Journal of Mathematics and Music最新文献_第4页

Two letters by Jack Douthett on uniform triadic transformations Jack Douthett关于一致三元变换的两封信

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2022-09-02 DOI: 10.1080/17459737.2022.2157062

Julian L. Hook

{"title":"Two letters by Jack Douthett on uniform triadic transformations","authors":"Julian L. Hook","doi":"10.1080/17459737.2022.2157062","DOIUrl":"https://doi.org/10.1080/17459737.2022.2157062","url":null,"abstract":"Two letters that Jack wrote soon after I introduced uniform triadic transformations in 1999 exemplify the energy with which he threw himself into work on subjects that stirred his interest. As I note in a tribute elsewhere in this issue (Krantz 2022), I first met Jack at a meeting of the Society for Music Theory in the fall of 1999 – a conference at which I also presented my work on UTTs (later published in Hook 2002). By April of 2000, Jack had distributed two substantial letters with his evolving thoughts on the subject. The wreath-product structure of the UTT group, the simply transitive subgroups of that group, and “skew groups” (which combine mode-preserving transformations of one kind with mode-reversing transformations of another kind) were subjects of special fascination to him from the start, as they remained a few years later when we produced our joint paper on applications of UTTs to serialism (Hook and Douthett 2008). The second letter is particularly notable for a few ideas that have not been pursued elsewhere. Here Jack relates UTTs to the seventh-chord transformations that he had studied with Peter Steinbach (Douthett and Steinbach 1998), and also to Jonathan Kochavi’s work (Kochavi 1998) on contextual inversions (presenting what Jack calls “Kochavi diagrams” for some groups of UTTs). He also refines my embryonic suggestion for generalizing UTTs to situations where there are more than two classes of objects (such as inversionally related chord qualities).","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88047746","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

Colleague, collaborator, friend Jack Douthett (1942–2021) 同事、合作者、朋友杰克·杜塞特(1942-2021)

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2022-09-02 DOI: 10.1080/17459737.2022.2140214

R. Krantz

引用次数: 2

Explicit presentations of topological categories of gestures 手势拓扑类别的显式呈现

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2022-08-31 DOI: 10.1080/17459737.2022.2111612

J. Arias-Valero, E. Lluis-Puebla

{"title":"Explicit presentations of topological categories of gestures","authors":"J. Arias-Valero, E. Lluis-Puebla","doi":"10.1080/17459737.2022.2111612","DOIUrl":"https://doi.org/10.1080/17459737.2022.2111612","url":null,"abstract":"Thanks to Mazzola's notion of gestures on topological categories we can appreciate how the notion of gesture transcends its manifestation as the movement of the body's limbs and takes a more abstract form that blends diagrammatic (discrete gesturality) and bodily aspects (continuous gesturality). These two aspects are strongly related to two main branches of mathematical music theory, namely, a discrete branch and a continuous branch. The discrete branch corresponds to the diagrams of transformational theory, that is, to networks in musical analysis. The continuous branch corresponds to the movement of the musical performer's body. Informally, a gesture on a topological category is a diagram of continuous paths of morphisms in the category. This definition amounts to that of topological category of gestures, whose structure we study in this article. Specifically, we study the presentation of topological categories of gestures as suitable categories of topological functors and as suitable categories of sequences, and the explicit presentation of morphisms of a typical topological category of gestures. In particular, we present an exhaustive study, not included in previous publications, of the topological category of continuous paths of an arbitrary digraph. This article can be regarded as a continuation of a previous publication, in a previous issue of this journal, on the presentation of spaces of gestures as function spaces. We include an application of the theory to the variations in Mozart's Piano Sonata K. 331. We provide an Online Supplement, in which we include some technical passages.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80091538","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

The scale of the Old Hispanic chant 古西班牙圣歌的音阶

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2022-08-11 DOI: 10.1080/17459737.2022.2105411

Elsa De Luca

引用次数: 0

In Memoriam 为纪念

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2022-07-15 DOI: 10.1080/17459737.2022.2084569

Darrell Conklin

引用次数: 0

The inconstancy of music 音乐的反复无常

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2022-05-16 DOI: 10.1080/17459737.2022.2068687

Florence Levé, G. Micchi, J. Allouche

{"title":"The inconstancy of music","authors":"Florence Levé, G. Micchi, J. Allouche","doi":"10.1080/17459737.2022.2068687","DOIUrl":"https://doi.org/10.1080/17459737.2022.2068687","url":null,"abstract":"A melody is often described as a line of music that evolves through time and, therefore, it is possible to draw its 2D pitch-time representation as a series of points implicitly defining a curve. We introduce to computational musicology a descriptor of this music curve: the inconstancy, a function that gives information on the curve's smoothness as well as some of its topological properties. A mathematical analysis of the inconstancy of music is provided, followed by a lengthy application of inconstancy to musicological tasks. We compare the inconstancy of melodic lines with that of typical accompaniment patterns such as the Alberti bass; this analysis, together with the case study of W.A. Mozart's Variations on Ah! vous dirai-je, maman, suggests a significant difference in the value of the inconstancy of a music line depending on its function. The inconstancy seems to be correlated also with the compositional style: the analysis on almost 10,000 musical themes of the common practice repertoire shows that Baroque music has higher inconstancy. Finally, we also define a windowed version of the inconstancy for studying longer scores and show the insights one can gain into, for example, structural analysis and cadence detection.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83845079","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

Rhythm, mathematics, and Godfried Toussaint 节奏，数学，还有哥德弗里德·杜桑

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2022-05-04 DOI: 10.1080/17459737.2022.2088875

Jason Yust, C. White, Leigh VanHandel

引用次数: 0

Ostinatos in Black-Atlantic traditions: generic-specific similarity and proximity 大西洋黑人传统中的固定音:一般-特定的相似性和接近性

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2022-05-04 DOI: 10.1080/17459737.2022.2071491

J. Rahn

{"title":"Ostinatos in Black-Atlantic traditions: generic-specific similarity and proximity","authors":"J. Rahn","doi":"10.1080/17459737.2022.2071491","DOIUrl":"https://doi.org/10.1080/17459737.2022.2071491","url":null,"abstract":"Ostinatos of sub-Saharan Africa, South America, and the Caribbean are continually repeated rhythms also known as “timelines.” Taking as a starting point the ostinato termed the “Standard Pattern,” generic and specific features of Black-Atlantic ostinatos are analyzed: in European-derived theory, these features correspond to the quantity and quality of musical intervals. Like the standard pattern, other ostinatos that have been employed in several Black-Atlantic traditions and comprise a rhythmic structure that corresponds to the structure of hyperdiatonic scales in contemporary European-derived pitch theory; other widespread ostinatos considered have a complementary, hyperpentatonic structure. Interpreted in terms of Gestalt grouping principles, both of these kinds of ostinatos maximize similarity and proximity. Other ostinatos of these traditions can be construed as variants of hyperdiatonic or hyperpentatonic ostinatos. Differences of similarity and proximity that these variants manifest are analyzed in terms of adjacent swaps, fusions and fissions, and moduli that encompass two or more ostinatos’ least common multiples. In turn, similarity and proximity measures for rhythmic ostinatos are shown to parsimoniously clarify aspects of pitch relations, including the general notion of evenness, within 1- dimensional frameworks for pitch and time.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79165638","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

A comparative analysis of melodic rhythm in two corpora of American popular music 两个美国流行音乐语料库中旋律节奏的比较分析

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2022-05-04 DOI: 10.1080/17459737.2022.2075946

C. White, Joe Pater, Mara Breen

{"title":"A comparative analysis of melodic rhythm in two corpora of American popular music","authors":"C. White, Joe Pater, Mara Breen","doi":"10.1080/17459737.2022.2075946","DOIUrl":"https://doi.org/10.1080/17459737.2022.2075946","url":null,"abstract":"This paper compares two corpora of melodies drawn from premillennial and postmillennial American popular music, and identifies several notable differences in their use of rhythm. The premillennial corpus contains melodies written between 1957 and 1997 [deClercq and Temperley (2011. “A Corpus Analysis of Rock Harmony.” Popular Music 30 (1): 47–70)], while the postmillennial corpus (compiled for this study) consists of songs popular between 2015 and 2019. For both corpora, we analysed (1) the distribution of note onsets within measures; (2) the distribution of four-note rhythmic cells, (3) the speed of melodic delivery, and (4) the tempo of the tactus. Our analyses indicated that the postmillennial melodies are delivered more quickly, are distributed more evenly throughout their measures, repeat rhythmic cells more frequently, and are annotated at slower tempos. Even when the tactus tempos were standardized into an allowable window of 70–140 BPM, this effect, though smaller, remained. We then use our techniques to observe the properties of three representative postmillennial tracks, finding that salient information can be located in both standardized and non-standardized tactus data, and that tempo-variant differences between corpora are closely connected to musical genre, with music designated as “pop” being more similar over both genres, and postmillennial rap and hip-hop introducing the most uniqueness.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84811855","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 framework for topological music analysis (TMA) 拓扑音乐分析(TMA)框架

IF 1.1 2区数学

Journal of Mathematics and Music Pub Date : 2022-04-20 DOI: 10.1080/17459737.2023.2219994

Alberto Alcal'a-Alvarez, P. Padilla-Longoria

引用次数: 2