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Journal of Mathematics and Music最新文献

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Parsimonious graphs for the most common trichords and tetrachords 最常见的三和弦和四和弦简约曲线图
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-05-04 DOI: 10.1080/17459737.2021.1923844
L. Nuño
{"title":"Parsimonious graphs for the most common trichords and tetrachords","authors":"L. Nuño","doi":"10.1080/17459737.2021.1923844","DOIUrl":"https://doi.org/10.1080/17459737.2021.1923844","url":null,"abstract":"Parsimonious transformations are common patterns in different musical styles and eras. In some cases, they can be represented on the Tonnetz, Cube Dance, Power Towers, or the central region of an orbifold, mainly when they only include the most even trichords and tetrachords. In this paper, two novel graphs, called Cyclopes, are presented, which include more than double the number of chord types in previously published graphs, thus allowing to represent a larger musical repertoire in a practical way. Apart from parsimonious transformations, they are also especially suitable for representing trichords a major third apart, tetrachords a minor third apart, and the cadences V7–I(m) and II –V7–I(m) with major or minor tonic chords. Therefore, they allow to clearly visualize the relationship among the corresponding chords and better understand those patterns, as well as being efficient mnemonic resources, all of which make them useful tools both for music analysis and composition.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84935860","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: 2
Pattern in music 音乐模式
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-05-04 DOI: 10.1080/17459737.2021.1947404
D. Conklin
{"title":"Pattern in music","authors":"D. Conklin","doi":"10.1080/17459737.2021.1947404","DOIUrl":"https://doi.org/10.1080/17459737.2021.1947404","url":null,"abstract":"Pattern in music, referring to the discovery, representation, selection, and interpretation of repeated structures within single pieces (intra-opus) or corpora (inter-opus), is a central part of music analysis, musical style and genre, improvisation, music perception, and composition. This special issue of the Journal of Mathematics and Music presents a diverse selection of papers on the topic of pattern in music from computational and mathematical perspectives. The following overview will introduce the papers considering three facets: representation, discovery, and evaluation and interpretation.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85590868","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
Mining contour sequences for significant closed patterns 挖掘重要闭合模式的轮廓序列
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-04-12 DOI: 10.1080/17459737.2021.1903591
D. Conklin
{"title":"Mining contour sequences for significant closed patterns","authors":"D. Conklin","doi":"10.1080/17459737.2021.1903591","DOIUrl":"https://doi.org/10.1080/17459737.2021.1903591","url":null,"abstract":"Sequential pattern mining in music is a central part of automated music analysis and music generation. This paper evaluates sequential pattern mining on a corpus of Mozarabic chant neume sequences that have been annotated by a musicologist with intra-opus patterns. Significant patterns are discovered in three settings: all closed patterns, maximal closed patterns, and minimal closed patterns. Each setting is evaluated against the annotated patterns using the measures of recall and precision. The results indicate that it is possible to retrieve all known patterns with an acceptable precision using significant closed pattern discovery.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89421452","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: 2
Discovering distorted repeating patterns in polyphonic music through longest increasing subsequences 通过最长递增子序列发现复调音乐中扭曲的重复模式
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-04-05 DOI: 10.1080/17459737.2021.1896811
A. Laaksonen, Kjell Lemström
{"title":"Discovering distorted repeating patterns in polyphonic music through longest increasing subsequences","authors":"A. Laaksonen, Kjell Lemström","doi":"10.1080/17459737.2021.1896811","DOIUrl":"https://doi.org/10.1080/17459737.2021.1896811","url":null,"abstract":"We study the problem of identifying repetitions under transposition and time-warp invariances in polyphonic symbolic music. Using a novel onset-time-pair representation, we reduce the repeating pattern discovery problem to instances of the classical problem of finding the longest increasing subsequences. The resulting algorithm works in time where n is the number of notes in a musical work. We also study windowed variants of the problem where onset-time differences between notes are restricted, and show that they can also be solved in time using the algorithm.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79306339","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: 2
Modelling pattern interestingness in comparative music corpus analysis 比较音乐语料库分析中模式趣味性的建模
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-04-05 DOI: 10.1080/17459737.2021.1900436
Kerstin Neubarth, D. Conklin
{"title":"Modelling pattern interestingness in comparative music corpus analysis","authors":"Kerstin Neubarth, D. Conklin","doi":"10.1080/17459737.2021.1900436","DOIUrl":"https://doi.org/10.1080/17459737.2021.1900436","url":null,"abstract":"In computational pattern discovery, pattern evaluation measures select or rank patterns according to their potential interestingness in a given analysis task. Many measures have been proposed to accommodate different pattern types and properties. This paper presents a method and case study employing measures for frequent, characteristic, associative, contrasting, dependent, and significant patterns to model pattern interestingness in a reference analysis, Frances Densmore's study of Teton Sioux songs. Results suggest that interesting changes from older to more recent Sioux songs according to Densmore's analysis are best captured by contrast, dependency, and significance measures.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85102379","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
Topological data analysis of Korean music in Jeongganbo: a cycle structure 正干布韩国音乐的拓扑数据分析:一个循环结构
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-03-11 DOI: 10.1080/17459737.2022.2164626
M. Tran, Changbom Park, Jae-Hun Jung
{"title":"Topological data analysis of Korean music in Jeongganbo: a cycle structure","authors":"M. Tran, Changbom Park, Jae-Hun Jung","doi":"10.1080/17459737.2022.2164626","DOIUrl":"https://doi.org/10.1080/17459737.2022.2164626","url":null,"abstract":"Jeongganbo is a unique music representation invented by Sejong the Great. Contrary to the Western music notation, the pitch of each note is encrypted and the length is visualized directly in a matrix form. We use topological data analysis (TDA) to analyze the Korean music written in Jeongganbo for Suyeonjang, Songuyeo, and Taryong, those well-known pieces played among noble community. We define the nodes of each music with pitch and length and transform the music into a graph with the distance between the nodes defined as their adjacent occurrence rate. The graph homology is investigated by TDA. We identify cycles of each music and show how those cycles are interconnected. We found that the cycles of Suyeonjang and Songuyeo, categorized as a special type of cyclic music, frequently overlap each other in the music, while those of Taryong, which does not belong to the same class, appear only individually.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87148031","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
Local minima of dissonance functions 失谐函数的局部极小值
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-03-11 DOI: 10.1080/17459737.2021.1882600
D. Mukherjee
{"title":"Local minima of dissonance functions","authors":"D. Mukherjee","doi":"10.1080/17459737.2021.1882600","DOIUrl":"https://doi.org/10.1080/17459737.2021.1882600","url":null,"abstract":"When the same sound is produced simultaneously with two different fundamental frequencies, auditory roughness is observed. If the first sound is fixed and the fundamental frequency of the second is varied continuously, auditory roughness also varies continuously. A vowel sound is distinguished by its spectral envelope – which is independent of the fundamental frequency. This is a motivation to define the metric space of timbres. Each timbre is associated with a dissonance function which has local minima at certain intervals of local consonance related to the timbre. This is related to the music-theoretical notion of consonant intervals and scales. For the subspace consisting of all timbres with an interval of local consonance at a chosen point β, the main theorem describes certain points on the boundary by the vanishing of one-sided derivatives of dissonance functions at β.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72565650","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
Deep Rhythms VIIIWood block music* 深节奏八木块音乐*
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-03-11 DOI: 10.1080/17459737.2021.1871789
T. Johnson
{"title":"Deep Rhythms VIIIWood block music*","authors":"T. Johnson","doi":"10.1080/17459737.2021.1871789","DOIUrl":"https://doi.org/10.1080/17459737.2021.1871789","url":null,"abstract":"Deep Rhythms are normally constructed by choosing a length (l), and the difference (d) between one basic note and the next. If one begins at 0, and one wishes to construct rhythms in measures containing 8 notes, with 3 notes in each measure, and the difference between basic notes is 3, then l = 8, n = 3, one follows the cycle (0, 3, 6, 1, 4, 7, 2, 5, 0 . . . ) and the rhythms are (0, 3, 6), (1, 3, 6), (1,4,6) and so forth, as in the beginning measures of the music. Only (0,3,6) is given in Franck Jedrzejewski’s complete list of deep rhythms on the facing page, because this list includes only basic deep rhythms beginning with zero. But since we are dealing with a circle of 8, we can rotate around the cycle and find seven other deep rhythms, all of which are interesting to my ears. An infinite number of rhythms may be constructed in this way, but as the circles get larger, the rhythms get longer, and tend to follow repeating sequences in a boring way, so I just added a few more sections that I particularly liked and then stopped. The lower staff is simply accompaniment and should be more felt than heard. I find it easiest and most satisfying to repeat each rhythm four times before going on to the next, and to keep a steady tempo of about 120 quarter notes per minute. Since each variation is an independent little piece, one may select and order them however one wishes. I recommend outdoor performances, where the music becomes camouflaged, always blending well with the ambient sounds.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79219563","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
Musicological, computational, and conceptual aspects of first-species counterpoint theory 第一物种对位理论的音乐学、计算和概念方面
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-02-23 DOI: 10.1080/17459737.2022.2136775
J. Arias-Valero, O. A. Agust'in-Aquino, E. Lluis-Puebla
{"title":"Musicological, computational, and conceptual aspects of first-species counterpoint theory","authors":"J. Arias-Valero, O. A. Agust'in-Aquino, E. Lluis-Puebla","doi":"10.1080/17459737.2022.2136775","DOIUrl":"https://doi.org/10.1080/17459737.2022.2136775","url":null,"abstract":"We re-create the essential results of a 1989 unpublished article by Mazzola and Muzzulini that contains the musicological aspects of a first-species counterpoint model. We include a summary of the mathematical counterpoint theory and several variations of the model that offer different perspectives on Mazzola's original principles.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79284806","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
A musical reading of a contemporary installation and back: mathematical investigations of patterns in Qwalala 当代装置的音乐阅读和回归:Qwalala模式的数学研究
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-02-01 DOI: 10.1080/17459737.2021.1871787
Maria Mannone
{"title":"A musical reading of a contemporary installation and back: mathematical investigations of patterns in Qwalala","authors":"Maria Mannone","doi":"10.1080/17459737.2021.1871787","DOIUrl":"https://doi.org/10.1080/17459737.2021.1871787","url":null,"abstract":"Mathematical music theory helps us investigate musical compositions in mathematical terms. Some hints can be extended towards the visual arts. Mathematical approaches can also help formalize a “translation” from the visual domain to the auditory one and vice versa. Thus, a visual artwork can be mathematically investigated, then translated into music. The final, refined musical rendition can be compared to the initial visual idea. Can an artistic idea be preserved through these changes of media? Can a non-trivial pattern be envisaged in an artwork, and then still be identified after the change of medium? Here, we consider a contemporary installation and an ensemble musical piece derived from it. We first mathematically investigate the installation, finding its patterns and structure, and then we compare them with structure and patterns of the musical composition. In particular, we apply two concepts of mathematical music theory, the Quantum GestART and the gestural similarity conjecture, to the analysis of Qwalala, realized for the Venice Biennale by Pae White, comparing it to its musical rendition in the homonymous piece for harp and ensemble composed by Federico Favali. Some sketches of generalizations follow, with the “Souvenir Theorem” and the “Art Conjecture.”","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85847250","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: 3
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