Emmanuel Amiot Modèles algébriques et algorithmes pour la ...

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English title: Algebraic models and algorithms for the mathematical formali- Abstract: zation of musical structures. This PhD is based on a selection of five previously published papers. They have been singled out for their scientific interest. The synthesis document aims at making clear the role and purpose of these papers in the field of contemporary research across mathematics and music. Their author makes use of sophisticated algebraic notions the better to study three main topics of musical lineage: rhythmic canons, musical scales, and autosimilar melodies. His approach intertwines with information sciences, on the one hand as a means of experimenta- tion and on the other hand in producing software for musical analysis and composition. Keywords: Mathematics, music, tiling, mosaic, rythmiques canons, spectral conjecture, Fugle- de, Vuza canons, musical scales, Maximally Even Sets, discrete Fourier transform, tempera- ments, tuning, autosimilarity, melody, affine, modular. p. 4
Table des matières Introduction 6 Bref historique 6 Mes différents champs de recherche 8 Produits de mes recherches 14 Canons rythmiques 14 Gammes et transformée de Fourier discrète 22 Mélodies Autosimilaires 30 Conclusion et perspectives 37 Remerciements 42 Liste de travaux 45 p. 5
Page 1 and 2: Thèse de Doctorat de l'Université
Page 3: Résumé : Cette thèse sur travaux
Page 7 and 8: kis. De ce fait, j'ai tout naturell
Page 9 and 10: fois ce problème de combinatoire r
Page 11 and 12: de Quinn 12, qui, pour la première
Page 13 and 14: OpenMusic permettant, entre autres
Page 15 and 16: Le premier article offre une synth
Page 17: A = {0,1,2,4,5,6}, i.e. A(X) = (1 +
Page 20 and 21: ✦ Fabriquer par l'algorithme de C
Page 23 and 24: (ou une gamme) remonte à David Lew
Page 25 and 26: Mon article du Journal of Mathemati
Page 28 and 29: et de considérer les DFT des appli
Page 30 and 31: Pour rendre compte de cette dispari
Page 32 and 33: limitées 54, les pavages, divers t
Page 34 and 35: OpenMusic réalise les transformati
Page 36 and 37: ment versé en mathématiques, pour
Page 38 and 39: Mémoire de thèse Amiot 38 Un sign
Page 40 and 41: Mémoire de thèse Amiot 40 Or l' o
Page 42 and 43: Mémoire de thèse Amiot 42 Remerci
Page 44 and 45: Mémoire de thèse Amiot 44 Je tien
Page 46 and 47: Mémoire de thèse Amiot 46 ✦ Ami
Page 49: Annexe I Articles figurant dans le
Page 52 and 53: du pattern, qui va donc commencer p
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Un musicien attend pour rentrer ICI
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ainsi que leurs produits. Comme ce
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par l’automorphisme de FROBENIUS
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PROPOSITION. ≀ Soit A(X) un polyn
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FIG. 12 - Orbite d’un motif sous
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. Un domaine K (compact d’intéri
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période 900 : A = (0, 36, 72, 100,
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Journal of Mathematics and Music Vo
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alternative title 3 Lemma 1.2 The F
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alternative title 5 Proof If A ∈
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2.4 Pich Class Sets and related Mul
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in so doing, the sum S = FA ′(1)
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12 10 8 6 4 2 4 0 ME7,3 4 alternati
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alternative title 13 For instance,
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alternative title 15 To state it wi
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Supplementary II: pictures and proo
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3 chunk of whole tone 1 2 3 4 5 6 7
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alternative title 21 A B C A' B' C'
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2 autosimilar melodies flake, Sierp
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4 autosimilar melodies Example 1.3
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6 autosimilar melodies Proposition
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8 autosimilar melodies Proposition
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10 autosimilar melodies homothety h
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12 autosimilar melodies These compu
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14 autosimilar melodies Theorem 3.6
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16 autosimilar melodies 5.2 Example
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18 autosimilar melodies at most q
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20 autosimilar melodies [8] Fripert
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22 autosimilar melodies Now we woul
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24 autosimilar melodies But in Z15
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26 autosimilar melodies At this jun
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2 circle of fifths begins with five
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4 (it is the Fourier Transform of t
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6 Definition 2. A temperament, or t
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8 MSS A Bb B C C D Eb E F F G G Pyt
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10 sequence of 3 (and preferably mo
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12 i.e. an arithmetic progression w
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2 EMMANUEL AMIOT If we visualize Zn
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4 EMMANUEL AMIOT Theorem 3. (1) Til
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NEW PERSPECTIVES ON RHYTHMIC CANONS
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NEW PERSPECTIVES ON RHYTHMIC CANONS
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