations between mathematics, art, and perceptual organization","authors":"Maria Mannone, Federico Favali, Balandino Di Donato, L. Turchet","doi":"10.1080/17459737.2020.1726691","DOIUrl":"https://doi.org/10.1080/17459737.2020.1726691","url":null,"abstract":"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 of complex images, and Dirac notation, imagining a world of “prototypes” that can be connected to obtain a fine or coarse-graining approximation of a given visual image. Visual prototypes are exchanged with auditory ones, and the information (position, size) characterizing visual prototypes is connected with the information (onset, duration, loudness, pitch range) characterizing auditory prototypes. The topic is contextualized within a philosophical debate (discreteness and comparison of apparently unrelated objects), it develops through mathematical formalism, and it leads to programming, to spark interdisciplinary thinking and ignite creativity within STEAM.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"46 1","pages":"62 - 94"},"PeriodicalIF":1.1,"publicationDate":"2019-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77602410","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: 12
Audio Synthesis in Music 音乐中的音频合成
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2019-09-24 DOI: 10.1201/9780429506185-8
James S. Walker, Gary W. Don
{"title":"Audio Synthesis in Music","authors":"James S. Walker, Gary W. Don","doi":"10.1201/9780429506185-8","DOIUrl":"https://doi.org/10.1201/9780429506185-8","url":null,"abstract":"","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"8 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75033697","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
A Geometry of Harmony 和谐的几何
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2019-09-24 DOI: 10.1201/9780429506185-7
James S. Walker, Gary W. Don
{"title":"A Geometry of Harmony","authors":"James S. Walker, Gary W. Don","doi":"10.1201/9780429506185-7","DOIUrl":"https://doi.org/10.1201/9780429506185-7","url":null,"abstract":"","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"13 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82474358","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
Pitch, Frequency, and Musical Scales 音高、频率和音阶
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2019-09-24 DOI: 10.1201/9780429506185-1
James S. Walker, Gary W. Don
{"title":"Pitch, Frequency, and Musical Scales","authors":"James S. Walker, Gary W. Don","doi":"10.1201/9780429506185-1","DOIUrl":"https://doi.org/10.1201/9780429506185-1","url":null,"abstract":"","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"50 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80333629","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
Analyzing Pitch and Rhythm 分析音高和节奏
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2019-09-24 DOI: 10.1201/9780429506185-6
James S. Walker, Gary W. Don
{"title":"Analyzing Pitch and Rhythm","authors":"James S. Walker, Gary W. Don","doi":"10.1201/9780429506185-6","DOIUrl":"https://doi.org/10.1201/9780429506185-6","url":null,"abstract":"","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"120 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89627301","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
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