Pub Date : 2022-04-13DOI: 10.1080/17459737.2022.2058636
Daniele Ghisi, Carmine-Emanuele Cella
Creating a formal model for timbre is one of the most compelling open questions in music research. In contrast to more traditional perceptually-oriented approaches, often aimed at sound analysis, we introduce a three-dimensional geometric model of timbre, specifically designed for sound synthesis. The proposed model relies on the properties of space-filling curves for multidimensional scaling, and represents via three parameters, any static combination of sinusoidal partials with an additional noisiness component. We detail the construction of the model and its properties and discuss future implications for music research.
{"title":"A three-dimensional timbre model via Peano curves","authors":"Daniele Ghisi, Carmine-Emanuele Cella","doi":"10.1080/17459737.2022.2058636","DOIUrl":"https://doi.org/10.1080/17459737.2022.2058636","url":null,"abstract":"Creating a formal model for timbre is one of the most compelling open questions in music research. In contrast to more traditional perceptually-oriented approaches, often aimed at sound analysis, we introduce a three-dimensional geometric model of timbre, specifically designed for sound synthesis. The proposed model relies on the properties of space-filling curves for multidimensional scaling, and represents via three parameters, any static combination of sinusoidal partials with an additional noisiness component. We detail the construction of the model and its properties and discuss future implications for music research.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90620716","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}
Pub Date : 2022-04-07DOI: 10.1080/17459737.2022.2042410
Jason Yust
Recent research has demonstrated a number of applications of the discrete Fourier transform to cyclic rhythms, addressing amongst other issues questions about conceptualizations of metre. One can apply a similar operation, the Hadamard transform, when the rhythmic cycle is a power of two. This paper explores some analytical applications of the Hadamard transform to repertoires where pure-duple metrical settings are the norm, such as American ragtime and Balinese gamelan. I compare it to the Fourier transform and highlight special features of the Hadamard transform of particular theoretical value, such as its sorting of rhythmic information into metrical levels, which leads to methods of classifying and quantifying syncopation.
{"title":"Hadamard transforms of pure-duple rhythms","authors":"Jason Yust","doi":"10.1080/17459737.2022.2042410","DOIUrl":"https://doi.org/10.1080/17459737.2022.2042410","url":null,"abstract":"Recent research has demonstrated a number of applications of the discrete Fourier transform to cyclic rhythms, addressing amongst other issues questions about conceptualizations of metre. One can apply a similar operation, the Hadamard transform, when the rhythmic cycle is a power of two. This paper explores some analytical applications of the Hadamard transform to repertoires where pure-duple metrical settings are the norm, such as American ragtime and Balinese gamelan. I compare it to the Fourier transform and highlight special features of the Hadamard transform of particular theoretical value, such as its sorting of rhythmic information into metrical levels, which leads to methods of classifying and quantifying syncopation.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90483127","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}
Pub Date : 2022-04-05DOI: 10.1080/17459737.2022.2049383
B. Fugiel
I propose a quantum-like approach to the description of melody perception where classic intervals that constitute a melody are replaced by acoustical qubits, i.e. two-level acoustic systems, using Shepard tones for this purpose. Each of such qubits is considered to be a superposition of two intervals, ascending and descending, that form an octave when put together. Any melody perception can thus be treated analogously to a sequence of quantum measurements. Because of an acoustical collapse, analogous to the wave function reduction in quantum mechanics, just a single interval, ascending or descending, can be heard each time. Different melodies generated by the same sequence of acoustical qubits can be then perceived.
{"title":"Quantum-like melody perception","authors":"B. Fugiel","doi":"10.1080/17459737.2022.2049383","DOIUrl":"https://doi.org/10.1080/17459737.2022.2049383","url":null,"abstract":"I propose a quantum-like approach to the description of melody perception where classic intervals that constitute a melody are replaced by acoustical qubits, i.e. two-level acoustic systems, using Shepard tones for this purpose. Each of such qubits is considered to be a superposition of two intervals, ascending and descending, that form an octave when put together. Any melody perception can thus be treated analogously to a sequence of quantum measurements. Because of an acoustical collapse, analogous to the wave function reduction in quantum mechanics, just a single interval, ascending or descending, can be heard each time. Different melodies generated by the same sequence of acoustical qubits can be then perceived.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85787825","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}
Pub Date : 2022-03-17DOI: 10.1080/17459737.2022.2044927
Fabian C. Moss, M. Neuwirth, M. Rohrmeier
In this study, we determine the fundamental role of the line of fifths for the organization of tonal material by applying dimensionality reduction to a large historical corpus of pitch-class counts (ca. 1360–1940). We observe a historically growing trend in the exploitation of the fifths range, i.e. the size of segments that pitch-class distributions cover on the line of fifths. Moreover, we introduce the novel concept of pitch-class (co-)evolution, which traces the changing co-occurrence of pitch classes over time and likewise reaffirms the centrality of this linear tonal space from a historical angle, allowing us also to distinguish between historical periods in terms of the usage of pitch classes.
{"title":"The line of fifths and the co-evolution of tonal pitch-classes","authors":"Fabian C. Moss, M. Neuwirth, M. Rohrmeier","doi":"10.1080/17459737.2022.2044927","DOIUrl":"https://doi.org/10.1080/17459737.2022.2044927","url":null,"abstract":"In this study, we determine the fundamental role of the line of fifths for the organization of tonal material by applying dimensionality reduction to a large historical corpus of pitch-class counts (ca. 1360–1940). We observe a historically growing trend in the exploitation of the fifths range, i.e. the size of segments that pitch-class distributions cover on the line of fifths. Moreover, we introduce the novel concept of pitch-class (co-)evolution, which traces the changing co-occurrence of pitch classes over time and likewise reaffirms the centrality of this linear tonal space from a historical angle, allowing us also to distinguish between historical periods in terms of the usage of pitch classes.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80270596","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}
Pub Date : 2022-02-19DOI: 10.1080/17459737.2022.2025625
Francisco Gómez-Martín
This is both a personal and academic review of Godfried Toussaint's The Geometry of Musical Rhythm.
这是对哥德弗里德·杜桑的《音乐节奏的几何》的个人和学术评论。
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Pub Date : 2022-01-10DOI: 10.1080/17459737.2021.2008035
Dmitri Tymoczko
Musicians often operate with a hierarchy of scale-like collections, each embedded within the next, and with transposition and inversion available at every level. A particularly common technique is to counteract a transformation at one level with an analogous transformation in the intrinsic scale consisting of a chord’s own notes.
{"title":"Hierarchical set theory","authors":"Dmitri Tymoczko","doi":"10.1080/17459737.2021.2008035","DOIUrl":"https://doi.org/10.1080/17459737.2021.2008035","url":null,"abstract":"Musicians often operate with a hierarchy of scale-like collections, each embedded within the next, and with transposition and inversion available at every level. A particularly common technique is to counteract a transformation at one level with an analogous transformation in the intrinsic scale consisting of a chord’s own notes.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79226101","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}
Pub Date : 2021-12-09DOI: 10.1080/17459737.2021.2002446
Olof Misgeld, A. Holzapfel, Petter Kallioinen, Sven Ahlbäck
Some triple-beat forms in Scandinavian Folk Music are characterized by non-isochronous beat durations: asymmetric beats. Theorists of folk music have suggested that the variability of rhythmic figures and asymmetric metre are fundamental to these forms. The aim of this study is to obtain a deeper understanding of the relationship between melodic structure and asymmetric metre by analysing semi-automatically annotated performances. Our study considers archive and contemporary recordings of fiddlers' different versions of the same musical pieces: polska tunes in a local Swedish tradition. Results show that asymmetric beat patterns are consistent between performances and that they correspond with structural features of rhythmic figures, such as the note density within beats. The present study goes beyond previous work by exploring the use of a state-of-the-art automatic music notation tool in a corpus study of Swedish traditional music, and by employing statistical methods for a comparative analysis of performances across different players.
{"title":"The melodic beat: exploring asymmetry in polska performance","authors":"Olof Misgeld, A. Holzapfel, Petter Kallioinen, Sven Ahlbäck","doi":"10.1080/17459737.2021.2002446","DOIUrl":"https://doi.org/10.1080/17459737.2021.2002446","url":null,"abstract":"Some triple-beat forms in Scandinavian Folk Music are characterized by non-isochronous beat durations: asymmetric beats. Theorists of folk music have suggested that the variability of rhythmic figures and asymmetric metre are fundamental to these forms. The aim of this study is to obtain a deeper understanding of the relationship between melodic structure and asymmetric metre by analysing semi-automatically annotated performances. Our study considers archive and contemporary recordings of fiddlers' different versions of the same musical pieces: polska tunes in a local Swedish tradition. Results show that asymmetric beat patterns are consistent between performances and that they correspond with structural features of rhythmic figures, such as the note density within beats. The present study goes beyond previous work by exploring the use of a state-of-the-art automatic music notation tool in a corpus study of Swedish traditional music, and by employing statistical methods for a comparative analysis of performances across different players.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88397763","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}
Pub Date : 2021-12-07DOI: 10.1080/17459737.2021.2001699
Daniele Ghisi
“Barberpole” tempo illusions are a family of auditory illusions based on the synchronization of faded rhythmic streams playing at different rates, often manufacturing experiences of seemingly eternal acceleration or deceleration. The forefather of all such illusions, based on layers whose rates are powers of two apart (“octaves”), was studied by Jean-Claude Risset in the late seventies and is now known as Risset rhythm. This article provides a mathematical framework for barberpole tempo illusions, generalizing Risset rhythms for arbitrary numbers of subdivisions, non-integer proportions, arbitrary rate modulation, and increasingly accelerating tempi. Furthermore, this article describes a new illusion of eternal rallentando/accelerando based on the full harmonic spectrum of rates. This construction shows that Risset rhythms are related to barberpole variable-rate polyrhythms. A notable application of the study of divisional structures that barberpole illusions underpin is the construction of bistable auditory figures (accelerating or decelerating depending on the stream being focused).
{"title":"Barberpole tempo illusions","authors":"Daniele Ghisi","doi":"10.1080/17459737.2021.2001699","DOIUrl":"https://doi.org/10.1080/17459737.2021.2001699","url":null,"abstract":"“Barberpole” tempo illusions are a family of auditory illusions based on the synchronization of faded rhythmic streams playing at different rates, often manufacturing experiences of seemingly eternal acceleration or deceleration. The forefather of all such illusions, based on layers whose rates are powers of two apart (“octaves”), was studied by Jean-Claude Risset in the late seventies and is now known as Risset rhythm. This article provides a mathematical framework for barberpole tempo illusions, generalizing Risset rhythms for arbitrary numbers of subdivisions, non-integer proportions, arbitrary rate modulation, and increasingly accelerating tempi. Furthermore, this article describes a new illusion of eternal rallentando/accelerando based on the full harmonic spectrum of rates. This construction shows that Risset rhythms are related to barberpole variable-rate polyrhythms. A notable application of the study of divisional structures that barberpole illusions underpin is the construction of bistable auditory figures (accelerating or decelerating depending on the stream being focused).","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87187677","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}
Pub Date : 2021-12-06DOI: 10.1080/17459737.2021.2002956
Tiasa Mondol, Daniel G. Brown
We apply Context-free Grammars (CFG) to measure the structural information content of a symbolic music string. CFGs are appropriate to this domain because they highlight hierarchical patterns, and their dictionary of rules can be used for compression. We adapt this approach to estimate the conditional Kolmogorov complexity of a string with a concise CFG of another string. Thus, a related string may be compressed with the production rules for the first string. We then define an information distance between two symbolic music strings, and show that this measure can separate genres, composers and musical styles. Next, we adapt our approach to a model-selection problem, expressing the model as a CFG with restricted size, generated from a set of representative strings. We show that a well-generated CFG for a composer identifies characteristic patterns that can significantly compress other pieces from the same composer, while not being useful on pieces from different composers. We identify further opportunities of this approach, including using CFGs for generating new music in the style of a composer.
{"title":"Grammar-based compression and its use in symbolic music analysis","authors":"Tiasa Mondol, Daniel G. Brown","doi":"10.1080/17459737.2021.2002956","DOIUrl":"https://doi.org/10.1080/17459737.2021.2002956","url":null,"abstract":"We apply Context-free Grammars (CFG) to measure the structural information content of a symbolic music string. CFGs are appropriate to this domain because they highlight hierarchical patterns, and their dictionary of rules can be used for compression. We adapt this approach to estimate the conditional Kolmogorov complexity of a string with a concise CFG of another string. Thus, a related string may be compressed with the production rules for the first string. We then define an information distance between two symbolic music strings, and show that this measure can separate genres, composers and musical styles. Next, we adapt our approach to a model-selection problem, expressing the model as a CFG with restricted size, generated from a set of representative strings. We show that a well-generated CFG for a composer identifies characteristic patterns that can significantly compress other pieces from the same composer, while not being useful on pieces from different composers. We identify further opportunities of this approach, including using CFGs for generating new music in the style of a composer.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83815427","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}
Pub Date : 2021-09-18DOI: 10.1080/17459737.2021.1969599
M. Buongiorno Nardelli
I introduce the concept of dynamical score networks for the representation and analysis of tonal compositions: a score is interpreted as a dynamical network where every chord is a node and each progression links successive chords. This network can be viewed as a time series of a non-stationary signal, and as such, it can be partitioned for the automatic identification of tonal regions using time series analysis and change point detection without relying on comparisons with pre-determined reference sets or extensive corpora. I demonstrate that the essential features of tonal harmony, centricity, referentiality, directedness and hierarchy, emerge naturally from the network topology and its scale-free properties. Finally, solving for the minimal length path through a route optimization algorithm on these graphs provides an abstraction of harmonic sequences that can be generalized for the conception of generative models of tonal compositional design.
{"title":"Tonal harmony and the topology of dynamical score networks","authors":"M. Buongiorno Nardelli","doi":"10.1080/17459737.2021.1969599","DOIUrl":"https://doi.org/10.1080/17459737.2021.1969599","url":null,"abstract":"I introduce the concept of dynamical score networks for the representation and analysis of tonal compositions: a score is interpreted as a dynamical network where every chord is a node and each progression links successive chords. This network can be viewed as a time series of a non-stationary signal, and as such, it can be partitioned for the automatic identification of tonal regions using time series analysis and change point detection without relying on comparisons with pre-determined reference sets or extensive corpora. I demonstrate that the essential features of tonal harmony, centricity, referentiality, directedness and hierarchy, emerge naturally from the network topology and its scale-free properties. Finally, solving for the minimal length path through a route optimization algorithm on these graphs provides an abstraction of harmonic sequences that can be generalized for the conception of generative models of tonal compositional design.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87072573","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}
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