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The Deep Learning Revolution in MIR: The Pros and Cons, the Needs and the Challenges Read chapter Read first chapter

2021 | OriginalPaper | Chapter

Mathematics and Music: Loves and Fights

Author : Thierry Paul

Published in: Perception, Representations, Image, Sound, Music

Publisher: Springer International Publishing

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Abstract

We present different aspects of the special relationship that music has with mathematics, in particular the concepts of rigour and realism in both fields. These directions are illustrated by comments on the personal relationship of the author with Jean-Claude, together with examples taken from his own works, specially the “Duos pour un pianiste".

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Footnotes
1
The same anecdote has been also told to me with another main character in place of Chevalley.
 
2
Boucourechliev [1] claims that Stravinsky is wrong and that is possible but, actually, doesn’t give the recovered series.
 
3
Pierre Boulez comdans voluntary the third part of “Structure I for two pianos"[2] for the argument that “a computer could have composed it in a few minutes". Et alors ?.
 
4
Let us remark that, at the same period, Bourbaki’s attempt to constrict what could be called a kind of absolutely pure mathematics was offering a vision of mathematics where the only figures are commuting diagrams, which by the way are not figures but just notations.
 
5
“On dit qu’un nombre variable x a pour limite un nombre fixé a, ou tend vers a, lorsque la valeur absolue de la différence \(x-a\) finit par devenir et “rester" plus petite que n’importe quel nombre positif donné à l’avance. Lorsque \(a = 0\), le nombre x est dit “un infiniment petit“.", Gourçat [6].
 
6
The reader interested in the concept of rigour in mathematics, philosophy and music, might consult the proceedings [3] of the conference RIGUEUR held in Paris, July 2 and 3 2019, to be published by Spartacus editions (Paris).
 
7
Though wrong proofs are usaully very beautiful.
 
8
What limits the true is not the false, it is the insignificant.
 
9
Like a calisson shaped box of calissons where all calissons are replaced by ... a box of callisons where all calissons are replaced by ... a box of callisons...etc.
 
Literature
1.
Boucourechliev, A.: Stravinsky. Fayard, Paris (1982)
2.
Boulez, P.: Structures I Pour Deux Pianos. Universal Edition, Vienna (1952)
3.
4.
Drouin, G.: Les deux moments de la rigueur du compositeur. In: [3]
5.
Giavitto, J.L.: Formalisme, Exactitude, Rigueur. In: [3]
6.
Goursat, É.: Cours d’Analyse Mathématique. Gauthier-Villars, Paris (1933)MATH
7.
Paul, T.: Des sons et des Quanta. In: Alunni, C., Andreatta, M., Nicolas, F. (eds.) Mathématique/Musique/Philosophie. Collection “Musique/Sciences” IRCAM-Delatour, Paris (2012)
8.
Paul, T.: Rigueur-contraintes: mathématiques-musique. Gaz. Mathématiciens 139, 71–77 (2014)MATH
9.
Paul, T.: platonisme - intrication - aléa (mathématique - physique - musique), à la mémoire de Jean-Claude Risset, magicien des sons impossibles. In: Hautbois, X., Laliberté, M., Stransky, L., Stransky, V. (eds.) L’émergence en musique - dialogue des sciences, Delatour, Paris, pp. 37–52 (2019)
10.
Paul, T.: Mathematical entities without objects, on the realism in mathematics and a possible mathematization of the (non)Platonism - Does Platonism dissolve in mathematics? Eur. Rev. 29(2), 1–21 (2021)
11.
12.
Poincaré, H.: Sur la théorie des quanta. J. Phys. Théorique Appl. 2, 5–34 (1912)CrossRef
13.
Stockhausen, K.: ...wie die Zeit vergeht.... Die Reihe, 3 (1957) In: French: ...comment passe le temps.... Analyse musicale 6 (1987)
14.
Stravinsky, I.: Movements for Piano and Orchestra. Boosey and Hawkes, London (1959)
15.
Thom, R.: Prédire n’est pas Expliquer. Eshel, Paris (1991)MATH
Metadata
Title
Mathematics and Music: Loves and Fights
Author
Thierry Paul
Copyright Year
2021
Book
Perception, Representations, Image, Sound, Music

Print ISBN: 978-3-030-70209-0

Electronic ISBN: 978-3-030-70210-6

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-70210-6_45