Pub Date : 2024-08-14DOI: 10.1080/17459737.2024.2362132
Konstanze Rietsch
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 theoriae musicae ex certissismis harmon...
我们给出了三角形曲面上所谓 "顿涅茨 "的定义，概括了著名的欧拉顿涅茨（Euler, Leonhard.1739.Tentamen novae theoriae musicae ex certissismis harmon...
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Pub Date : 2024-06-06DOI: 10.1080/17459737.2024.2344095
Maria Mannone, Mariana Montiel, Miguel R. Wilhelmi
{"title":"Music-driven geometric and topologic intuition: a case study with the Klein bottle","authors":"Maria Mannone, Mariana Montiel, Miguel R. Wilhelmi","doi":"10.1080/17459737.2024.2344095","DOIUrl":"https://doi.org/10.1080/17459737.2024.2344095","url":null,"abstract":"","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141377903","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}
Pub Date : 2024-03-04DOI: 10.1080/17459737.2024.2315120
Bogusław Fugiel
A quantum mechanical approach to the psychoacoustic effect of Shepard tones has been explored. Melodic intervals are represented by qubits. The phenomenon of bistable perception of intervals and th...
{"title":"Quantum approach to jam session","authors":"Bogusław Fugiel","doi":"10.1080/17459737.2024.2315120","DOIUrl":"https://doi.org/10.1080/17459737.2024.2315120","url":null,"abstract":"A quantum mechanical approach to the psychoacoustic effect of Shepard tones has been explored. Melodic intervals are represented by qubits. The phenomenon of bistable perception of intervals and th...","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140116078","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}
Pub Date : 2024-02-29DOI: 10.1080/17459737.2024.2312578
Rafael Cubarsi
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 interval structure. Root and mode are the ...
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Pub Date : 2023-12-26DOI: 10.1080/17459737.2023.2290275
Evan M. O'Dorney
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 sonorities is especially challenging. Us...
{"title":"Renaissance canons with asymmetric schemes","authors":"Evan M. O'Dorney","doi":"10.1080/17459737.2023.2290275","DOIUrl":"https://doi.org/10.1080/17459737.2023.2290275","url":null,"abstract":"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 sonorities is especially challenging. Us...","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056489","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}
Pub Date : 2023-08-27DOI: 10.1080/17459737.2023.2248124
Jordan Lenchitz
{"title":"Exploring Musical Spaces: A Synthesis of Mathematical Approaches","authors":"Jordan Lenchitz","doi":"10.1080/17459737.2023.2248124","DOIUrl":"https://doi.org/10.1080/17459737.2023.2248124","url":null,"abstract":"","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76801869","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}
Pub Date : 2023-08-22DOI: 10.1080/17459737.2023.2233972
Konstantin L. Gurin
The logarithm mapping of natural numbers is a sum of products of coefficients. If these coefficients are arbitrary parameters, a new mapping of natural numbers to some subset of real numbers appears. This mapping preserves some crucial logarithm properties and constructs a new musical sound with a spectrum of inharmonic overtones. The simplest one-parameter mapping to a subset of polynomials with integer coefficients is constructed. The parameter defines a new “perfect fifth” similarly to the meantone temperament. It is an interesting case when the mapping parameter is defined from the linear relation between the new “major third” and the new “perfect fifth.” The most interesting case of a linear relation is the condition of zeroing the syntonic comma. Here, the new meantone temperament, based on the new “perfect fifth,” simultaneously coincides with Pythagorean- and five-limit-like tunings.
{"title":"A different kind of meantone temperament and a novel mapping from the harmonic series to Pythagorean pitch classes","authors":"Konstantin L. Gurin","doi":"10.1080/17459737.2023.2233972","DOIUrl":"https://doi.org/10.1080/17459737.2023.2233972","url":null,"abstract":"The logarithm mapping of natural numbers is a sum of products of coefficients. If these coefficients are arbitrary parameters, a new mapping of natural numbers to some subset of real numbers appears. This mapping preserves some crucial logarithm properties and constructs a new musical sound with a spectrum of inharmonic overtones. The simplest one-parameter mapping to a subset of polynomials with integer coefficients is constructed. The parameter defines a new “perfect fifth” similarly to the meantone temperament. It is an interesting case when the mapping parameter is defined from the linear relation between the new “major third” and the new “perfect fifth.” The most interesting case of a linear relation is the condition of zeroing the syntonic comma. Here, the new meantone temperament, based on the new “perfect fifth,” simultaneously coincides with Pythagorean- and five-limit-like tunings.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74124852","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}
Pub Date : 2023-08-17DOI: 10.1080/17459737.2023.2244480
H. Bedouelle
{"title":"Parsimonious sequences of finite sets and their applications to chord progressions and music composition","authors":"H. Bedouelle","doi":"10.1080/17459737.2023.2244480","DOIUrl":"https://doi.org/10.1080/17459737.2023.2244480","url":null,"abstract":"","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81512715","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}
Pub Date : 2023-08-10DOI: 10.1080/17459737.2023.2232811
Martín Mijangos, Alessandro Bravetti, Pablo Padilla
AbstractWe 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 this method to weighted directed graphs obtained from pitch transitions information of a given musical fragment and use these techniques to the quantitative study of stylistic trends. As a first illustration, we analyse a selection of string quartets by Haydn, Mozart and Beethoven and discuss possible implications of our results in terms of different approaches by these composers to stylistic exploration and variety. We observe that Haydn is stylistically the most conservative, followed by Mozart, while Beethoven is the most innovative. Finally we also compare the variability of different genres, namely minuets, allegros, prestos, and adagios, by a given composer and conclude that the minuet is the most stable form of the string quartet movements.Keywords: Topological data analysispersistent homologystring quartetintervallic transitionsstylistic analysis2020 Mathematics Subject Classifications: 55N3162R4005C9000A65 AcknowledgementsThe authors would like to thank the anonymous reviewers for their helpful comments that improved the quality of the manuscript. MM would like to thank CONACyT for the financial support. A. Bravetti acknowledges financial support by DGAPA-UNAM, programme PAPIIT, Grant No. IA-102823. PP would like to thank DGAPA (PASPA) and Clare Hall at the University of Cambridge.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingMM was supported by a CONACyT postdoctoral fellowship. PP would like to thank Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México (DGAPA (PASPA)) and Clare Hall at the University of Cambridge. The work of AB was partially supported by DGAPA-UNAM, programme PAPIIT, Grant No. IA-102823.
摘要提出了一种将加权有向图表示为有限度量空间的新方法，并利用持久同调提取有用的特征。我们将这种方法应用于从给定音乐片段的音高过渡信息中获得的加权有向图，并将这些技术用于风格趋势的定量研究。作为第一个例子，我们分析了海顿、莫扎特和贝多芬的弦乐四重奏选段，并讨论了这些作曲家在风格探索和多样性方面的不同方法对我们的结果可能产生的影响。我们观察到海顿在风格上是最保守的，其次是莫扎特，而贝多芬最具创新性。最后，我们还比较了不同流派的可变性，即小步舞曲、快板、强音和慢板，由一个给定的作曲家，并得出结论，小步舞曲是最稳定的形式的弦乐四重奏运动。关键词:拓扑数据分析持久同源字符串四重奏区间过渡文体分析2020数学学科分类:55N3162R4005C9000A65致谢作者要感谢匿名审稿人的有益意见，这些意见提高了稿件的质量。MM感谢CONACyT的财政支持。A. Bravetti感谢DGAPA-UNAM的财政支持，PAPIIT项目，批准号:ia - 102823。PP要感谢DGAPA (PASPA)和剑桥大学的Clare Hall。披露声明作者未报告潜在的利益冲突。本研究由CONACyT博士后奖学金资助。人民党要感谢Dirección de Asuntos de Personal acadacimico将军、国立大学Autónoma de macimico (DGAPA (PASPA))和剑桥大学的Clare Hall。AB的工作得到了DGAPA-UNAM的部分支持，计划PAPIIT，批准号:ia - 102823。
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