[lilypond.git] / Documentation / tex / lilypond-overview.doc

%-*-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 PAPER 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{mudela}[verbatim]
      \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: