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<tr><td valign="middle" align="left" colspan="1">[<a href="Tutorial.html#Tutorial" title="Beginning of this chapter or previous chapter"> << Tutorial </a>]</td><td valign="middle" align="center" colspan="3">[<a href="index.html#Top" title="Cover (top) of document" rel="start">Top</a>][<a href="index_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="LilyPond-index.html#LilyPond-index" title="Index" rel="index">Index</a>][<a href="index_abt.html#SEC_About" title="About (help)" rel="help"> ? </a>]</td><td valign="middle" align="right" colspan="1">[<a href="Fundamental-concepts.html#Fundamental-concepts" title="Next chapter"> Fundamental concepts >> </a>]</td></tr><tr><td valign="middle" align="left" colspan="2">[<a href="Multiple-notes-at-once.html#Multiple-notes-at-once" title="Previous section in reading order" accesskey="p" rel="previous"> < Multiple notes at once </a>]</td><td valign="middle" align="center" colspan="1">[<a href="Multiple-notes-at-once.html#Multiple-notes-at-once" title="Up section" accesskey="u" rel="up"> Up : Multiple notes at once </a>]</td><td valign="middle" align="right" colspan="2">[<a href="Multiple-staves.html#Multiple-staves" title="Next section in reading order" accesskey="n" rel="next"> Multiple staves > </a>]</td></tr></table>
<a name="Music-expressions-explained"></a>
<h3 class="subsection">2.3.1 Music expressions explained</h3>
<a name="index-music-expression"></a>
<a name="index-expression_002c-music"></a>
<a name="index-compound-music-expression"></a>
<a name="index-music-expression_002c-compound"></a>
<p>In LilyPond input files, music is represented by <em>music
expressions</em>. A single note is a music expression:
</p>
<blockquote><pre class="verbatim">a4
</pre><p>
<a href="../a8/lily-1265379a.ly">
<img align="middle"
border="0"
src="../a8/lily-1265379a.png"
alt="[image of music]">
</a>
</p>
</blockquote>
<p>Enclosing a note in braces creates a <em>compound music
expression</em>. Here we have created a compound music expression
with two notes:
</p>
<blockquote><pre class="verbatim">{ a4 g4 }
</pre><p>
<a href="../72/lily-48c50cd8.ly">
<img align="middle"
border="0"
src="../72/lily-48c50cd8.png"
alt="[image of music]">
</a>
</p>
</blockquote>
<p>Putting a group of music expressions (e.g. notes) in braces means
that they are in sequence (i.e. each one follows the previous
one). The result is another music expression:
</p>
<blockquote><pre class="verbatim">{ { a4 g } f g }
</pre><p>
<a href="../03/lily-0832009b.ly">
<img align="middle"
border="0"
src="../03/lily-0832009b.png"
alt="[image of music]">
</a>
</p>
</blockquote>
<a name="Analogy_003a-mathematical-expressions"></a>
<h3 class="subheading">Analogy: mathematical expressions</h3>
<p>This mechanism is similar to mathematical formulas: a big formula
is created by composing small formulas. Such formulas are called
expressions, and they can contain other expressions, so you can
make arbitrarily complex and large expressions. For example,
</p>
<blockquote><pre class="example">1
1 + 2
(1 + 2) * 3
((1 + 2) * 3) / (4 * 5)
</pre></blockquote>
<p>This is a sequence of expressions, where each expression is
contained in the next (larger) one. The simplest expressions are
numbers, and larger ones are made by combining expressions with
operators (like <code>+</code>, <code>*</code> and <code>/</code>) and parentheses.
Like mathematical expressions, music expressions can be nested
arbitrarily deep, which is necessary for complex music like
polyphonic scores.
</p>
<a name="Simultaneous-music-expressions_003a-multiple-staves"></a>
<h3 class="subheading">Simultaneous music expressions: multiple staves</h3>
<a name="index-multiple-staves"></a>
<a name="index-staves_002c-multiple"></a>
<a name="index-polyphony-1"></a>
<a name="index-combining-expressions-in-parallel"></a>
<a name="index-parallel-expressions"></a>
<a name="index-expressions_002c-parallel"></a>
<a name="index-relative-notes-and-simultaneous-music"></a>
<a name="index-relative-notes-and-parallel-expressions"></a>
<a name="index-simultaneous-music-and-relative-notes"></a>
<a name="index-parallel-expressions-and-relative-notes"></a>
<a name="index-_003c_003c"></a>
<a name="index-_003c_003c-1"></a>
<a name="index-_003e_003e"></a>
<a name="index-_003e_003e-1"></a>
<a name="index-_003c_003c-_002e_002e_002e-_003e_003e"></a>
<a name="index-_003c_003c-_002e_002e_002e-_003e_003e-1"></a>
<p>Music Glossary: <a name="index-polyphony-2"></a>
<a href="../music-glossary/polyphony.html#polyphony">polyphony</a>.
</p>
<p>This technique is useful for <var>polyphonic</var> music. To
enter music with more voices or more staves, we combine
expressions in parallel. To indicate that two voices should play
at the same time, simply enter a simultaneous combination of music
expressions. A ‘simultaneous’ music expression is formed by
enclosing expressions inside <code><<</code> and <code>>></code>. In the
following example, three sequences (all containing two separate
notes) are combined simultaneously:
</p>
<blockquote><pre class="verbatim">\relative c'' {
<<
{ a4 g }
{ f e }
{ d b }
>>
}
</pre><p>
<a href="../72/lily-6ff397d7.ly">
<img align="middle"
border="0"
src="../72/lily-6ff397d7.png"
alt="[image of music]">
</a>
</p>
</blockquote>
<p>Note that we have indented each level of the input with a
different amount of space. LilyPond does not care how much (or
little) space there is at the beginning of a line, but indenting
LilyPond code like this makes it much easier for humans to read.
</p>
<table class="cartouche" border="1"><tr><td>
<p><b>Note:</b> each note is relative to the previous note in
the input, not relative to the <code>c''</code> in the initial
<code>\relative</code> command.
</p></td></tr></table>
<a name="Simultaneous-music-expressions_003a-single-staff"></a>
<h3 class="subheading">Simultaneous music expressions: single staff</h3>
<p>To determine the number of staves in a piece, LilyPond looks at
the beginning of the first expression. If is a single note, there
is one staff; if there is a simultaneous expression, there is more
than one staff.
</p>
<blockquote><pre class="verbatim">\relative c'' {
c2 <<c e>>
<< { e f } { c <<b d>> } >>
}
</pre><p>
<a href="../69/lily-a9e64f48.ly">
<img align="middle"
border="0"
src="../69/lily-a9e64f48.png"
alt="[image of music]">
</a>
</p>
</blockquote>
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<li><a name="toc-Preface-1" href="Preface.html#Preface">Preface</a> </li>
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<li class="toc_current"><a name="toc-Multiple-notes-at-once-1" href="Multiple-notes-at-once.html#Multiple-notes-at-once">2.3 Multiple notes at once</a>
<ul class="toc">
<li class="toc_current"><a name="toc-Music-expressions-explained-1" href="Music-expressions-explained.html#Music-expressions-explained">2.3.1 Music expressions explained</a> </li>
<li><a name="toc-Multiple-staves-1" href="Multiple-staves.html#Multiple-staves">2.3.2 Multiple staves</a> </li>
<li><a name="toc-Staff-groups-1" href="Staff-groups.html#Staff-groups">2.3.3 Staff groups</a> </li>
<li><a name="toc-Combining-notes-into-chords-1" href="Combining-notes-into-chords.html#Combining-notes-into-chords">2.3.4 Combining notes into chords</a> </li>
<li><a name="toc-Single-staff-polyphony-1" href="Single-staff-polyphony.html#Single-staff-polyphony">2.3.5 Single staff polyphony</a> </li>
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<li><a name="toc-Songs-1" href="Songs.html#Songs">2.4 Songs</a> </li>
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<ul class="toc">
<li><a name="toc-How-LilyPond-input-files-work-1" href="How-LilyPond-input-files-work.html#How-LilyPond-input-files-work">3.1 How LilyPond input files work</a> </li>
<li><a name="toc-Voices-contain-music-1" href="Voices-contain-music.html#Voices-contain-music">3.2 Voices contain music</a> </li>
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</ul>
</li>
<li><a name="toc-Working-on-LilyPond-projects-1" href="Working-on-LilyPond-projects.html#Working-on-LilyPond-projects">5. Working on LilyPond projects</a>
<ul class="toc">
<li><a name="toc-Suggestions-for-writing-LilyPond-input-files-1" href="Suggestions-for-writing-LilyPond-input-files.html#Suggestions-for-writing-LilyPond-input-files">5.1 Suggestions for writing LilyPond input files</a> </li>
<li><a name="toc-When-things-don_0027t-work-1" href="When-things-don_0027t-work.html#When-things-don_0027t-work">5.2 When things don’t work</a> </li>
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</ul>
</li>
<li><a name="toc-Templates-1" href="Templates.html#Templates">A. Templates</a>
<ul class="toc">
<li><a name="toc-Single-staff-1" href="Single-staff.html#Single-staff">A.1 Single staff</a> </li>
<li><a name="toc-Piano-templates-1" href="Piano-templates.html#Piano-templates">A.2 Piano templates</a> </li>
<li><a name="toc-String-quartet-2" href="String-quartet.html#String-quartet">A.3 String quartet</a> </li>
<li><a name="toc-Vocal-ensembles-1" href="Vocal-ensembles.html#Vocal-ensembles">A.4 Vocal ensembles</a> </li>
<li><a name="toc-Ancient-notation-templates-1" href="Ancient-notation-templates.html#Ancient-notation-templates">A.5 Ancient notation templates</a> </li>
<li><a name="toc-Jazz-combo-1" href="Jazz-combo.html#Jazz-combo">A.6 Jazz combo</a> </li>
<li><a name="toc-lilypond_002dbook-templates-1" href="lilypond_002dbook-templates.html#lilypond_002dbook-templates">A.7 lilypond-book templates</a> </li>
</ul>
</li>
<li><a name="toc-Scheme-tutorial-1" href="Scheme-tutorial.html#Scheme-tutorial">B. Scheme tutorial</a>
<ul class="toc">
<li><a name="toc-Tweaking-with-Scheme-1" href="Tweaking-with-Scheme.html#Tweaking-with-Scheme">B.1 Tweaking with Scheme</a> </li>
</ul>
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<li><a name="toc-GNU-Free-Documentation-License-1" href="GNU-Free-Documentation-License.html#GNU-Free-Documentation-License">C. GNU Free Documentation License</a> </li>
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