--- /dev/null
+%-*-LaTeX-*-
+
+\documentclass{article}
+\usepackage{a4}
+\def\postMudelaExample{\setlength{\parindent}{1em}}
+\title{LilyPond, a Music Typesetter}
+\author{HWN}
+\usepackage{musicnotes}
+\usepackage{graphics}
+
+
+\begin{document}
+\maketitle
+
+[THIS IS WORK IN PROGRESS. THIS IS NOT FINISHED]
+
+% -*-LaTeX-*-
+\section{Introduction}
+
+The Internet has become a popular medium for collaborative work on
+information. Its success is partly due to its use of simple, text-based
+formats. Examples of these formats are HTML and \LaTeX. Anyone can
+produce or modify such files using nothing but a text editor, they are
+easily processed with run-of-the-mill text tools, and they can be
+integrated into other text-based formats.
+
+Software for processing this information and presenting these formats
+in an elegant form is available freely (Netscape, \LaTeX, etc.).
+Ubiquitousness of the software and simplicity of the formats have
+revolutionised the way people publish text-based information
+nowadays.
+
+In the field of performed music, where the presentation takes the form
+of sheet music, such a revolution has not started yet. Let us review
+some alternatives that have been available for transmitting sheet
+music until now:
+\begin{itemize}
+\item MIDI\cite{midi}. This format was designed for interchanging performances
+ of music; one should think of it as a glorified tape recorder
+ format. It needs dedicated editors, since it is binary. It does
+ not provide enough information for producing musical scores: some of
+ the abstract musical content of what is performed is thrown away.
+
+\item PostScript\cite{Postscript}. This format is a printer control
+ language. Printed musical scores can be transmitted in PostScript,
+ but once a score is converted to PostScript, it is virtually
+ impossible to modify the score in a meaningful way.
+
+\item Formats for various notation programs. Notation programs either
+ work with binary formats (e.g., NIFF\cite{niff-web}), need specific
+ platforms (e.g., Sibelius\cite{sibelius}), are proprietary or
+ non-portable tools themselves (idem), produce inadequate output
+ (e.g., MUP\cite{mup}), are based on graphical content (e.g.,
+ MusixTeX\cite{musixtex1}), limit themselves to specific subdomains
+ (e.g., ABC\cite{abc2mtex}), or require considerable skill and
+ knowledge to use (e.g., SCORE\cite{score})
+
+\item SMDL\cite{smdl-web}. This is a very rich ASCII format, that is
+ designed for storing many types of music. Unfortunately, there is
+ no implementation of a program to print music from SMDL available.
+ Moreover, SMDL is so verbose, that it is not suitable for human
+ production.
+
+\item TAB\cite{tablature-web}. Tab (short for tablature) is a popular
+ format, for interchanging music over e-mail, but it can only be used
+ for guitar music.
+\end{itemize}
+
+In summary, sheet music is not published and edited on a wide scale
+across the internet because no format for music
+interchange exists that is:
+\begin{itemize}
+\item open, i.e., with publically available specifications.
+\item based on ASCII, and therefore suitable for human consumption and
+ production.
+\item rich enough for producing publication quality sheet music from
+ it.
+\item based on musical content (unlike, for example, PostScript), and
+ therefore suitable for making modifications.
+\item accompanied by tools for processing it that are freely available
+ across multiple platforms.
+\end{itemize}
+
+
+With the creation of LilyPond, we have tried to create both a
+convenient format for storing sheet music, and a portable,
+high-quality implementation of a compiler, that compiles the input
+into a printable score. You can find a small example of LilyPond
+input along with output in Figure~\ref{fig:intro-fig}.
+%
+\begin{figure}[htbp]
+ \begin{center}
+\begin[verbatim]{mudela}
+ \score {
+ \notes
+ \context GrandStaff <
+ \transpose c'' { c4 c4 g4 g4 a4 a4 g2 }
+ { \clef "bass"; c4 c'4
+ \context Staff <e'2 {\stemdown c'4 c'4}> f'4 c'4 e'4 c'4 }
+ >
+ \paper {
+ linewidth = -1.0\cm ;
+ }
+ }
+\end{mudela}
+ \caption{A small example of LilyPond input}
+ \label{fig:intro-fig}
+ \end{center}
+\end{figure}
+%
+
+
+The input language encodes musical events (such as notes and rests) on
+the basis of their time-ordering. For example, the grammar includes
+constructs that specify that notes start simultaneous and that notes
+are to be played in sequence. In this encoding some context that is
+present in sheet music is lost.
+
+The compiler reconstructs the notation from the encoded music. Its
+operation comprises four different steps (see
+Figure~\ref{fig:intro-steps}).
+
+\begin{description}
+\item[Parsing] During parsing, the input is converted in a syntax tree.
+
+\item[Interpreting] In the \emph{interpreting} step, it is determined
+ which symbols have to be printed. Objects that correspond to
+ notation (\emph{Graphical objects}) are created from the syntax tree
+ in this phase. Generally speaking, for every symbol printed there is
+ one graphical object. These objects are incomplete: their position
+ and their final shape is unknown.
+
+ The context that was lost by encoding the input in a language is
+ reconstructed during this conversion.
+\item[Formatting] The next step is determing where symbols are to be
+ placed, this is called \emph{formatting}.
+\item[Outputting]
+ Finally, all Graphical objects are outputted as PostScript or \TeX\ code.
+\end{description}
+
+\def\staffsym{\vbox to 16pt{
+ \hbox{\vrule width 1cm depth .2pt height .2pt}\nointerlineskip
+ \vfil
+ \hbox{\vrule width 1cm depth .2pt height .2pt}\nointerlineskip
+ \vfil
+ \hbox{\vrule width 1cm depth .2pt height .2pt}\nointerlineskip
+ \vfil
+ \hbox{\vrule width 1cm depth .2pt height .2pt}\nointerlineskip
+ \vfil
+ \hbox{\vrule width 1cm depth .2pt height .2pt}\nointerlineskip
+}}
+
+\def\vspacer{\vbox to 20pt{\vss}}
+\begin{figure}[h]
+\def\spacedhbox#1{\hbox{\ #1\ }}
+\begin{eqnarray*}
+ {\spacedhbox{Input}\atop \hbox{\texttt{\{c8 c8\}}}} {\spacedhbox{Parsing}\atop\longrightarrow}
+ {\spacedhbox{Syntax tree}\atop\spacedhbox{\textsf{Sequential(Note,Note)}}}
+ {\spacedhbox{Interpreting}\atop\longrightarrow}\\
+ \vspacer\\
+ {\spacedhbox{Graphic objects}\atop\spacedhbox{\texttrebleclef \textquarterhead\texteighthflag\textquarterhead\texteighthflag \staffsym }}
+ {\spacedhbox{Formatting}\atop\longrightarrow}
+ {\spacedhbox{Formatted objects}\atop\hbox{
+ \mudela{c''8 c''8}
+ }}\\
+\vspacer\\
+ {\spacedhbox{Outputting}\atop\longrightarrow}
+ {\spacedhbox{PostScript code}\atop\hbox{\texttt{\%!PS-Adobe}\ldots}}
+\end{eqnarray*}
+ \caption{Parsing, Interpreting, Formatting and Outputting}
+ \label{fig:intro-steps}
+\end{figure}
+
+
+The second step, the interpretation phase of the compiler, can be
+manipulated as a separate entity: the interpretation process is
+composed of many separate modules, and the behaviour of the modules is
+parameterised. By recombining these interpretation modules,
+and changing parameter settings, the same piece of music can be
+printed differently, as is shown in Figure~\ref{fig:intro-interpret}.
+
+This makes it easy to extend the program. Moreover, this enables the
+same music to be printed in different versions, e.g., in a conductors
+score and in extracted parts.
+
+
+\begin{figure}[h]
+ \begin{center}
+ \begin{mudela}
+ \score {
+ \notes
+ \context GrandStaff <
+ \transpose c'' { c4 c4 g4 g4 a4 a4 g2 }
+ { \clef "bass"; c4 c'4
+ \context Staff <e'2 {\stemdown c'4 c'4}> f'4 c'4 e'4 c'4 }
+ >
+ \paper {
+ linewidth = -1.0\cm ;
+ \translator {
+ \VoiceContext
+ \remove "Stem_engraver";
+ }
+ \translator {
+ \StaffContext
+ numberOfStaffLines = 3;
+ }
+ }
+ }
+ \end{mudela}
+ \caption{The interpretation phase can be manipulated: the same
+ music as in Figure~\ref{fig:intro-fig} is interpreted
+ differently: three staff lines and no stems.}
+ \label{fig:intro-interpret}
+ \end{center}
+\end{figure}
+
+
+
+\section{Preliminaries}
+
+To understand the rest of the article, it is necessary to know
+something about music notation and music typography. Since both
+communicate music, we will explain some characteristics of instruments
+and western music that motivate some notational constructs.
+
+\subsection{Music}
+
+Music notation is meant to be read by human performers. They sing or
+play instruments that can produce sounds of different pitches. These
+sounds are called \emph{notes}. Additionally, the sounds can be
+articulated in differents ways, e.g., staccato (short and separated)
+or legato (fluently bound together). The loudness of the notes can
+also be varied. Changes in loudness are called \emph{dynamics}.
+
+Silence is also an element of music. The musical terminology for
+silence within music is \emph{rest}.
+
+The basic unit of pitch is the \emph{octave}. The octave corresponds
+to a frequency ratio of 1:2. For example the pitch denoted by a'
+(frequency: 440 hertz) is one octave lower than a'' (frequency: 880
+hertz). Various instruments have a limited \emph{pitch range}, for
+example, a trumpet has a range of about 2.5 octaves. Not all
+instruments have ranges in the same register: a tuba also has a range
+of 2.5 octaves, but the range of the tuba is much lower.
+
+Musicology has a confusing mix of relative and absolute measures for
+pitches: the term `octave' refers to both a difference between two
+pitches (the frequency ratio of 1:2), and to a range of pitches. For
+example, the term `[eengestreept] octave' refers to the pitch range
+between 261.6 Hz and 523.3 Hz.
+
+
+The octave is divided into smaller pitch steps. In modern western
+music, every octave is divided into twelve approximately equidistant
+pitch steps, and each step is called a \emph{semitone}. Usually, the
+pitches in a musical piece come from a smaller subset of these twelve
+possible pitches. This smaller subset along with the musical
+functions fo the pitches is called the
+\emph{tonality}\footnote{Tonality also refers to the relations between
+ and functions of certain pitches. Since these do not have any
+ impact on notation, we ignore this} of the piece.
+
+
+The standard tonality that forms the basis of music notation
+(the key of C major) is a set of seven pitches within every octave.
+Each of these seven is denoted by a name. In English, these are names
+are (in rising pitch) denoted by c, d, e, f, g, a and b. Pitches that
+are a semitone higher or lower than one of these seven can be
+represented by suffixing the name with `sharp' or `flat'
+respectively (this is called an \emph{chromatic alteration}).
+
+A pitch therefore can be fully specified by a combination of the
+octave number, the note name and a chromatic alteration.
+Figure~\ref{fig:intro-pitches} shows the relation between names and
+frequencies.
+
+
+
+
+\begin{figure}[h]
+ \begin{center}
+ [te doen]
+ \end{center}
+ \caption{Pitches in western music. The octave number is denoted
+ by a superscript.}
+ \label{fig:intro-pitches}
+\end{figure}
+
+
+Many instruments can produce more than one note at the same time, e.g.
+pianos and guitars. When more notes are played simultaneously, they
+form a so-called \emph{chord}.
+
+The unit of duration is the \emph{beat}. When playing, the tempo is
+determined by setting the number of beats per minute. In western
+music, beats are often stressed in a regular pattern: for example
+Waltzes have a stress pattern that is strong-weak-weak, i.e. every
+note that starts on a `strong' beat is louder and has more pronounced
+articulation. This stress pattern is called \emph{meter}.
+
+\subsection{Music notation}
+
+Music notation is a system that tries to represent musical ideas
+through printed symbols. Music notation has no precise definition,
+but most conventions have described in reference manuals on music
+notation\cite{read-notation}.
+
+In music notation, sounds and silences are represented by symbols that
+are called note and rest respectively.\footnote{These names serve a
+ double purpose: the same terms are used to denote the musical
+ concepts.} The shape of notes and rests indicates their duration
+(See figure~\ref{noteshapes}) relative to the whole note.
+
+
+\begin{figure}[h]
+ \begin{center}
+\begin{mudela}
+ \score {
+ \notes \transpose c''{ c\longa*1/4 c\breve*1/2 c1 c2 c4 c8 c16 c32 c64 }
+ \paper {
+ \translator {
+ \StaffContext
+ \remove "Staff_symbol_engraver";
+ \remove "Time_signature_engraver";
+% \remove "Bar_engraver";
+ \remove "Clef_engraver";
+ }
+linewidth = -1.;
+ }
+}
+\end{mudela}
+\begin{mudela}
+ \score {
+ \notes \transpose c''\context Staff { r\longa*1/4 r\breve*1/2 r1 r2 r4 r8 r16 r32 r64 }
+ \paper {
+ \translator {
+ \StaffContext
+ \remove "Staff_symbol_engraver";
+ \remove "Time_signature_engraver";
+% \remove "Bar_engraver";
+ \remove "Clef_engraver";
+ }
+ linewidth = -1.;
+ }
+}
+\end{mudela}
+ \caption{Note and rest shapes encode the length. At the top notes
+ are shown, at the bottom rests. From left to right a quadruple
+ note (\emph{longa}), double (\emph{breve}), whole, half,
+ quarter, eigth, sixteenth, thirtysecond and sixtyfourth. Each
+ note has half of the duration of its predecessor.}
+ \label{fig:noteshapes}
+\end{center}
+\end{figure}
+
+
+Notes are printed in a grid of horizontal lines called \emph{staff} to
+denote their pitch: each line represents the pitch of from the
+standard scale (c, d, e, f, g, a, b). The reference point is the
+\emph{clef}, eg., the treble clef marks the location of the $g^1$
+pitch. The notes are printed in their time order, from left to right.
+
+
+\begin{figure}[h]
+ \begin{center}
+ \begin{mudela}
+ \score { \notes {
+ a4 b c d e f g a \clef bass;
+ a4 b c d e f g a \clef alto;
+ a4 b c d e f g a \clef treble;
+ }
+ \paper { linewidth = 15.\cm; }
+ }
+ \end{mudela}
+ \caption{Pitches ranging from $a, b, c',\ldots a'$, in different
+ clefs. From left right the bass, alto and treble clef are
+ featured.}
+ \label{fig:pitches}
+ \end{center}
+\end{figure}
+
+The chromatic alterations are indicated by printing a flat sign or a
+sharp sign in front of the note head. If these chromatic alterations
+occur systematically (if they are part of the tonality of the piece),
+then this indicated with a \emph{key signature}. This is a list of
+sharp/flat signs which is printed next to the clef.
+
+Articulation is notated by marking the note shapes wedges, hats and
+dots all indicate specific articulations. If the notes are to be
+bound fluently (legato), the note shapes are encompassed by a smooth
+curve called \emph{slur},
+
+\begin{figure}[h]
+ \begin{center}
+ \begin{mudela}
+ c'4-> c'4-. g'4 ( b'4 ) g''4
+ \end{mudela}
+ \caption{Some articulations. From left to right: extra stress
+ (\emph{marcato}), short (staccato), slurred notes (legato).}
+ \label{fig:articulation}
+ \end{center}
+\end{figure}
+
+
+
+Dynamics are notated in two ways: absolute dynamics are indicated by
+letters: \textbf{f} (from Italian ``forte'') stands for loud,
+\textbf{p} (from Italian ``piano'') means soft. Gradual changes in
+loudness are notated by (de)crescendos. These are hairpin like shapes
+below the staff.
+
+\begin{figure}[h]
+ \begin{center}
+ \begin{mudela}
+ g'4\pp \< g'4 \! g'4 \ff \> g'4 g' \! g'\ppp
+ \end{mudela}
+ \caption{Dynamics: start very soft (pp), grow to loud (ff) and
+ decrease to extremely soft (ppp)}
+ \label{fig:dynamics}
+ \end{center}
+\end{figure}
+
+
+The meter is indicated by barlines: every start of the stress pattern
+is preceded by a vertical line, the \emph{bar line}. The space
+between two bar lines is called measure. It is therefore the unit of
+the rhythmic pattern.
+
+The time signature also indicates what kind of rhythmic pattern is
+desired. The time signature takes the form of two numbers stacked
+vertically. The top number is the number of beats in one measure, the
+bottom number is the duration (relative to the whole note) of the note
+that takes one beat. Example: 2/4 time signature means ``two beats
+per measure, and a quarter note takes one beat''
+
+Chords are written by attaching multiple note heads to one stem. When
+the composer wants to emphasize the horizontal relationships between
+notes, the simultaneous notes can be written as voices (where every
+note head has its own stem). A small example is given in
+Figure~\ref{fig:simultaneous}.
+
+\begin{figure}[h]
+ \begin{center}
+ \begin{mudela}
+ \relative c'' {\time 2/4; <c4 e> <d f>
+ \context Staff < \context Voice = VA{
+ \stemdown
+ c4 d
+ b16 b b b b b b b }
+ \context Voice = VB {
+ \stemup e4 f g8 g4 g8 } >
+ }
+ \end{mudela}
+ \caption{Notes sounding together. Chord notation (left, before
+ the bar line) emphasizes vertical relations, voice notation
+ emphasizes horizontal relations. Separate voices needn't have
+ synchronous rhythms (third measure).
+ }
+ \label{fig:simultaneous}
+ \end{center}
+\end{figure}
+
+Separate voices do not have to share one rhythmic pattern---this is
+also demonstrated in Figure~\ref{fig:simultaneous}--- they are in a sense%vaag
+independent. A different way to express this in notation, is by
+printing each voice on a different staff. This is customary when
+writing for piano (both left and right hand have a staff of their own)
+and for ensemble (every instrument has a staff of its own).
+
+
+
+\subsection{Music typography}
+
+Music typography is the art of placing symbols in esthetically
+pleasing configuration. Little is explicitly known about music
+typography. There are only a few reference works
+available\cite{ross,wanske}. Most of the knowledge of this art has
+been transmitted verbally, and was subsequently lost.
+
+The motivation behind choices in typography is to represent the idea
+as clearly as possible. Among others, this results in the following
+guidelines:
+\begin{itemize}
+\item The printed score should use visual hints to accentuate the
+ musical content
+\item The printed score should not contain distracting elements, such
+ as large empty regions or blotted regions.
+\end{itemize}
+
+An example of the first guideline in action is the horizontal spacing.
+The amount of space following a note should reflect the duration of
+that note: short notes get a small amount of space, long notes larger
+amounts. Such spacing constraints can be subtle, for the
+``amount of space'' is only the impression that should be conveyed; there
+has to be some correction for optical illusions. See
+Figure~\ref{fig:spacing}.
+
+\begin{figure}[h]
+ \begin{center}
+ \begin{mudela}
+ \relative c'' { \time 3/4; c16 c c c c8 c8 | f4 f, f' }
+ \end{mudela}
+ \caption{Spacing conveys information about duration. Sixteenth
+ notes at the left get less space than quarter notes in the
+ middle. Spacing is ``visual'', there should be more space
+ after the first note of the last measure, and less after second. }
+ \label{fig:spacing}
+ \end{center}
+\end{figure}
+
+Another example of music typography is clearly visible in collisions.
+When chords or separate voices are printed, the notes that start at
+the same time should be printed aligned (ie., with the same $x$
+position). If the pitches are close to each other, the note heads
+would collide. To prevent this, some notes (or note heads) have to be
+shifted horizontally. An example of this is given in
+Figure~\ref{fig:collision}.
+\begin{figure}[h]
+ \begin{center}
+ [todo]
+ \caption{Collisions}
+ \label{fig:collision}
+ \end{center}
+\end{figure}
+
+\bibliographystyle{hw-plain}
+\bibliography{engraving,boeken,colorado,computer-notation,other-packages}
+
+\section{Requirements}
+
+
+\section{Approach}
+
+\subsection{Input}
+
+The input format consists of combining a symbolic representation of
+music with style sheet that describes how the symbolic presentation
+can converted to notation. The symbolic representation is based on a
+context free language called \textsf{music}. Music is a recursively
+defined construction in the input language. It can be constructed by
+combining lists of \textsf{music} sequentially or parallel or from
+terminals like notes or lyrics.
+
+The grammar for \textsf{music} is listed below. It has been edited to
+leave out the syntactic and ergonomic details.
+
+\begin{center}
+ \begin{tabular}{ll}
+Music: & SimpleMusic\\
+ & $|$ REPEATED int Music ALTERNATIVE MusicList\\
+ & $|$ SIMULTANEOUS MusicList\\
+ & $|$ SEQUENTIAL MusicList\\
+ & $|$ CONTEXT STRING '=' STRING Music\\
+ & $|$ TIMES int int Music \\
+ & $|$ TRANSPOSE PITCH Music \\
+SimpleMusic: & $|$ Note\\
+ & $|$ Lyric\\
+ & $|$ Rest\\
+ & $|$ Chord\\
+ & $|$ Command\\
+Command: & METERCHANGE\\
+ & $|$ CLEFCHANGE\\
+ &$|$ PROPERTY STRING '=' STRING\\
+Chord: &PitchList DURATION\\
+Rest: &REST DURATION\\
+Lyric: &STRING DURATION\\
+Note: &PITCH DURATION\\
+\end{tabular}
+\end{center}
+
+The terminals are both purely musical concepts that have a duration,
+and take a non-zero amount of musical time, like notes and lyrics, and
+commands that behave as if they have no duration.\footnote{The
+ PROPERTY command is a generic mechanism for controlling the
+ interpretation, i.e. the musical style sheets. See [forward ref]}
+
+The nonterminal productions can
+\begin{itemize}
+\item Some productions combine multiple elements: one can specify that
+ element are to be played in sequence, simultaneously or repetitively.
+\item There are productions for transposing music, and for dilating
+ durations of music: the TIMES production can be used to encode a
+ triplet.\footnote{A triplet is a group of three notes marked by a
+ bracket, that are played 3/2 times faster.}
+\item
+ There are productions that give directions to the interpretation
+ engine (the CONTEXT production)
+\end{itemize}
+
+
+\section{Context in notation}
+
+Music notation relies heavily on context. Notational symbols do not
+have meaning if they are not surrounded by other context elements. In
+this section we give some examples how the reader uses this context do
+derive meaning of a piece of notation. We will focus on the prime
+example of context: the staff.
+
+A staff is the grid of five horizontal lines, but it contains more components :
+\begin{itemize}
+\item A staff can have a key signature (printed at the left)
+\item A staff can have a time signature (printed at the left)
+\item A staff has bar lines
+\item A staff has a clef (printed at the left)
+\end{itemize}
+
+It is still possible to print notes without these components, but one
+cannot determine the meaning of the notes.
+\begin{mudela}
+\score{
+\notes \relative c' { \time 2/4; g'4 c,4 a'4 f4 e c d2 }
+\paper {
+ linewidth = -1.;
+ \translator {
+ \StaffContext
+ \remove "Time_signature_engraver";
+% \remove "Bar_engraver";
+ \remove "Staff_symbol_engraver";
+ \remove "Clef_engraver";
+ \remove "Key_engraver";
+ }
+ }
+}
+\end{mudela}
+
+As you can see, you can still make out the general form of the melody
+and the rhythm that is to be played, but the notation is difficult to
+read and the musical information is not complete. The stress
+pattern in the notes can't be deduced from this output. For this, we
+need a time signature. Adding barlines helps with finding the strong
+and weak beats.
+\begin{mudela}
+\score {
+ \notes \relative c' { \time 2/4; g'4 c,4 a'4 f4 e c d2 }
+ \paper{
+ linewidth = -1.;
+\translator{
+ \StaffContext
+ \remove "Staff_symbol_engraver";
+ \remove "Clef_engraver";
+ \remove "Key_engraver";}
+ }
+ }
+\end{mudela}
+
+It is impossible to deduce the exact pitch of the notes. One needs a
+clef to do so. Staff lines help the eye in determining the vertical
+position of a note wrt. to the clef.
+\begin{mudela}
+\score {
+ \notes \relative c' {\clef alto; \time 2/4; g'4 c,4 a'4 f4 e c d2 }
+ \paper {
+ linewidth = -1.;
+ }
+}
+\end{mudela}
+
+Now you know the pitch of the notes: you look at the start of the line
+and see a clef, and with this clef, you can determine the notated pitches.
+You have found the em(context) in which the notation is to be
+interpreted!
+
+
+\section{Interpretation context}
+
+Context (clef, time signature etc.) determines the relationship
+between musical and its notation in notes. Because LilyPond writes
+notation, context works the other way around for LilyPond: with
+context a piece of music can be converted to notation.
+
+A reader remembers this context while reading the notation from left
+to right. By analogy, LilyPond constructs this context while
+constructing notes from left to right. This is what happens in the
+``Interpretation'' phase from~\ref{fig:intro-fig}. In LilyPond, the
+state of this context is a set of variables with their values; A staff
+context contains variables like
+
+\begin{itemize}
+\item current clef
+\item current time signature
+\item current key
+\end{itemize}
+
+These variables determine when and how clefs, time signatures, bar
+lines and accidentals are printed.
+
+
+Staff is not the only form of context in notation. In polyphonic
+music, the stem direction shows which notes form a voice: all notes of
+the same voice have stems pointing in the same direction. The value
+of this variable determines the appearance of the printed stems.
+
+In LilyPond ``Notation context'' is abstracted to a data structure
+that is used, constructed and modified during the interpretation
+phase. It contains context properties, and is responsible for
+creating notational elements: the staff context creates symbols for
+clefs, time signatures and key signatures. The Voice context creates
+stems, note heads.
+
+For the fragment of polyphonic music below,
+\begin{mudela}
+ \context Staff { c'4 < { \stemup c'4 } \context Voice = VB { \stemdown a4 } > }
+\end{mudela}
+A staff context is created. Within this staff context (which printed
+the clef), a Voice context is created, which prints the first note.
+Then, a second Voice context is created, with stem direction set to
+``up'', and the direction for the other is set to down. Both Voice
+contexts are still part of the same Staff context.
+
+In the same way, multiple staff scores are created: within the score
+context, multiple staff contexts are created. Every staff context
+creates the notation associated with a staff.
+
+\section{Discussion}
+
+
+
+\end{document}
+
+The complexity of music notation was tackled by adopting a modular
+design: both the formatting system (which encodes the esthetic rules of
+notation), and the interpretation system (which encodes the semantic
+rules) are highly modular.
+
+
+The difficulty in creating a format for music notation is rooted in
+the fact that music is multi dimensional: each sound has its own
+duration, pitch, loudness and articulation. Additionally, multiple
+sounds may be played simultaneously. Because of this, there is no
+obvious way to ``flatten'' music into a context-free language.
+
+The difficulty in creating a printing engine is rooted in the fact
+that music notation complicated: it is very large graphical
+``language'' with many arbitrary esthetic and semantic conventions.
+Building a system that formats full fledged musical notation is a
+challenge in itself, regardless of whether it is part of a compiler or
+an editor.
+
+The fact that music and its notation are of a different nature,
+implies that the conversion between input notation is non-trivial.
+
+In LilyPond we solved the above problem in the following way:
+
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