comparison draft.tex @ 42:1161caf0bdda

Reflowed text in sec 4 and 5, changed en dashes to em dashes.

       bar lengths) and phases (\ie positions within a bar).
       }
     \end{fig}
 
     \subsection{Content analysis/Sound Categorisation}.
-    Using analogous definitions of differential entropy, the methods outlined in the previous section are equally applicable to continuous random variables. In the case of music, where expressive properties such as dynamics, tempo, timing and timbre are readily quantified on a continuous scale, the information dynamic framework thus may also be considered.
-
-    In \cite{Dubnov2006}, Dubnov considers the class of stationary Gaussian processes. For such processes, the entropy rate may be obtained analytically from the power spectral density of the signal, allowing the multi-information rate to be subsequently obtained. Local stationarity is assumed, which may be achieved by windowing or change point detection \cite{Dubnov2008}. %TODO mention non-gaussian processes extension
-    Similarly, the predictive information rate may be computed using a Gaussian linear formulation CITE. In this view, the PIR is a function of the correlation  between random innovations supplied to the stochastic process.
-    %Dubnov, MacAdams, Reynolds (2006)
-    %Bailes and Dean (2009)
+	 Using analogous definitions of differential entropy, the methods outlined
+	 in the previous section are equally applicable to continuous random variables.
+	 In the case of music, where expressive properties such as dynamics, tempo,
+	 timing and timbre are readily quantified on a continuous scale, the information
+	 dynamic framework thus may also be considered.
+
+	 In \cite{Dubnov2006}, Dubnov considers the class of stationary Gaussian
+	 processes. For such processes, the entropy rate may be obtained analytically
+	 from the power spectral density of the signal, allowing the multi-information
+	 rate to be subsequently obtained. Local stationarity is assumed, which may
+	 be achieved by windowing or change point detection \cite{Dubnov2008}. %TODO
+	 mention non-gaussian processes extension Similarly, the predictive information
+	 rate may be computed using a Gaussian linear formulation CITE. In this view,
+	 the PIR is a function of the correlation  between random innovations supplied
+	 to the stochastic process.  %Dubnov, MacAdams, Reynolds (2006) %Bailes and
+	 Dean (2009)
 
         \begin{itemize}
             \item Continuous domain information
                         \item Audio based music expectation modelling
             \item Proposed model for Gaussian processes
         \end{itemize}
-    \emph{Peter}
 
 
 \subsection{Beat Tracking}
- \emph{Andrew}  
 
 
 \section{Information dynamics as compositional aid}
 
-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.
+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}  
 
 \begin{figure}
 	\centering

 	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}
 
-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.       
- 	
-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 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.
+
+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.
 	
-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.
-
-	
-
-
-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.  
+
+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.
 
  \begin{figure}
 \centering
 \includegraphics[width=0.9\linewidth]{figs/TheTriangle.pdf}
 \caption{The Melody Triangle\label{TheTriangle}}
 \end{figure}	
 
 
-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.  
+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.
 
 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 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.  
-
-The Melody Triangle is can assist a composer in the creation not only of melodies, but, by placing multiple tokens in the triangle, can generate 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.   	
+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.
+
+The Melody Triangle is can assist a composer in the creation not only of melodies,
+but, by placing multiple tokens in the triangle, can generate 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.
 
 
 
 \subsection{Information Dynamics as Evaluative Feedback Mechanism}
 %NOT SURE THIS SHOULD BE HERE AT ALL..?
 	
 
-Information measures on a stream of symbols can form a feedback mechanism; a rudamentary `critic' of sorts. 
-For instance symbol by symbol measure of predictive information rate, entropy rate and redundancy could tell us if a stream of symbols is currently `boring', either because it is too repetitive, or because it is too chaotic.  
-Such feedback would be oblivious to more long term and large scale structures, but it nonetheless could be provide a composer valuable insight on the short term properties of a work.  
-This could not only be used for the evaluation of pre-composed streams of symbols, but could also provide real-time feedback in an improvisatory setup.  	
+Information measures on a stream of symbols can form a feedback mechanism; a
+rudamentary `critic' of sorts.  For instance symbol by symbol measure of predictive
+information rate, entropy rate and redundancy could tell us if a stream of symbols
+is currently `boring', either because it is too repetitive, or because it is too
+chaotic.  Such feedback would be oblivious to more long term and large scale
+structures, but it nonetheless could be provide a composer valuable insight on
+the short term properties of a work.  This could not only be used for the
+evaluation of pre-composed streams of symbols, but could also provide real-time
+feedback in an improvisatory setup.
 
 \section{Musical Preference and Information Dynamics}
-We are carrying out a study to investigate the relationship between musical preference and the information dynamics models, the experimental interface a simplified version of the screen-based Melody Triangle.  
-Participants are asked to use this music pattern generator under various experimental conditions in a composition task.  
-The data collected includes usage statistics of the system: where in the triangle they place the tokens, how long they leave them there and the state of the system when users, by pressing a key, indicate that they like what they are hearing.  
-As such the experiments will help us identify any correlation between the information theoretic properties of a stream and its perceived aesthetic worth.  
+We are carrying out a study to investigate the relationship between musical
+preference and the information dynamics models, the experimental interface a
+simplified version of the screen-based Melody Triangle.  Participants are asked
+to use this music pattern generator under various experimental conditions in a
+composition task.  The data collected includes usage statistics of the system:
+where in the triangle they place the tokens, how long they leave them there and
+the state of the system when users, by pressing a key, indicate that they like
+what they are hearing.  As such the experiments will help us identify any
+correlation between the information theoretic properties of a stream and its
+perceived aesthetic worth.
 
 
 %\emph{comparable system}  Gordon Pask's Musicolor (1953) applied a similar notion
 %of boredom in its design.  The Musicolour would react to audio input through a
 %microphone by flashing coloured lights.  Rather than a direct mapping of sound