From Music to Mathematics and Backwards: Introducing Algebra, Topology and Category Theory into Computational Musicology

Andreatta, Moreno

doi:10.1007/978-3-319-93949-0_7

Cited by 6 publications

(5 citation statements)

References 20 publications

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“…Although both subjects have been connected for centuries, comparing musical structures to mathematics is a fairly new research domain [14]. For a different perspective, the readers may consult Reference [15].…”

Section: A Brief Review Of the Literaturementioning

confidence: 99%

Graph Coverings for Investigating Non Local Structures in Proteins, Music and Poems

Planat

Aschheim

Amaral

et al. 2021

Sci

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We explore the structural similarities in three different languages, first in the protein language whose primary letters are the amino acids, second in the musical language whose primary letters are the notes, and third in the poetry language whose primary letters are the alphabet. For proteins, the non local (secondary) letters are the types of foldings in space (α-helices, β-sheets, etc.); for music, one is dealing with clear-cut repetition units called musical forms and for poems the structure consists of grammatical forms (names, verbs, etc.). We show in this paper that the mathematics of such secondary structures relies on finitely presented groups fp on r letters, where r counts the number of types of such secondary non local segments. The number of conjugacy classes of a given index (also the number of graph coverings over a base graph) of a group fp is found to be close to the number of conjugacy classes of the same index in the free group Fr−1 on r−1 generators. In a concrete way, we explore the group structure of a variant of the SARS-Cov-2 spike protein and the group structure of apolipoprotein-H, passing from the primary code with amino acids to the secondary structure organizing the foldings. Then, we look at the musical forms employed in the classical and contemporary periods. Finally, we investigate in much detail the group structure of a small poem in prose by Charles Baudelaire and that of the Bateau Ivre by Arthur Rimbaud.

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Section: A Brief Review Of the Literaturementioning

confidence: 99%

Graph Coverings for Investigating Non Local Structures in Proteins, Music and Poems

Planat

Aschheim

Amaral

et al. 2021

Sci

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“…Therefore, the willingness to endow the infinite set of the musical phrases with operations in order to obtain suitable algebraic structures is a promising approach. Such interactions between music and algebra form a fruitful field of investigation (Andreatta, 2018;Hudak, 2004;Jedrzejewski, 2019;Tymoczko, 2011;Warrack, 1945). For instance, in (Hudak, 2004) (see also (Hudak & Quick, 2018)), musical phrases are encoded as treelike structures wherein phrases are associated by concatenation or by superposition.…”

Section: Introductionmentioning

confidence: 99%

The music box operad: Random generation of musical phrases from patterns

Giraudo

2024

Journal of Creative Music Systems

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We introduce the notion of multi-pattern, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach to encode musical phrases lies in the fact that it becomes possible to compose multi-patterns in order to produce new ones. This composition is parametrized by a monoid structure on the scale degrees. This dives the set of the musical phrases into an algebraic framework since the set of the multi-patterns is endowed with the structure of an operad. Operads are algebraic structures offering a formalization and an abstraction of the notion of operators and their compositions. Seeing musical phrases as operators allows us to perform computations on phrases and admits applications in generative music. Indeed, given a set of initial multi-patterns, we propose various algorithms to randomly generate a new and longer phrase emulating the style suggested by the inputted multi-patterns. The designed algorithms use sorts of grammars working with operads and colored operads, known as bud generating systems.

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“…Therefore, the willingness to endow the infinite set of all musical phrases with operations in order to obtain suitable algebraic structures is a promising approach. Such interactions between music and algebra is a fruitful field of investigation [1,9].…”

Section: Introductionmentioning

confidence: 99%

Generation of musical patterns through operads

Giraudo

2021

Preprint

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Nous introduisons la notion de multi-motif, une abstraction combinatoire des phrases musicales à plusieurs voix. L'intérêt de cette approche réside dans le fait qu'il devient possible de composer deux multi-motifs pour en produire un plus long. Ceci s'inscrit dans un contexte algébrique puisque l'ensemble des multi-motifs possède une structure dite d'opérade ; les opérades étant des structures offrant une formalisation de la notion d'opérateur et de leurs compositions. Cette vision des phrases musicales comme des opérateurs permet de réaliser ainsi des calculs sur ces dernières et admet des applications en musique générative : étant donné un ensemble de courts motifs, nous proposons divers algorithmes pour produire de manière aléatoire une nouvelle phrase plus longue inspirée des motifs initiaux.-We introduce the notion of multi-pattern, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach lies in the fact that this offers a way to compose two multi-patterns in order to produce a longer one. This dives musical phrases into an algebraic context since the set of multi-patterns has the structure of an operad; operads being structures offering a formalization of the notion of operators and their compositions. Seeing musical phrases as operators allows us to perform computations on phrases and admits applications in generative music: given a set of short patterns, we propose various algorithms to randomly generate a new and longer phrase inspired by the inputted patterns.

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From Music to Mathematics and Backwards: Introducing Algebra, Topology and Category Theory into Computational Musicology

Cited by 6 publications

References 20 publications

Graph Coverings for Investigating Non Local Structures in Proteins, Music and Poems

Graph Coverings for Investigating Non Local Structures in Proteins, Music and Poems

The music box operad: Random generation of musical phrases from patterns

Generation of musical patterns through operads

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