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Journal of Mathematics and Music最新文献

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Minimally non-diatonic pc-sets 最低限度的非全音阶pc机
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-06-17 DOI: 10.1080/17459737.2021.1933631
Jay Schweig, Aurian Kutner
{"title":"Minimally non-diatonic pc-sets","authors":"Jay Schweig, Aurian Kutner","doi":"10.1080/17459737.2021.1933631","DOIUrl":"https://doi.org/10.1080/17459737.2021.1933631","url":null,"abstract":"We discuss and enumerate pc-sets that are both not contained in any diatonic collection and are minimal with respect to this property, and we generalize this idea to other collections. We also consider related simplicial complexes and examine how some of their geometric properties reflect qualities of the associated pc-sets.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"61 1","pages":"38 - 45"},"PeriodicalIF":1.1,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80480256","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
Iterative method of construction for smooth rhythms 流畅节奏的迭代构造方法
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-06-06 DOI: 10.1080/17459737.2021.1924303
F. Hazama
{"title":"Iterative method of construction for smooth rhythms","authors":"F. Hazama","doi":"10.1080/17459737.2021.1924303","DOIUrl":"https://doi.org/10.1080/17459737.2021.1924303","url":null,"abstract":"The present article introduces the notion of smoothness of rhythm and proposes a unified method that transforms an arbitrary rhythm into a smooth one. The method employs a self-map Rav, discrete average map, on the space of rhythms of arbitrary length with a fixed number of onsets. It is shown that, for any rhythm in the space, the iterations become eventually periodic, and that the final cycle consists only of smooth rhythms. The discrete average map leads naturally to a finite directed graph, which visualizes the realm of smooth rhythms in the whole world of rhythms. This article has an Online Supplement, in which we give detailed proof of the main result.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"21 1","pages":"216 - 235"},"PeriodicalIF":1.1,"publicationDate":"2021-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74584225","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
A model for tonal progressions of seventh chords 七和弦的调性进展模型
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-06-02 DOI: 10.1080/17459737.2021.1928311
Luka Marohnić
{"title":"A model for tonal progressions of seventh chords","authors":"Luka Marohnić","doi":"10.1080/17459737.2021.1928311","DOIUrl":"https://doi.org/10.1080/17459737.2021.1928311","url":null,"abstract":"In this paper, we propose a model for idealized diatonic and chromatic voice leadings between seventh chords and study its computational aspects. The model provides a mathematical formalization of the concept of tonal seventh chord realizations including augmented sixth chords. Certain contrapuntal aspects, such as preparation and resolution of certain dissonant intervals, are taken into account. Possible applications of the model are discussed using a graph-theoretic approach. In particular, we present an algorithm for generating concrete voicings from sequences of seventh-chord symbols.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"47 1","pages":"78 - 99"},"PeriodicalIF":1.1,"publicationDate":"2021-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90574724","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 two-dimensional representation of musical chords using the simplicity of frequency and period ratios as coordinates 用简单的频率和周期比率作为坐标的二维和弦表示
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-06-01 DOI: 10.1080/17459737.2021.1924304
I. Nemoto, M. Kawakatsu
{"title":"A two-dimensional representation of musical chords using the simplicity of frequency and period ratios as coordinates","authors":"I. Nemoto, M. Kawakatsu","doi":"10.1080/17459737.2021.1924304","DOIUrl":"https://doi.org/10.1080/17459737.2021.1924304","url":null,"abstract":"Musical chords play an essential role, especially in Western music, and the corresponding consonance–dissonance contrasts and emotional continua are still the targets of investigation in psychoacoustics and neurophysiology. In the present study, we define the simplicity of frequency ratios and simplicity of period ratios for the constituents of a chord and propose that those measures should be used as the two coordinate axes in the plane for plotting chords. In this plane, the major and minor chords are reflections of each other with respect to the diagonal . The other chord pair in the same relationship is the major–minor seventh (dominant seventh) and the half-diminished seventh chords. The other triads and seventh chords do not make such pairs of different categories of chords. It was also found that at least for triads, the sum and the difference seem to correspond to subjective consonance and the melancholic/sad emotional ratings, respectively. Implications of these findings are discussed. The proposed simple presentation may help interpret and model psychoacoustic and neurophysiological results on musical chords.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"2 1","pages":"65 - 77"},"PeriodicalIF":1.1,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83150055","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
Some observations on autocorrelated patterns within computational meter identification 计算仪表识别中自相关模式的一些观察
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-05-04 DOI: 10.1080/17459737.2021.1923843
C. White
{"title":"Some observations on autocorrelated patterns within computational meter identification","authors":"C. White","doi":"10.1080/17459737.2021.1923843","DOIUrl":"https://doi.org/10.1080/17459737.2021.1923843","url":null,"abstract":"The computational approach of autocorrelation relies on recurrent patterns within a musical signal to identify and analyze the meter of musical passages. This paper suggests that the autocorrelation process can act as a computational proxy for the act of period extraction, a crucial aspect of the cognition of musical meter, by identifying periodicities with which similar events tend to occur within a musical signal. Three analytical vignettes highlight three aspects of the identified patterns: (1) that the similarities between manifestations of the same patterns are often inexact, (2) that these patterns have ambiguous boundaries, and (3) that many more patterns exist on the musical surface than contribute to the passage's notated/felt meter, each of which overlaps with observations from music theory and behavioral research. An Online Supplement at chriswmwhite.com/autocorrelation contains accompanying data.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"13 1","pages":"181 - 193"},"PeriodicalIF":1.1,"publicationDate":"2021-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88444178","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
Triadic patterns across classical and popular music corpora: stylistic conventions, or characteristic idioms? 古典和流行音乐语料库中的三合一模式:风格惯例，还是特征习语?
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-05-04 DOI: 10.1080/17459737.2021.1925762
David R. W. Sears, D. Forrest
{"title":"Triadic patterns across classical and popular music corpora: stylistic conventions, or characteristic idioms?","authors":"David R. W. Sears, D. Forrest","doi":"10.1080/17459737.2021.1925762","DOIUrl":"https://doi.org/10.1080/17459737.2021.1925762","url":null,"abstract":"Many musical traditions – from Western art, to popular and commercial – organize pitch phenomena around a referential pitch class (or tonic) and feature triads and seventh chords. As a result, triadic progressions associated with one tradition sometimes resurface in others. How, then, are we to distinguish between the conventional harmonic patterns that span several time periods, and the characteristic idioms that delimit a single period? This essay presents a comparative study of triadic progressions in four data sets comprised of expert harmonic annotations: Annotated Beethoven Corpus (ABC), Theme and Variation Encodings with Roman Numerals (TAVERN), Rolling Stone-200 (RS-200), and McGill Billboard (Billboard). Using methods for counting, filtering, and ranking multichord expressions, we reveal conventional and characteristic progressions and examine broad trends over time. We also include an accompanying standalone application that allows users to adjust various stages of the model pipeline and export the data for further exploration and analysis.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"91 1","pages":"140 - 153"},"PeriodicalIF":1.1,"publicationDate":"2021-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85665951","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: 6
Exploring annotations for musical pattern discovery gathered with digital annotation tools 探索使用数字注释工具收集的音乐模式发现注释
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-05-04 DOI: 10.1080/17459737.2021.1943026
Darian Tomašević, S. Wells, I. Ren, A. Volk, Matevž Pesek
{"title":"Exploring annotations for musical pattern discovery gathered with digital annotation tools","authors":"Darian Tomašević, S. Wells, I. Ren, A. Volk, Matevž Pesek","doi":"10.1080/17459737.2021.1943026","DOIUrl":"https://doi.org/10.1080/17459737.2021.1943026","url":null,"abstract":"The study of inter-annotator agreement in musical pattern annotations has gained increased attention over the past few years. While expert annotations are often taken as the reference for evaluating pattern discovery algorithms, relying on just one reference is not usually sufficient to capture the complex musical relations between patterns. In this paper, we address the potential of digital annotation tools to enable large-scale annotations of musical patterns, by comparing datasets gathered with two recently developed digital tools. We investigate the influence of the tools and different annotator backgrounds on the annotation process by performing inter-annotator agreement analysis and feature-based analysis on the annotated patterns. We discuss implications for further adaptation of annotation tools, and the potential for deriving reference data from such rich annotation datasets for the evaluation of automatic pattern discovery algorithms in the future.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"31 1","pages":"194 - 207"},"PeriodicalIF":1.1,"publicationDate":"2021-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76047054","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: 14
A computational exploration of melodic patterns in Arab-Andalusian music 阿拉伯-安达卢西亚音乐旋律模式的计算探索
IF 1.1 2区 数学
Journal of Mathematics and Music Pub Date : 2021-05-04 DOI: 10.1080/17459737.2021.1917010
Thomas Nuttall, M. Casado, Andrés Ferraro, D. Conklin, Rafael Caro Repetto
{"title":"A computational exploration of melodic patterns in Arab-Andalusian music","authors":"Thomas Nuttall, M. Casado, Andrés Ferraro, D. Conklin, Rafael Caro Repetto","doi":"10.1080/17459737.2021.1917010","DOIUrl":"https://doi.org/10.1080/17459737.2021.1917010","url":null,"abstract":"Here we present a computational approach to identifying melodic patterns in a dataset of 145 MusicXML scores with the aim of contributing to centonization theory in the Moroccan tradition of Arab-Andalusian Music – a theory in development by expert performer and researcher of this tradition, Amin Chaachoo. Central to his work is the definition of a set of characteristic patterns, or centos, for each ṭab‘, or melodic mode. We apply three methods: TF-IDF, Maximally General Distinctive Patterns (MGDP) and the Structure Induction Algorithm (SIA) to identify characteristic patterns at the level of ṭab‘. A substantial number of the centos proposed by Chaachoo are identified and new melodic patterns are retrieved. A discussion with Chaachoo about the obtained results promoted the elicitation of other categories of recurrent patterns in the tradition different from the centos, contributing to a deeper musicological knowledge of the tradition.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"31 1","pages":"168 - 180"},"PeriodicalIF":1.1,"publicationDate":"2021-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90889934","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
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":"7 1","pages":"125 - 139"},"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":"33 1","pages":"95 - 98"},"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
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