Journal of Mathematics and Music最新文献

{"title":"Generalizations of Euler's Tonnetz on triangulated surfaces","authors":"Konstanze Rietsch","doi":"10.1080/17459737.2024.2362132","DOIUrl":"https://doi.org/10.1080/17459737.2024.2362132","url":null,"abstract":"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...","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"2386 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196968","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}

{"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":"12 1","pages":""},"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}

{"title":"An algebra of chords for a non-degenerate Tonnetz","authors":"Rafael Cubarsi","doi":"10.1080/17459737.2024.2312578","DOIUrl":"https://doi.org/10.1080/17459737.2024.2312578","url":null,"abstract":"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 ...","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"53 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140004864","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}

{"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":"14 1","pages":""},"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}

{"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":"83 1","pages":"531 - 535"},"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}

{"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":"39 1","pages":"487 - 513"},"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}

{"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":"40 1","pages":""},"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}

{"title":"Musical stylistic analysis: a study of intervallic transition graphs via persistent homology","authors":"Martín Mijangos, Alessandro Bravetti, Pablo Padilla","doi":"10.1080/17459737.2023.2232811","DOIUrl":"https://doi.org/10.1080/17459737.2023.2232811","url":null,"abstract":"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.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135491940","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}

{"title":"Algebraic tunings","authors":"C. Dettmann, Liam Taylor-West","doi":"10.1080/17459737.2023.2234126","DOIUrl":"https://doi.org/10.1080/17459737.2023.2234126","url":null,"abstract":",","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"56 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82441821","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}

{"title":"Mathematical foundations of complex tonality","authors":"Jeffrey R. Boland, Lane P. Hughston","doi":"10.1080/17459737.2023.2228546","DOIUrl":"https://doi.org/10.1080/17459737.2023.2228546","url":null,"abstract":"<p>Equal temperament, in which semitones are tuned in the irrational ratio of <span><noscript><img alt=\"\" src=\"/na101/home/literatum/publisher/tandf/journals/content/tmam20/0/tmam20.ahead-of-print/17459737.2023.2228546/20230717/images/tmam_a_2228546_ilm0001.gif\"/></noscript><img alt=\"\" data-formula-source='{\"type\" : \"image\", \"src\" : \"/na101/home/literatum/publisher/tandf/journals/content/tmam20/0/tmam20.ahead-of-print/17459737.2023.2228546/20230717/images/tmam_a_2228546_ilm0001.gif\"}' src=\"//:0\"/><span></span></span><span><span style=\"color: inherit; display: none;\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mn>2</mn><mrow><mn>1</mn><mrow><mo>/</mo></mrow><mn>12</mn></mrow></msup><mo>:</mo><mn>1</mn></math>' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 3.951em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 3.322em; height: 0px; font-size: 118%;\"><span style=\"position: absolute; clip: rect(1.292em, 1003.25em, 2.504em, -1000em); top: -2.359em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 1.989em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.186em, 1000.45em, 4.141em, -1000em); top: -3.997em; left: 0em;\"><span style=\"font-family: MathJax_Main;\">2</span><span style=\"display: inline-block; width: 0px; height: 3.997em;\"></span></span><span style=\"position: absolute; top: -4.39em; left: 0.5em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Main;\">1</span><span><span style=\"font-size: 70.7%; font-family: MathJax_Main;\">/</span></span><span style=\"font-size: 70.7%; font-family: MathJax_Main;\">12</span></span><span style=\"display: inline-block; width: 0px; height: 3.997em;\"></span></span></span></span><span style=\"font-family: MathJax_Main; padding-left: 0.278em;\">:</span><span style=\"font-family: MathJax_Main; padding-left: 0.278em;\">1</span></span><span style=\"display: inline-block; width: 0px; height: 2.359em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.057em; border-left: 0px solid; width: 0px; height: 1.203em;\"></span></span></nobr><span role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mn>2</mn><mrow><mn>1</mn><mrow><mo>/</mo></mrow><mn>12</mn></mrow></msup><mo>:</mo><mn>1</mn></math></span></span><script type=\"math/mml\"><math><msup><mn>2</mn><mrow><mn>1</mn><mrow><mo>/</mo></mrow><mn>12</mn></mrow></msup><mo>:</mo><mn>1</mn></math></script></span>, is best seen as a serviceable compromise, sacrificing purity for flexibility. Just intonation, in which intervals are given by products of powers of 2, 3, and 5, is more natural, but of limited flexibility. We propose a new scheme in which ratios of Gaussian integers form the basis of an abstract tonal sys","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"605 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138540072","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}