From 280bd3ea61c871bd2639154e33adaf411e869c04 Mon Sep 17 00:00:00 2001 From: Martin Potier Date: Tue, 31 Jul 2012 09:27:46 +0200 Subject: [PATCH] Initial commit --- .CMakeLists.txt.swp | Bin 0 -> 12288 bytes .SonificationHandbook.bib.swp | Bin 0 -> 16384 bytes .StageSonification2012.bib.swp | Bin 0 -> 16384 bytes .catalog.tex.swp | Bin 0 -> 12288 bytes .content.tex.swp | Bin 0 -> 16384 bytes .memoire.tex.swp | Bin 0 -> 12288 bytes CMakeLists.txt | 27 ++ SonificationHandbook.bib | 370 ++++++++++++++++ StageSonification2012.bib | 214 ++++++++++ catalog.tex | 53 +++ content.tex | 582 ++++++++++++++++++++++++++ img/SSMSC1.pdf | Bin 0 -> 38847 bytes img/SSMSC2.pdf | Bin 0 -> 35452 bytes img/SSMSC3.pdf | Bin 0 -> 37591 bytes img/eulers-tonnetz.png | Bin 0 -> 30582 bytes img/foam-coarsening.png | Bin 0 -> 448727 bytes img/foam1.png | Bin 0 -> 188224 bytes img/foam2.png | Bin 0 -> 178791 bytes img/foam3.png | Bin 0 -> 8271 bytes img/galileo-inclined-plane-detail.jpg | Bin 0 -> 143557 bytes 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node[above,midway] {+1} (C2.south west); +\end{tikzpicture} +\caption{Répartition des demi-tons dans la gamme de Do Majeur} +\label{fig:gamme} +\end{figure} + +En utilisant la réduction à l'octave (l'intervalle de Do$_i$ à Do$_{i+1}$), on +réduit l'espace combinatoire en 12 intervalles qui sont les 12 classes de +résidus modulo 12 de $\mathbb{Z}_{12}$. Chacun de ces intervalles a un nom et +on peut utiliser une représentation circulaire comme support visuel pour des +opérations algébriques élémentaires entre autres : +\begin{itemize} +\item la transposition (rotation sur le cercle, fig. \ref{fig:transposition}), +\item l'inversion (symétrie sur le cercle, fig. \ref{fig:inversion}), +\end{itemize} +qui constituent une première formalisation algébrique. + +\begin{figure}[ht] +\hfill +\subfloat[Transposition : $x \rightarrow x + k \bmod 12$]{ + \begin{tikzpicture}[scale=.3\textwidth/2cm,delta angle=-30,radius=1.06cm] + \draw (0cm,0cm) circle (1cm); + \foreach \i/\j in + {90/0,60/1,30/2,0/3,330/4,300/5,270/6,240/7,210/8,180/9,150/10,120/11} { + \node[fill,circle,inner sep=.5mm] (\j) at (\i:1cm) {}; + \node at (\i:1.2cm) {\j}; + } + \draw (0) -- (3) -- (7) -- (0); + \draw[gray] (1) -- (4) -- (8) -- (1); + \draw[gray,dashed,->] (0,0) +(90:1.06cm) arc [start angle=90]; + \end{tikzpicture} + \label{fig:transposition}} + \hfill +\subfloat[Inversion : $x \rightarrow -x \bmod 12 $.]{ + \begin{tikzpicture}[scale=.3\textwidth/2cm] + \draw (0cm,0cm) circle (1cm); + \foreach \i/\j in + {90/0,60/1,30/2,0/3,330/4,300/5,270/6,240/7,210/8,180/9,150/10,120/11} { + \node[fill,circle,inner sep=.5mm] (\j) at (\i:1cm) {}; + \node at (\i:1.2cm) {\j}; + } + \draw[dashed,gray] (0,-1.3cm) -- (0,1.3cm); + \draw (0) -- (3) -- (7) -- (0); + \draw[gray] (0) -- (5) -- (9) -- (0); + \end{tikzpicture} + \label{fig:inversion}} +\hfill~ +\caption{Intervalles et opérations algébriques sur un cercle} +\end{figure} + +Une autre représentation qui nous intéresse est l'organisation spatiale des +intervalles au sein d'un \emph{tonnetz} (Fig.~\ref{fig:tonnetz}), décrit en +premier par Leonhard Euler. Ce dernier a choisi une disposition spatiale +compacte valorisant les intervalles\footnote{% (((----------------------------- +L. Euler utilise une notation allemande où le $H$ correspond au $B$ anglo-saxon +et le $B$ correspond à $A\#$. Cette notation vient du système de notation +\textsc{Bach}. Voir la page \url{http://en.wikipedia.org/wiki/H_(musical_note)} +pour de plus amples détails.}% )))--------------------------------------------- +~de tierce majeure (4 demi-tons, vers la droite) et de quinte juste (7 +demi-tons, vers le bas). Cette représentation est équivalente à la donnée d'un +groupe cyclique d'ordre 12 (comme précédemment) mais exprimé sous forme d'un +graphe planaire. Ces deux intervalles sont les plus consonnants (après +l'octave) ; il est donc agréable et pratique de pouvoir passer d'une note à une +autre en les privilégiants. + +\begin{figure}[ht] +\centering + +\subfloat[Tonnetz de L. Euler (1739)]{ +\includegraphics[width=.45\textwidth]{img/eulers-tonnetz} +\label{fig:tonnetz}} +\subfloat[Tonnetz de L. Euler vu comme une partie du graphe de Cayley du groupe +$\mathbb{Z}_{12}$ avec pour partie génératrice $\{4,7\}$]{ +\begin{tikzpicture} +[note/.style={draw,black,circle,inner sep=2mm}, +label distance=-1mm,label position=below left, +double distance=.5mm] +\node[note,double] (C) [label=Do ] {}; +\node[note,left=of C] (F) [label=Fa ] {}; +\node[note,right=of C] (G) [label=Sol ] {}; +\node[note,right=of G] (D) [label=Ré ] {}; + +\node[note,above=of F] (A) [label=La ] {}; +\node[note,right=of A] (E) [label=Mi ] {}; +\node[note,right=of E] (B) [label=Si ] {}; +\node[note,right=of B] (Fd) [label= Fa♯] {}; + +\node[note,above=of A] (Cd) [label= Do♯] {}; +\node[note,right=of Cd] (Gd) [label=Sol♯] {}; +\node[note,right=of Gd] (Dd) [label= Ré♯] {}; +\node[note,right=of Dd] (Ad) [label= La♯] {}; + +\draw (F) -- (C) -- node[above,midway] {+7} (G) -- (D); +\draw (A) -- (E) -- (B) -- (Fd); +\draw (Cd) -- (Gd) -- (Dd) -- (Ad); + +\draw (F) -- (A) -- (Cd); +\draw (C) -- node[right,midway] {+4} (E) -- (Gd); +\draw (G) -- (B) -- (Dd); +\draw (D) -- (Fd) -- (Ad); + +\draw[dashed] (Cd.north) -- +(0cm ,6mm ); +\draw[dashed] (Gd.north) -- +(0cm ,6mm ); +\draw[dashed] (Dd.north) -- +(0cm ,6mm ); +\draw[dashed] (Ad.north) -- +(0cm ,6mm ); +\draw[dashed] (F.south) -- +(0cm ,-6mm); +\draw[dashed] (C.south) -- +(0cm ,-6mm); +\draw[dashed] (G.south) -- +(0cm ,-6mm); +\draw[dashed] (D.south) -- +(0cm ,-6mm); +\draw[dashed] (F.west) -- +(-6mm,0cm ); +\draw[dashed] (A.west) -- +(-6mm,0cm ); +\draw[dashed] (Cd.west) -- +(-6mm,0cm ); +\draw[dashed] (Ad.east) -- +(6mm ,0cm ); +\draw[dashed] (Fd.east) -- +(6mm ,0cm ); +\draw[dashed] (D.east) -- +(6mm ,0cm ); +\end{tikzpicture} +\label{fig:cayley}} +\caption{Répartition spatiale des intervalles en tant que +tonnetz~\subref{fig:tonnetz} et en tant que graphe de +Cayley~\subref{fig:cayley}} +\end{figure} + +Le musicologue Hugo Riemann explorera ensuite ce mode de représentation des +relations intervaliques entre notes influençant toute la musicologie à venir. +En gardant cet agencement et en récupérant une triangulation de l'espace +comme sur la figure~\ref{fig:trig}, on obtient immédiatement toutes +les triades Majeures et mineures de la gamme ainsi que les tonalités voisinnes, +comme Do Majeur (La mineur) est la tonalité relative Majeure (mineure) à La +mineur (Do Majeur) respectivement. + +\begin{figure}[ht] +\centering +\begin{tikzpicture} +[note/.style={draw,black,circle,inner sep=2mm}, +label distance=-1mm,label position=below left, +double distance=.5mm] +\node[note,double] (C) [label=Do ] {}; +\node[note,left=of C] (F) [label=Fa ] {}; +\node[note,right=of C] (G) [label=Sol ] {}; +\node[note,right=of G] (D) [label=Ré ] {}; + +\node[note,above=of F] (A) [label=La ] {}; +\node[note,right=of A] (E) [label=Mi ] {}; +\node[note,right=of E] (B) [label=Si ] {}; +\node[note,right=of B] (Fd) [label= Fa♯] {}; + +\node[note,above=of A] (Cd) [label= Do♯] {}; +\node[note,right=of Cd] (Gd) [label=Sol♯] {}; +\node[note,right=of Gd] (Dd) [label= Ré♯] {}; +\node[note,right=of Dd] (Ad) [label= La♯] {}; + +\draw (F) -- (C) -- (G) -- (D); +\draw (A) -- (E) -- (B) -- (Fd); +\draw (Cd) -- (Gd) -- (Dd) -- (Ad); + +\draw (F) -- (A) -- (Cd); +\draw (C) -- (E) -- (Gd); +\draw (G) -- (B) -- (Dd); +\draw (D) -- (Fd) -- (Ad); + +\begin{scope}[fill=black!50] +\filldraw (C) -- (E) -- (G) -- cycle; % DOM +\filldraw (A) -- (Cd) -- (E) -- cycle; % LAm +\end{scope} + +\draw[dashed] (Cd.north) -- +(0cm ,6mm ); +\draw[dashed] (Gd.north) -- +(0cm ,6mm ); +\draw[dashed] (Dd.north) -- +(0cm ,6mm ); +\draw[dashed] (Ad.north) -- +(0cm ,6mm ); +\draw[dashed] (F.south) -- +(0cm ,-6mm); +\draw[dashed] (C.south) -- +(0cm ,-6mm); +\draw[dashed] (G.south) -- +(0cm ,-6mm); +\draw[dashed] (D.south) -- +(0cm ,-6mm); +\draw[dashed] (F.west) -- +(-6mm,0cm ); +\draw[dashed] (A.west) -- +(-6mm,0cm ); +\draw[dashed] (Cd.west) -- +(-6mm,0cm ); +\draw[dashed] (Ad.east) -- +(6mm ,0cm ); +\draw[dashed] (Fd.east) -- +(6mm ,0cm ); +\draw[dashed] (D.east) -- +(6mm ,0cm ); +\end{tikzpicture} + +\caption{Triangulation d'accords sur un graphe de Cayley} +\label{fig:trig} +\end{figure} + +\section{Formalisation} +\subsection{Un tonnetz comme graphe de Cayley} +\label{subsec:tonnetz-cayley} +%(thèse de julien cohen) +Le graphe de Cayley d'un groupe G permet de visualiser les éléments de G et +leur relation de voisinnage. Soit G un groupe et S une partie génératrice de +G~: +\begin{itemize} +\item chaque sommet $V_i$ représente un élément du groupe $G$, +\item chaque arc $e_i$ est étiqueté par un générateur de $S$, +\item un arc étiqueté $e$ setrouve entre les sommets $U$ et $V$ si $U + e = V$. +\end{itemize} + +Un tonnetz peut être vu comme le graphe de Cayley du groupe cyclique +$\mathbb{Z}_{12}$ des 12 demi-tons de la gamme occidentale muni de l'addition +comme loi commutative et d'une partie génératrice $S$ ; pour garder l'analogie +dans la figure \ref{fig:cayley}, nous utilisons deux générateurs libres : la +tierce Majeur et la quinte juste. Le sommet à l'origine du graphe de Cayley est +l'élément \emph{neutre} du groupe. + +Chemins hamiltoniens dans le tonnetz \cite{albini_hamiltonian_2009}. + +\subsection{Quelques mappings} +Pour apporter des éléments de réponse aux questions des physiciens (§~% +\ref{subsec:mousses}), nous proposons les mappings suivants. Le premier porte +sur l'aspect signal et entre de ce fait complètement dans le cadre de la +sonification classique, les trois suivantes tirent partie des théories +musicales néo-Riemanniennes et portent sur des études rythmiques et mélodiques. + +\subsubsection{Synthèse modale} +Un objet physique vibre librement après avoir été excité et présente des modes +propres de vibration dépendant entre autres de sa géométrie et des matériaux le +constituant. Ces modes peuvent être observés sur le spectre des fréquences du +signal émis et sont utilisés par \modalys\ pour sauvegarder l'empreinte sonore +d'un objet physique. Le signal émis est un timbre particulier que notre système +auditif \emph{reconnaît} et associe à l'objet qui l'a émis. Par exemple, une +cuiller en bois tombant au sol a un son caractéristique et facilement +différenciable d'une cuiller en métal. + +Nous utilisons cette capacité de reconnaissance pour reconnaître et +différencier différentes organisations spatiales des bulles dans une mousse en +deux dimensions et plus tard reconnaître leur évolution. + +\subsubsection{Organisation rythmique} +À l'image d'un exemple de sonification du §~\ref{subsec:sonification}, le +compteur Geiger, nous pouvons utiliser le rythme comme lien à l'organisation +spatiale des bulles d'une mousse liquide en deux dimensions. + +On parcours par balayage le long d'une segment de droite $(\Delta)$ l'image +d'une mousse en sélectionnant tous les centre de bulle étant à une distance $d$ +de la droite. Ces échantillons récoltés sont ensuites projetés orthogonalement +sur $(\Delta)$. On sonifie ensuite la distance entre chaque point projeté pour +obtenir un motif rythmique. + +Cette technique est mise en pratique par S. Adhitya dans \textsc{Sum} +\cite{adhitya_audio-assisted_2011}, un outil permettant de sonifier +l'organisation urbaine à partir de plans surimposés. + +\subsubsection{Chemins sonores} +Les mappings précédents omettent la dimension musicale du son ; de plus, ils se +concentrent trop sur une approche globale de l'ordre alors que nous pourrions +être intéressés par des variations au niveau local, afin par exemple de trouver +des zones d'ordre parmis un désordre moyen. + +Pour ce faire, nous utilisons le lien mis en lumière précédemment +(§~\ref{subsec:tonnetz-cayley}) entre tonnetz et graphe de Cayley afin de +\emph{musifier} des parcours dans une mousse plus ou moins régulière. Un chemin +dans une mousse est une suite de sauts entre bulles voisinnes. Nous numérotons +de manière unique le voisinnage de chaque bulle et nous indiquons ainsi un +chemin par une suite d'entiers correspondant aux directions à prendre. + +Dans le graphe de Cayley du groupe $\mathbb{Z}_{12}$, chaque élément a six +voisins, en prenant les directions \texttt{a}, \texttt{b}, \texttt{a+b}, +\texttt{-a}, \texttt{-b} et \texttt{-(a+b)}. Plongé dans un tonnetz, ceci +correspond à une suite de notes. + +\subsubsection{Chemins sonores augmentés} +Nous avons rajouté des extensions au dessus des chemins sonores tels que +décrits dans la section précédente : accords, mélodies plus complexes et +rythme. + +L'usage d'accords nous permet de comparer immédiatement deux parcours +simultanés, les mélodies nous permettent de déformer des thèmes connus (par +exemple la comptine Frère Jacques) et le rythme rajoute une information sur les +différences de distance entre le parcours dans un espace \emph{régulier} et +déformé. + +\section{Implementation} +Tous les mappings ont été implémentés grâce aux outils présents à +l'\ircam, notamment \modalys, pour la synthèse modale, et +\openmusic\ comme environnement de programmation principal. + +D'autres outils ont été employés pour les tests mais n'ont été utilisés +pour l'implémentation finale : Max et \textsc{Mgs}. + +\subsection{Modalys} +\modalys\ (anciennement appelé Mosaïc) est un outil de synthèse modale par +modèle physique basée sur \lisp\ \cite{eckel_sound_1995}. Cet outil permet +de modéliser un objet physique et +une (ou des) interaction(s) avec ce dernier . +\modalys\ simule les modes de vibration de cet objet et calcul le signal reçu à +un point donné de l'espace. Par exemple, le chevalet d'un violon alto et +l'archer frottant sur la corde pourraient être respectivement l'objet modélisé +et l'interaction. + +Le profil vibratoire (??) d'un objet modélisé peut être sauvegardé comme une +liste de modes propres de vibration (fréquence, bande passante, amplitude). + +\subsection{OpenMusic} +Environnement de programmation visuelle et fonctionnelle basée sur +\lisp\ (LispWorks). Développé par G. Assayag et C. Agon. + +La programmation s'effectue à base de patch, que l'on peut connecter à l'aide +de liens en sortie et en entrée pour passer des valeurs, un patch pouvant faire +office de fonction anonyme à passer à un autre patch ou à une fonction écrite +en \lisp\ directement. Plusieurs primitives de \modalys\ sont directement +accessibles dans \openmusic. + +\section{Validation} +Chaque mapping a été testé avec différents paramètres et sur différents +échantillons de départ. + +\subsection{Un protocole pour la validation} +Nous proposons ici un modeste protocole pour la validation des données + +\subsection{Écoutes préliminaires} +Détection d'ordre changeant fortement lors d'un épisode catastrophique, +données de simulation, identification de battements. + +\section{Perspectives} +De part la courte durée du stage et de part le côté fortement exploratoire du +sujet, certaines parties n'ont été que partiellement traitées et d'autres n'ont +été qu'entrevues. Voici quelques explications sur les points insuffisamment +abordés. + +\subsection{Une amélioration des mapping} +comparaison delaunay / voisin mousse + +Un meilleur traitement local/global (id Laurent) + +\subsection{Une validation approfondie} +Écoutes beaucoup sujets, statistiques + +\subsection{Développement d'un cadre général} +Fait l'objet d'un sujet de thèse à l'\textsc{Édite} de Paris VI. diff --git a/img/SSMSC1.pdf b/img/SSMSC1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b161b10cbe7583f92803f3f3259d889a0cf6c9d8 GIT binary patch literal 38847 zcmb@t1CTAt!Zp~oZFirxZQHhOp0;hCwt3pNZQHi(?m73~_vXJdf5dzdGZQ;@Rqm{; zTr0C8D%RR7lT=<#UQB0Gq66!N_0qhhHsaj(6;+iAZv=6UMtp@~r7MD<&lHWyViG*rAV z-}leT7xC5B7oYNUU`q^KHX7lF7r#Gz9y1nwt97}*W~#d0{i|=c;kPS!y)|9l0%8qf zlSA`-*(QUdq+hL^f|nLpp~ics8EE#P@& zYf0gMedXx4{vJaA{2uo-OURqu+0GS068&xsICA1UctnHaZCk%9xlx&iDt(_#^O6}O z^NUoNS;IM3;G8c(!4y10ao2QK;@#+bCN>i%t0Ab{?e1!7231j#v~;;&s<0k46VtYK 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+\usepackage{tikz} +\usetikzlibrary{positioning} +\usepackage[lofdepth,lotdepth]{subfig}% replaces subfigure +\usepackage{scrtime} +%\usepackage{hyperref} + +\defaultfontfeatures{Scale=MatchLowercase} +\setromanfont[Mapping=tex−text]{Linux Libertine O} +\setsansfont [Mapping=tex−text]{Linux Biolinum O} +\setmonofont [Mapping=tex−text]{Inconsolata} + +\newcommand{\ircam}{\textsc{Ircam}} +\newcommand{\lps}{\textsc{Lps}} +\newcommand{\lisp}{\textsc{Lisp}} +\newcommand{\modalys}{\textbf{Modalys}} +\newcommand{\openmusic}{\textbf{OpenMusic}} +\newcommand{\mpri}{\textsc{Mpri}} + +\newcommand{\todo}{\fbox{\texttt{todo}}} + +\hyphenation{con-cen-trent} + +\begin{document} +\titlehead{{\Large\ircam\hfill\lps}\\% +UMR 9912 - STMS \hfill Orsay \\% +1 place Igor Stravinsky \\% +75004 Paris} +\subject{Mémoire de M2} +\title{De la sonification à la « musification » des systèmes complexes} +\author{Martin \sc Potier} +\date{6 septembre 2012} +\publishers{\sc mpri} +\maketitle + +\vfill +Stage encadré par : +\begin{itemize} +\item Moreno \textsc{Andreatta} (\ircam) +\item Wiebke \textsc{Drenckhan} (\lps) +\end{itemize} + +\bigskip +Rapporteur : +\begin{itemize} +\item Gilles \textsc{Schaeffer} +\end{itemize} +\vfill + +\hfill{\small Document compilé le \today\ à \thistime} +\thispagestyle{empty} +\cleardoublepage + +% 2 pages +%\begin{abstract} +%Your abstract goes here... +%\end{abstract} +%\cleardoublepage + +\tableofcontents +\thispagestyle{empty} +\cleardoublepage + +% Content +\include{content} + +\bibliographystyle{plain} +\bibliography{SonificationHandbook,StageSonification2012} + +\appendix +\include{catalog} +\end{document}