diff nime2012/mtriange.tex @ 32:09faa61946bc

new pass at de-coupling triangle from markov in 'melody triangle' section

--- a/nime2012/mtriange.tex	Tue Feb 07 17:47:09 2012 +0000
+++ b/nime2012/mtriange.tex	Tue Feb 07 19:49:55 2012 +0000
@@ -58,7 +58,7 @@
 \begin{abstract}
 %The Melody Triangle is a Markov-chain based melody generator where the input - positions within a triangle - directly map to information theoretic measures of its output. 
 
-The Melody Triangle is an exploratory interface for the discovery of melodic content, where the input - positions within a triangle - directly map to information theoretic measures of the output.  The measures are the entropy rate, redundancy and \emph{predictive information rate}\cite{Abdallah:2009p4089} of the melody. Predictive information rate is an information measure developed as part of the Information Dynamics of Music project\footnote{(IDyOM) http://www.idyom.org/}.  It characterises temporal structure and is a way of modelling expectation and surprise in the perception of music. 
+The Melody Triangle is an exploratory interface framework for the discovery of melodic content, where the input - positions within a triangle - directly map to information theoretic measures of the output.  The measures are the entropy rate, redundancy and \emph{predictive information rate}\cite{Abdallah:2009p4089} of the melody. Predictive information rate is an information measure developed as part of the Information Dynamics of Music project\footnote{(IDyOM) http://www.idyom.org/}.  It characterises temporal structure and is a way of modelling expectation and surprise in the perception of music. 
 
 We describe the information dynamics approach and how it forms the basis of the Melody Triangle.  We outline two incarnations of the Melody Triangle where it was used with a Markov-chain based melody generator.  The first is a multi-user installation where collaboration in a performative setting provides a playful yet informative way to explore expectation and surprise in music.  The second is a screen based interface where the Melody Triangle becomes a compositional tool for the generation of intricate musical textures using an abstract, high-level description of predictability. Finally we outline a pilot study where the screen-based interface was used under experimental conditions to determine how the three measures of predictive information rate, entropy and redundancy might relate to musical preference.  	
 
@@ -73,7 +73,11 @@
 
 \section{The Melody Triangle}
 %%%How we created the transition matrixes and created the triangle.
-The Melody Triangle is based on first order Markov chains that generate streams of symbols.  By mapping the symbols to individual notes, melodies are generated.  Further by layering these streams of notes can result in intricate musical textures. The choice of notes or scale is not a part of the Melody Triangle's core functionality, in fact the symbols could be mapped to anything, even non sonic outputs.    
+The Melody Triangle enables the discovery of melodic content given some information theoretic criteria on that content.   This  criteria is the user input and maps to positions within a triangle.  How exactly the triangle is formed relative to the information theoretic measures is outlined in section \ref{makingthetriangle}.  The interface to the triangle may come in different forms; so far it has been realised as an interactive installation and as a traditional screen based interface.  
+
+The Melody Triangle does not generate the melodic content itself, but rather selects appropriate parameters for another system to generate it.  The implementations discussed in this paper use first order Markov chains as the content generator, however any generative system, so long as it possible to define a listener model to calculate the appropriate information measures can be used.     
+
+The Triangle operates on streams of symbols, and it is by mapping the symbols to individual notes that melodies are generated.  Further by layering these streams intricate musical textures can be created. The choice of notes or scale is not a part of the Melody Triangle's core functionality, in fact the symbols could be mapped to anything, even non sonic outputs.    
 
 Any sequence of symbols can be analysed and information theoretic measures taken from it.  The novelty of the Melody Triangle lies in that we go `backwards' - given desired values for these measures, as determined from the user interface, we return a stream of symbols that match those measures.  The information measures used are redundancy, entropy rate and predictive information rate.  
 
@@ -115,7 +119,7 @@
 \caption{The Melody Triangle\label{TheTriangle}}
 \end{figure}
 
-\subsection{Making the triangle}
+\subsection{Making the triangle}\label{makingthetriangle}
 We generate thousands of transition matrixes, representing first-order Markov chains, by a random sampling method.  These are then plotted in a 3d statistical space of redundancy, entropy rate and predictive information rate.  In figure \ref{InfoDynEngine} we see a representation of how these matrixes are distributed; each one of these points corresponds to a transition matrix.