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Mathematics
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Mathematics and Computation in Music
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Mathematics and Computation in Music

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (15 February 2024) | Viewed by 16835

Special Issue Editor

Dr. Luca Andrea Ludovico

E-Mail Website
Guest Editor
Laboratorio di Informatica Musicale (LIM), Dipartimento di Informatica, Università degli Studi di Milano, 20122 Milan, Italy
Interests: sound and music computing; mathematical formalisms for music representation and computational musicology

Special Issue Information

Dear Colleagues,

The relationship between music and mathematics has been investigated since the dawn of western culture, starting from the thought of the Pythagorean philosophers, deeply influencing the medieval, baroque, and renaissance contrapuntal processes, through the serial music of the twentieth century. In more recent times, the development of mathematical thinking and the advent of computational approaches have profoundly changed the way music is written, analyzed, and performed.

Through this Special Issue, we invite our colleagues to present the most advanced research results and cutting-edge technologies dealing with mathematics and computation in music. Both theoretical and experimental works describing mathematical ideas, methods, techniques, and results are welcome.

The fields of interest include (but are not limited to) mathematical music theory, mathematical approaches to understanding musical objects, computer-based methodologies for composition and score analysis, models for music cognition, and formalisms for the representation of music information, probability, and statistics in musical analysis and composition.

Dr. Luca Andrea Ludovico
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • music
  • digital technologies
  • computation
  • mathematics

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Published Papers (5 papers)

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Research

12 pages, 3942 KiB  
Article
Music through Curve Insights
by Shai Gul
Mathematics 2023, 11(20), 4398; https://doi.org/10.3390/math11204398 - 23 Oct 2023
Viewed by 1221
Abstract
This manuscript endeavors to establish a framework for the mapping of music onto a three-dimensional structure. Our objective is to transform the guitar choruses of Beatles songs into curves, with each chorus corresponding to its respective curve. We aim to investigate and characterize [...] Read more.
This manuscript endeavors to establish a framework for the mapping of music onto a three-dimensional structure. Our objective is to transform the guitar choruses of Beatles songs into curves, with each chorus corresponding to its respective curve. We aim to investigate and characterize the intricacy of each song by employing mathematical techniques derived from differential geometry, specifically focusing on the total curvature of the chorus curve. Given that a single song may possess varying chord progressions in different verses, the performer can determine the geometric representation they aim to convey through the number of loops and the direction of the curve. The overarching objective of our study is to enable viewers to identify specific songs or motives by visually examining an object and exploring its geometric properties. Furthermore, we posit that these ideas can provide composers with a fresh perspective on their own musical compositions while also granting non-professional audiences a glimpse into the intricacies involved in the process of composing. Full article
(This article belongs to the Special Issue Mathematics and Computation in Music)
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34 pages, 8058 KiB  
Article
Geometry of Music Perception
by Benjamin Himpel
Mathematics 2022, 10(24), 4793; https://doi.org/10.3390/math10244793 - 16 Dec 2022
Cited by 3 | Viewed by 3479
Abstract
Prevalent neuroscientific theories are combined with acoustic observations from various studies to create a consistent geometric model for music perception in order to rationalize, explain and predict psycho-acoustic phenomena. The space of all chords is shown to be a Whitney stratified space. Each [...] Read more.
Prevalent neuroscientific theories are combined with acoustic observations from various studies to create a consistent geometric model for music perception in order to rationalize, explain and predict psycho-acoustic phenomena. The space of all chords is shown to be a Whitney stratified space. Each stratum is a Riemannian manifold which naturally yields a geodesic distance across strata. The resulting metric is compatible with voice-leading satisfying the triangle inequality. The geometric model allows for rigorous studies of psychoacoustic quantities such as roughness and harmonicity as height functions. In order to show how to use the geometric framework in psychoacoustic studies, concepts for the perception of chord resolutions are introduced and analyzed. Full article
(This article belongs to the Special Issue Mathematics and Computation in Music)
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19 pages, 6545 KiB  
Article
Machine Learning for Music Genre Classification Using Visual Mel Spectrum
by Yu-Huei Cheng and Che-Nan Kuo
Mathematics 2022, 10(23), 4427; https://doi.org/10.3390/math10234427 - 24 Nov 2022
Cited by 14 | Viewed by 4034
Abstract
Music is the most convenient and easy-to-use stress release tool in modern times. Many studies have shown that listening to appropriate music can release stress. However, since it is getting easier to make music, people only need to make it on the computer [...] Read more.
Music is the most convenient and easy-to-use stress release tool in modern times. Many studies have shown that listening to appropriate music can release stress. However, since it is getting easier to make music, people only need to make it on the computer and upload it to streaming media such as Youtube, Spotify, or Beatport at any time, which makes it very infeasible to search a huge music database for music of a specific genre. In order to effectively search for specific types of music, we propose a novel method based on the visual Mel spectrum for music genre classification, and apply YOLOv4 as our neural network architecture. mAP was used as the scoring criterion of music genre classification in this study. After ten experiments, we obtained a highest mAP of 99.26%, and the average mAP was 97.93%. Full article
(This article belongs to the Special Issue Mathematics and Computation in Music)
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26 pages, 1233 KiB  
Article
Generalizing the Orbifold Model for Voice Leading
by James R. Hughes
Mathematics 2022, 10(6), 939; https://doi.org/10.3390/math10060939 - 15 Mar 2022
Cited by 3 | Viewed by 2136
Abstract
We generalize orbifold models for chords and voice leading to incorporate loudness, allowing for the modeling of resting voices, which are used frequently by composers and arrangers across genres. In our generalized setting (strictly speaking, that of orbispaces rather than an orbifolds), passages [...] Read more.
We generalize orbifold models for chords and voice leading to incorporate loudness, allowing for the modeling of resting voices, which are used frequently by composers and arrangers across genres. In our generalized setting (strictly speaking, that of orbispaces rather than an orbifolds), passages with resting voices, passages with two or more voices in unison, and fully harmonized passages occupy distinct subspaces that interact in mathematically precise and musically interesting ways. In particular, our setting includes previous orbifold models by way of constant-loudness subspaces, and provides a way to model voice leading between chords of different cardinalities. We model voice leading in this general setting by morphisms in the orbispace path groupoid, a category for which we give a formal definition. We demonstrate how to visualize such morphisms as singular braids, and explore how our approach relates to (and is consistent with) selected previous work. Full article
(This article belongs to the Special Issue Mathematics and Computation in Music)
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19 pages, 24857 KiB  
Article
Color and Timbre Gestures: An Approach with Bicategories and Bigroupoids
by Maria Mannone, Giovanni Santini, Esther Adedoyin and Carmine E. Cella
Mathematics 2022, 10(4), 663; https://doi.org/10.3390/math10040663 - 20 Feb 2022
Cited by 3 | Viewed by 2904
Abstract
White light can be decomposed into different colors, and a complex sound wave can be decomposed into its partials. While the physics behind transverse and longitudinal waves is quite different and several theories have been developed to investigate the complexity of colors and [...] Read more.
White light can be decomposed into different colors, and a complex sound wave can be decomposed into its partials. While the physics behind transverse and longitudinal waves is quite different and several theories have been developed to investigate the complexity of colors and timbres, we can try to model their structural similarities through the language of categories. Then, we consider color mixing and color transition in painting, comparing them with timbre superposition and timbre morphing in orchestration and computer music in light of bicategories and bigroupoids. Colors and timbres can be a probe to investigate some relevant aspects of visual and auditory perception jointly with their connections. Thus, the use of categories proposed here aims to investigate color/timbre perception, influencing the computer science developments in this area. Full article
(This article belongs to the Special Issue Mathematics and Computation in Music)
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