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Resurgence in the Transition Region: The Incomplete Gamma Function 过渡区的复苏：不完全伽马函数
Symmetry, Integrability and Geometry: Methods and Applications Pub Date : 2024-01-30 DOI: 10.3842/SIGMA.2024.026
GergHo Nemes
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引用次数: 0
Taking Music Seriously: on the Dynamics of 'Mathemusical' Research with a Focus on Hexachordal Theorems 认真对待音乐：以六和弦定理为重点的 "数学 "研究动态
Symmetry, Integrability and Geometry: Methods and Applications Pub Date : 2024-01-25 DOI: 10.3842/sigma.2024.009
Moreno Andreatta, C. Guichaoua, Nicolas Juillet
{"title":"Taking Music Seriously: on the Dynamics of 'Mathemusical' Research with a Focus on Hexachordal Theorems","authors":"Moreno Andreatta, C. Guichaoua, Nicolas Juillet","doi":"10.3842/sigma.2024.009","DOIUrl":"https://doi.org/10.3842/sigma.2024.009","url":null,"abstract":"After presenting the general framework of `mathemusical' dynamics, we focus on one music-theoretical problem concerning a special case of homometry theory applied to music composition, namely Milton Babbitt's hexachordal theorem. We briefly discuss some historical aspects of homometric structures and their ramifications in crystallography, spectral analysis and music composition via the construction of rhythmic canons tiling the integer line. We then present the probabilistic generalization of Babbitt's result we recently introduced in a paper entitled ''New hexachordal theorems in metric spaces with probability measure'' and illustrate the new approach with original constructions and examples.","PeriodicalId":515898,"journal":{"name":"Symmetry, Integrability and Geometry: Methods and Applications","volume":"23 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139597927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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