Journal of Mathematics and Music最新文献

{"title":"An integer linear programming model for tilings","authors":"Gennaro Auricchio, L. Ferrarini, Greta Lanzarotto","doi":"10.1080/17459737.2023.2180812","DOIUrl":"https://doi.org/10.1080/17459737.2023.2180812","url":null,"abstract":"In this paper, we propose an integer linear programming model whose solutions are the aperiodic rhythms tiling with a given rhythm A. We show how it can be used to define an iterative algorithm that, given a period n, finds all the rhythms which tile with a given rhythm A and also to efficiently check the necessity of the Coven-Meyerowitz condition (T2). To conclude, we run several experiments to validate the time efficiency of the model.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81134031","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":"José Manuel López López’s Chart for managing tempi","authors":"J. Besada","doi":"10.1080/17459737.2021.1927214","DOIUrl":"https://doi.org/10.1080/17459737.2021.1927214","url":null,"abstract":"In 2003, Spanish composer José Manuel López López (b. Madrid 1956) wrote his Estudio II sobre la modulación métrica for four percussionists, commissioned by the Portuguese ensemble Drumming. As the title of the percussion quartet reveals, Elliott Carter’s metric modulation was a key concept for López López during the compositional process. Nevertheless, his theoretical and aesthetic position up to this time was rather close to Karlheinz Stockhausen and to the French spectral composers. López López conceived a chart of tempi in order to reconcile the metric modulation with some ideas he borrowed from Stockhausen, in particular from his famous article “ . . . wie die Zeit vergeht . . . .” In the columns, López López calculated a series of metric modulations among basic notes – from a whole note to a 16th-note – and their dotted counterparts. Conversely, for each row, given a starting value, the cells were filled by iteratively multiplying this value by 12 √ 2, which is the frequency ratio of an equally tempered semitone. López López lastly rounded the obtained values to the nearest integer, giving rise in each row to a series of “chromatic tempi.” This chart puts in evidence a double analogy for understanding tempo relationships as tuning ones. On the one hand, the vertical rational proportions are equivalent to those of the partials of the harmonic series, which are concomitants of just intonation. On the other hand, the horizontal irrational proportions reflect those of the chromatic scale in the equal temperament. Notice that, although not present within the table, López López took also into account subdivisions based on tuplets for his metric modulations, as evident in several calculations below the charted values. This device is a significant milestone in López López’s creative development. Estudio II sobre la modulación métrica is an unpitched score, but this temporal conception was also present in the next piece he composed: Entrance-Exit. For this kind of pianistic tombeau for his dear friend Fausto Romitelli, López López paired tempi with spectral fundamentals by means of these methods. Next, López López implemented and refined his table via Excel, a platform allowing him to remap values as fast as possible. This choice also led him to choose new frequency ratios beyond 12 √ 2 – and therefore related to further tuning systems – for analogous purposes.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83960182","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":"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":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":"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}

{"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":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":"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}

{"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":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":"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}

{"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":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":"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}