diff draft.tex @ 35:194c7ec7e35d

Re-wrote section IV

--- a/draft.tex	Wed Mar 14 13:17:05 2012 +0000
+++ b/draft.tex	Wed Mar 14 18:21:16 2012 +0000
@@ -621,69 +621,46 @@
 
 \section{Information dynamics as compositional aid}
 
-In addition to applying information dynamics to analysis, it is also possible
-use this approach in design, such as the composition of musical materials.  By
-providing a framework for linking information theoretic measures to the control
-of generative processes, it becomes possible to steer the output of these processes
-to match a criteria defined by these measures.  For instance outputs of a
-stochastic musical process could be filtered to match constraints defined by a
-set of information theoretic measures.
+In addition to applying information dynamics to analysis, it is also possible to apply it to the generation of content, such as to the composition of musical materials. 
+The outputs of algorithmic or stochastic processes can be filtered to match a set of criteria defined in terms of the information dynamics model, this criteria thus becoming a means of interfacing with the generative process.  
+For instance a stochastic music generating process could be controlled by modifying constraints on its output in terms of predictive information rate or entropy rate.    
 
-The use of stochastic processes for the generation of musical material has been
-widespread for decades -- Iannis Xenakis applied probabilistic mathematical
-models to the creation of musical materials, including to the formulation of a
-theory of Markovian Stochastic Music.  However we can use information dynamics
-measures to explore and interface with such processes at the high and abstract
-level of expectation, randomness and predictability.  The Melody Triangle is
-such a system.
+The use of stochastic processes for the composition of musical material has been widespread for decades -- for instance Iannis Xenakis applied probabilistic mathematical models to the creation of musical materials\cite{Xenakis:1992ul}.   
+Information dynamics can serve as a novel framework for the exploration of the possibilities of such processes at the high and abstract level of expectation, randomness and predictability.
 
  \subsection{The Melody Triangle}  
-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 associated with the output.
-The measures are the entropy rate, redundancy and predictive information rate
-of the random process used to generate the sequence of notes.
-These are all related to the predictability of the the sequence and as such
-address the notions of expectation and surprise in the perception of
-music.\emph{self-plagiarised}
+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 -- entropy rate, redundancy and predictive information rate -- form a criteria with which to filter the output of the stochastic processes used to generate sequences of notes. 
+These measures address notions of expectation and surprise in music, and as such the Melody Triangle is a means of interfacing with a generative process in terms of the predictability of its output.       
  	
-Before the Melody Triangle can used, it has to be `populated' with possible
-parameter values for the melody generators.  These are then plotted in a 3d
-statistical space of redundancy, entropy rate and predictive information rate.
-In our case we generated thousands of transition matrixes, representing first-order
-Markov chains, by a random sampling method. In figure \ref{InfoDynEngine} we see
-a representation of how these matrixes are distributed in the 3d statistical
-space; each one of these points corresponds to a transition
-matrix.\emph{self-plagiarised}
+The triangle is `populated' with possible parameter values for melody generators. 
+These are plotted in a 3d statistical space of redundancy, entropy rate and predictive information rate. 
+ In our case we generated thousands of transition matrixes, representing first-order Markov chains, by a random sampling method. 
+ In figure \ref{InfoDynEngine} we see a representation of how these matrixes are distributed in the 3d statistical space; each one of these points corresponds to a transition matrix.
+
+
+ 
+	
+The distribution of transition matrixes plotted in this space forms an arch shape that is fairly thin.  
+It thus becomes a reasonable approximation to pretend that it is just a sheet in two dimensions; and so we stretch out this curved arc into a flat triangle.  
+It is this triangular sheet that is our `Melody Triangle' and forms the interface by which the system is controlled.  
+Using this interface thus involves a mapping to statistical space; a user selects a position within the triangle, and a corresponding transition matrix is returned.  
+Figure \ref{TheTriangle} shows how the triangle maps to different measures of redundancy, entropy rate and predictive information rate.
 
 	
-When we look at the distribution of transition matrixes plotted in this space,
-we see that it forms an arch shape that is fairly thin.  It thus becomes a
-reasonable approximation to pretend that it is just a sheet in two dimensions;
-and so we stretch out this curved arc into a flat triangle.  It is this triangular
-sheet that is our `Melody Triangle' and forms the interface by which the system
-is controlled. \emph{self-plagiarised}
-	
-When the Melody Triangle is used, regardless of whether it is as a screen based
-system, or as an interactive installation, it involves a mapping to this statistical
-space.  When the user, through the interface, selects a position within the
-triangle, the corresponding transition matrix is returned.  Figure \ref{TheTriangle}
-shows how the triangle maps to different measures of redundancy, entropy rate
-and predictive information rate.\emph{self-plagiarised}
 
-Each corner corresponds to three different extremes of predictability and
-unpredictability, which could be loosely characterised as `periodicity', `noise'
-and `repetition'.  Melodies from the `noise' corner have no discernible pattern;
-they have high entropy rate, low predictive information rate and low redundancy.
-These melodies are essentially totally random.  A melody along the `periodicity'
-to `repetition' edge are all deterministic loops that get shorter as we approach
-the `repetition' corner, until it becomes just one repeating note.  It is the
-areas in between the extremes that provide the more `interesting' melodies.  That
-is, those that have some level of unpredictability, but are not completely ran-
-dom. Or, conversely, that are predictable, but not entirely so.  This triangular
-space allows for an intuitive explorationof expectation and surprise in temporal
-sequences based on a simple model of how one might guess the next event given
-the previous one.\emph{self-plagiarised}
+
+Each corner corresponds to three different extremes of predictability and unpredictability, which could be loosely characterised as `periodicity', `noise' and `repetition'.  
+Melodies from the `noise' corner have no discernible pattern; they have high entropy rate, low predictive information rate and low redundancy. 
+These melodies are essentially totally random.  
+A melody along the `periodicity' to `repetition' edge are all deterministic loops that get shorter as we approach the `repetition' corner, until it becomes just one repeating note. 
+It is the areas in between the extremes that provide the more `interesting' melodies. 
+These melodies have some level of unpredictability, but are not completely random. 
+ Or, conversely, are predictable, but not entirely so.  
+
+The Melody Triangle exists in two incarnations; a standard screen based interface where a user moves tokens in and around a triangle on screen, and a multi-user interactive installation where a Kinect camera tracks individuals in a space and maps their positions in physical space to the triangle.
+In the latter visitors entering the installation generates a melody, and could collaborate with their co-visitors to generate musical textures -- a playful yet informative way to explore expectation and surprise in music.  
+Additionally different gestures could be detected to change the tempo, register, instrumentation and periodicity of the output melody.  
 
 \begin{figure}
 	\centering
@@ -698,43 +675,25 @@
 	not visible in this plot, it is largely hollow in the middle. 
 	\label{InfoDynEngine}}
 \end{figure}
- 
-	
-
-Any number of interfaces could be developed for the Melody Triangle.  We have
-developed two; a standard screen based interface where a user moves tokens with
-a mouse in and around a triangle on screen, and a multi-user interactive
-installation where a Kinect camera tracks individuals in a space and maps their
-positions in the space to the triangle.
- Each visitor would generate a melody, and could collaborate with their co-visitors
- to generate musical textures -- a playful yet informative way to explore
- expectation and surprise in music.
 
 As a screen based interface the Melody Triangle can serve as composition tool.
-A triangle is drawn on the screen, screen space thus mapped to the statistical
-space of the Melody Triangle.
-A number of round tokens, each representing a melody can be dragged in and
-around the triangle.  When a token is dragged into the triangle, the system
-will start generating the sequence of notes with statistical properties that
-correspond to its position in the triangle.\emph{self-plagiarised}
+A triangle is drawn on the screen, screen space thus mapped to the statistical space of the Melody Triangle.
+A number of round tokens, each representing a melody can be dragged in and around the triangle.  
+When a token is dragged into the triangle, the system will start generating the sequence of symbols with statistical properties that correspond to the position of the token.  
+These symbols are then mapped to notes of a scale. 
+ Keyboard input allow for control over additionally parameters.  
 
-In this mode, the Melody Triangle can be used as a kind of composition assistant
-for the generation of interesting musical textures and melodies.  However unlike
-other computer aided composition tools or programming environments, here the
-composer engages with music on the high and abstract level of expectation,
-randomness and predictability.\emph{self-plagiarised}
-
-	
-Additionally the Melody Triangle serves as an effective tool for experimental investigations into musical preference and their relationship to the information dynamics models.
-
-	%As the Melody Triangle essentially operates on a stream of symbols, it it is possible to apply the melody triangle to the design of non-sonic content.
-	
  \begin{figure}
 \centering
 \includegraphics[width=0.9\linewidth]{figs/TheTriangle.pdf}
 \caption{The Melody Triangle\label{TheTriangle}}
 \end{figure}	
 
+In this mode, the Melody Triangle is a compositional tool.  
+It can assist a composer in the creation not only of melodies, but by placing multiple tokens in the triangle, the generation of intricate musical textures.    
+Unlike other computer aided composition tools or programming environments, here the composer engages with music on the high and abstract level of expectation, randomness and predictability.   	
+
+
 \section{Musical Preference and Information Dynamics}
 We carried out a preliminary study that sought to identify any correlation between
 aesthetic preference and the information theoretical measures of the Melody