comparison draft.tex @ 35:194c7ec7e35d

Re-wrote section IV

  \emph{Andrew}  
 
 
 \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.
-
-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.
+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 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.
+
+
+ 
 	
-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}
+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 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
 	\includegraphics[width=\linewidth]{figs/mtriscat}
 	\caption{The population of transition matrices distributed along three axes of 

 	represents its PIR---note that the highest values are found at intermediate entropy
 	and redundancy, and that the distribution as a whole makes a curved triangle. Although
 	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}
-
-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.
-	
+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.  
+
  \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
 Triangle.  In this study participants were asked to use the screen based interface