3 \documentclass{article}
5 \def\postMudelaExample{\setlength{\parindent}{1em}}
6 \title{LilyPond, a Music Typesetter}
8 \usepackage{musicnotes}
16 \section{Introduction}
18 The Internet has become a popular medium for collaborative work on
19 information. Its success is partly due to its use of simple, text-based
20 formats. Examples of these formats are HTML and \LaTeX. Anyone can
21 produce or modify such files using nothing but a text editor, they are
22 easily processed with run-of-the-mill text tools, and they can be
23 integrated into other text-based formats.
25 Software for processing this information and presenting these formats
26 in an elegant form is available freely (Netscape, \LaTeX, etc.).
27 Ubiquitousness of the software and simplicity of the formats have
28 revolutionised the way people publish text-based information
31 In the field of performed music, where the presentation takes the form
32 of sheet music, such a revolution has not started yet. Let us review
33 some alternatives that have been available for transmitting sheet
36 \item MIDI\cite{midi}. This format was designed for interchanging performances
37 of music; one should think of it as a glorified tape recorder
38 format. It needs dedicated editors, since it is binary. It does
39 not provide enough information for producing musical scores: some of
40 the abstract musical content of what is performed is thrown away.
42 \item PostScript\cite{Postscript}. This format is a printer control
43 language. Printed musical scores can be transmitted in PostScript,
44 but once a score is converted to PostScript, it is virtually
45 impossible to modify the score in a meaningful way.
47 \item Formats for various notation programs. Notation programs either
48 work with binary formats (e.g., NIFF\cite{niff-web}), need specific
49 platforms (e.g., Sibelius\cite{sibelius}, Score\cite{score}), are
50 proprietary or non-portable tools themselves (idem), produce
51 inadequate output (e.g., MUP\cite{mup}), are based on graphical
52 content (e.g., MusixTeX\cite{musixtex1}), or limit themselves to
53 specific subdomains (e.g., ABC\cite{abc2mtex}).
55 \item SMDL\cite{smdl-web}. This is a very rich ASCII format, that is
56 designed for storing many types of music. Unfortunately, there is
57 no implementation of a program to print music from SMDL available.
58 Moreover, SMDL is so verbose, that it is not suitable for human
61 \item TAB\cite{tablature-web}. Tab (short for tablature) is a popular
62 format, for interchanging music over e-mail, but it can only be used
66 In summary, sheet music is not published and edited on a wide scale
67 across the internet because no format for music
68 interchange exists that is:
70 \item open, i.e., with publically available specifications.
71 \item based on ASCII, and therefore suitable for human consumption and
73 \item rich enough for producing publication quality sheet music from
75 \item based on musical content (unlike, for example, PostScript), and
76 therefore suitable for making modifications.
77 \item accompanied by tools for processing it that are freely available
78 across multiple platforms.
82 With the creation of LilyPond, we have tried to create both a
83 convenient format for storing sheet music, and a portable,
84 high-quality implementation of a compiler, that compiles the input
85 into a printable score. You can find a small example of LilyPond
86 input along with output in Figure~\ref{fig:intro-fig}.
90 \begin{mudela}[verbatim]
94 \transpose c'' { c4 c4 g4 g4 a4 a4 g2 }
95 { \clef "bass"; c4 c'4
96 \type Staff <e'2 {\stemdown c'4 c'4}> f'4 c'4 e'4 c'4 }
103 \caption{A small example of LilyPond input}
104 \label{fig:intro-fig}
110 The input language encodes musical events (such as notes and rests) on
111 the basis of their time-ordering. For example, the grammar includes
112 constructs that specify that notes start simultaneous and that notes
113 are to be played in sequence. In this encoding some context that is
114 present in sheet music is lost.
116 The compiler reconstructs the notation from the encoded music. Its
117 operation comprises four different steps (see
118 Figure~\ref{fig:intro-steps}).
121 \item[Parsing] During parsing, the input is converted in a syntax tree.
123 \item[Interpreting] In the \emph{interpreting} step, it is determined
124 which symbols have to be printed. Objects that correspond to
125 notation (\emph{Graphical objects}) are created from the syntax tree
126 in this phase. Generally speaking, for every symbol printed there is
127 one graphical object. These objects are incomplete: their position
128 and their final shape is unknown.
130 The context that was lost by encoding the input in a language is
131 reconstructed during this conversion.
132 \item[Formatting] The next step is determing where symbols are to be
133 placed, this is called \emph{formatting}.
135 Finally, all Graphical objects are outputted as PostScript or \TeX\ code.
138 \def\staffsym{\vbox to 16pt{
139 \hbox{\vrule width 1cm depth .2pt height .2pt}\nointerlineskip
141 \hbox{\vrule width 1cm depth .2pt height .2pt}\nointerlineskip
143 \hbox{\vrule width 1cm depth .2pt height .2pt}\nointerlineskip
145 \hbox{\vrule width 1cm depth .2pt height .2pt}\nointerlineskip
147 \hbox{\vrule width 1cm depth .2pt height .2pt}\nointerlineskip
150 \def\vspacer{\vbox to 20pt{\vss}}
152 \def\spacedhbox#1{\hbox{\ #1\ }}
154 {\spacedhbox{Input}\atop \hbox{\texttt{\{c8 c8\}}}} {\spacedhbox{Parsing}\atop\longrightarrow}
155 {\spacedhbox{Syntax tree}\atop\spacedhbox{\textsf{Sequential(Note,Note)}}}
156 {\spacedhbox{Interpreting}\atop\longrightarrow}\\
158 {\spacedhbox{Graphic objects}\atop\spacedhbox{\texttrebleclef \textquarterhead\texteighthflag\textquarterhead\texteighthflag \staffsym }}
159 {\spacedhbox{Formatting}\atop\longrightarrow}
160 {\spacedhbox{Formatted objects}\atop\hbox{
164 {\spacedhbox{Outputting}\atop\longrightarrow}
165 {\spacedhbox{PostScript code}\atop\hbox{\texttt{\%!PS-Adobe}\ldots}}
167 \caption{Parsing, Interpreting, Formatting and Outputting}
168 \label{fig:intro-steps}
172 The second step, the interpretation phase of the compiler, can be
173 manipulated as a separate entity: the interpretation process is
174 composed of many separate modules, and the behaviour of the modules is
175 parameterised. By recombining these interpretation modules,
176 and changing parameter settings, the same piece of music can be
177 printed differently, as is shown in Figure~\ref{fig:intro-interpret}.
179 This makes it easy to extend the program. Moreover, this enables the
180 same music to be printed in different versions, e.g., in a conductors
181 score and in extracted parts.
190 \transpose c'' { c4 c4 g4 g4 a4 a4 g2 }
191 { \clef "bass"; c4 c'4
192 \type Staff <e'2 {\stemdown c'4 c'4}> f'4 c'4 e'4 c'4 }
195 linewidth = -1.0\cm ;
198 \remove "Stem_engraver";
202 numberOfStaffLines = 3;
207 \caption{The interpretation phase can be manipulated: the same
208 music as in Figure~\ref{fig:intro-fig} is interpreted
209 differently: three staff lines and no stems.}
210 \label{fig:intro-interpret}
216 \section{Preliminaries}
218 To understand the rest of the article, it is necessary to know
219 something about music notation and music typography. Since both
220 communicate music, we will explain some characteristics of instruments
221 and western music that motivate some notational constructs.
225 Music notation is meant to be read by human performers. They sing or
226 play instruments that can produce sounds of different pitches. These
227 sounds are called \emph{notes}. Additionally, the sounds can be
228 articulated in differents ways, e.g., staccato (short and separated)
229 or legato (fluently bound together). The loudness of the notes can
230 also be varied. Changes in loudness are called \emph{dynamics}.
232 Silence is also an element of music. The musical terminology for
233 silence within music is \emph{rest}.
235 The basic unit of pitch is the \emph{octave}. The octave corresponds
236 to a frequency ratio of 1:2. For example the pitch denoted by a'
237 (frequency: 440 hertz) is one octave lower than a'' (frequency: 880
238 hertz). Various instruments have a limited \emph{pitch range}, for
239 example, a trumpet has a range of about 2.5 octaves. Not all
240 instruments have ranges in the same register: a tuba also has a range
241 of 2.5 octaves, but the range of the tuba is much lower.
243 Musicology has a confusing mix of relative and absolute measures for
244 pitches: the term `octave' refers to both a difference between two
245 pitches (the frequency ratio of 1:2), and to a range of pitches. For
246 example, the term `[eengestreept] octave' refers to the pitch range
247 between 261.6 Hz and 523.3 Hz.
250 The octave is divided into smaller pitch steps. In modern western
251 music, every octave is divided into twelve approximately equidistant
252 pitch steps, and each step is called a \emph{semitone}. Usually, the
253 pitches in a musical piece come from a smaller subset of these twelve
254 possible pitches. This smaller subset along with the musical
255 functions fo the pitches is called the
256 \emph{tonality}\footnote{Tonality also refers to the relations between
257 and functions of certain pitches. Since these do not have any
258 impact on notation, we ignore this} of the piece.
261 The standard tonality that forms the basis of music notation
262 (the key of C major) is a set of seven pitches within every octave.
263 Each of these seven is denoted by a name. In English, these are names
264 are (in rising pitch) denoted by c, d, e, f, g, a and b. Pitches that
265 are a semitone higher or lower than one of these seven can be
266 represented by suffixing the name with `sharp' or `flat'
267 respectively (this is called an \emph{chromatic alteration}).
269 A pitch therefore can be fully specified by a combination of the
270 octave number, the note name and a chromatic alteration.
271 Figure~\ref{fig:intro-pitches} shows the relation between names and
281 \caption{Pitches in western music. The octave number is denoted
283 \label{fig:intro-pitches}
287 Many instruments can produce more than one note at the same time, e.g.
288 pianos and guitars. When more notes are played simultaneously, they
289 form a so-called \emph{chord}.
291 The unit of duration is the \emph{beat}. When playing, the tempo is
292 determined by setting the number of beats per minute. In western
293 music, beats are often stressed in a regular pattern: for example
294 Waltzes have a stress pattern that is strong-weak-weak, i.e. every
295 note that starts on a `strong' beat is louder and has more pronounced
296 articulation. This stress pattern is called \emph{meter}.
298 \subsection{Music notation}
300 Music notation is a system that tries to represent musical ideas
301 through printed symbols. Music notation has no precise definition,
302 but most conventions have described in reference manuals on music
303 notation\cite{read-notation}.
305 In music notation, sounds and silences are represented by symbols that
306 are called note and rest respectively.\footnote{These names serve a
307 double purpose: the same terms are used to denote the musical
308 concepts.} The shape of notes and rests indicates their duration
309 (See figure~\ref{noteshapes}) relative to the whole note.
315 \notes \transpose c''{ c\longa*1/4 c\breve*1/2 c1 c2 c4 c8 c16 c32 c64 }
319 \remove "Staff_symbol_engraver";
320 \remove "Time_signature_engraver";
321 \remove "Bar_engraver";
322 \remove "Clef_engraver";
330 \notes \transpose c''{ r\longa*1/4 r\breve*1/2 r1 r2 r4 r8 r16 r32 r64 }
334 \remove "Staff_symbol_engraver";
335 \remove "Time_signature_engraver";
336 \remove "Bar_engraver";
337 \remove "Clef_engraver";
343 \caption{Note and rest shapes encode the length. At the top notes
344 are shown, at the bottom rests. From left to right a quadruple
345 note (\emph{longa}), double (\emph{breve}), whole, half,
346 quarter, eigth, sixteenth, thirtysecond and sixtyfourth. Each
347 note has half of the duration of its predecessor.}
348 \label{fig:noteshapes}
352 Notes are printed in a grid of horizontal lines called \emph{staff} to
353 denote their pitch: each line represents the pitch of from the
354 standard scale (c, d, e, f, g, a, b). The reference point is the
355 \emph{clef}, eg., the treble clef marks the location of the $g^1$
356 pitch. The notes are printed in their time order, from left to right.
363 a4 b c d e f g a \clef bass;
364 a4 b c d e f g a \clef alto;
365 a4 b c d e f g a \clef treble;
367 \paper { linewidth = 15.\cm; }
370 \caption{Pitches ranging from $a, b, c',\ldots a'$, in different
371 clefs. From left right the bass, alto and treble clef are
377 The chromatic alterations are indicated by printing a flat sign or a
378 sharp sign in front of the note head. If these chromatic alterations
379 occur systematically (if they are part of the tonality of the piece),
380 then this indicated with a \emph{key signature}. This is a list of
381 sharp/flat signs which is printed next to the clef.
383 Articulation is notated by marking the note shapes wedges, hats and
384 dots all indicate specific articulations. If the notes are to be
385 bound fluently (legato), the note shapes are encompassed by a smooth
386 curve called \emph{slur},
391 c'4-> c'4-. g'4 ( b'4 ) g''4
393 \caption{Some articulations. From left to right: extra stress
394 (\emph{marcato}), short (staccato), slurred notes (legato).}
395 \label{fig:articulation}
401 Dynamics are notated in two ways: absolute dynamics are indicated by
402 letters: \textbf{f} (from Italian ``forte'') stands for loud,
403 \textbf{p} (from Italian ``piano'') means soft. Gradual changes in
404 loudness are notated by (de)crescendos. These are hairpin like shapes
410 g'4\pp \< g'4 \! g'4 \ff \> g'4 g' \! g'\ppp
412 \caption{Dynamics: start very soft (pp), grow to loud (ff) and
413 decrease to extremely soft (ppp)}
419 The meter is indicated by barlines: every start of the stress pattern
420 is preceded by a vertical line, the \emph{bar line}. The space
421 between two bar lines is called measure. It is therefore the unit of
422 the rhythmic pattern.
424 The time signature also indicates what kind of rhythmic pattern is
425 desired. The time signature takes the form of two numbers stacked
426 vertically. The top number is the number of beats in one measure, the
427 bottom number is the duration (relative to the whole note) of the note
428 that takes one beat. Example: 2/4 time signature means ``two beats
429 per measure, and a quarter note takes one beat''
431 Chords are written by attaching multiple note heads to one stem. When
432 the composer wants to emphasize the horizontal relationships between
433 notes, the simultaneous notes can be written as voices (where every
434 note head has its own stem). A small example is given in
435 Figure~\ref{fig:simultaneous}.
440 \relative c'' {\time 2/4; <c4 e> <d f>
441 \type Staff < \type Voice = VA{
446 \stemup e4 f g8 g4 g8 } >
449 \caption{Notes sounding together. Chord notation (left, before
450 the bar line) emphasizes vertical relations, voice notation
451 emphasizes horizontal relations. Separate voices needn't have
452 synchronous rhythms (third measure).
454 \label{fig:simultaneous}
458 Separate voices do not have to share one rhythmic pattern---this is
459 also demonstrated in Figure~\ref{fig:simultaneous}--- they are in a sense%vaag
460 independent. A different way to express this in notation, is by
461 printing each voice on a different staff. This is customary when
462 writing for piano (both left and right hand have a staff of their own)
463 and for ensemble (every instrument has a staff of its own).
467 \subsection{Music typography}
469 Music typography is the art of placing symbols in esthetically
470 pleasing configuration. Little is explicitly known about music
471 typography. There are only a few reference works
472 available\cite{ross,wanske}. Most of the knowledge of this art has
473 been transmitted verbally, and was subsequently lost.
475 The motivation behind choices in typography is to represent the idea
476 as clearly as possible. Among others, this results in the following
479 \item The printed score should use visual hints to accentuate the
481 \item The printed score should not contain distracting elements, such
482 as large empty regions or blotted regions.
485 An example of the first guideline in action is the horizontal spacing.
486 The amount of space following a note should reflect the duration of
487 that note: short notes get a small amount of space, long notes larger
488 amounts. Such spacing constraints can be quite subtle, for the
489 ``amount of space'' is only the impression that should be conveyed; there
490 has to be some correction for optical illusions. See
491 Figure~\ref{fig:spacing}.
496 \relative c'' { \time 3/4; c16 c c c c8 c8 | f4 f, f' }
498 \caption{Spacing conveys information about duration. Sixteenth
499 notes at the left get less space than quarter notes in the
500 middle. Spacing is ``visual'', there should be more space
501 after the first note of the last measure, and less after second. }
506 Another clearly visible example of music typography is visible in
507 collisions. When chords or separate voices are printed, the notes
508 that start at the same time should be printed aligned (ie., with the
509 same $x$ position). If the pitches are close to each other, the note
510 heads would collide. To prevent this, some notes (or note heads) have
511 to be shifted horizontally. An example of this is given in Figure~\ref{fig:collision}.
518 \label{fig:collision}
522 \bibliographystyle{hw-plain}
523 \bibliography{engraving,boeken,colorado,computer-notation,other-packages}
529 The complexity of music notation was tackled by adopting a modular
530 design: both the formatting system (which encodes the esthetic rules of
531 notation), and the interpretation system (which encodes the semantic
532 rules) are highly modular.
535 The difficulty in creating a format for music notation is rooted in
536 the fact that music is multi dimensional: each sound has its own
537 duration, pitch, loudness and articulation. Additionally, multiple
538 sounds may be played simultaneously. Because of this, there is no
539 obvious way to ``flatten'' music into a context-free language.
541 The difficulty in creating a printing engine is rooted in the fact
542 that music notation complicated: it is very large graphical
543 ``language'' with many arbitrary esthetic and semantic conventions.
544 Building a system that formats full fledged musical notation is a
545 challenge in itself, regardless of whether it is part of a compiler or
548 The fact that music and its notation are of a different nature,
549 implies that the conversion between input notation is non-trivial.
551 In LilyPond we solved the above problem in the following way: