<chapter id="music-theory">
<title>Music theory</title>
<sect1 id="theory-scales">
<title>Scales</title>
<para>Davide Bonetti has contributed a large set of scale exercises and
some pages describing all the scales. You can see the pages <ulink
url="../C/scales/modes.html">here</ulink>.</para>
</sect1>
<sect1 id="theory-intervals">
<title>Intervals</title>
<para>In music theory we use the word interval when we talk about the pitch
difference between two notes. We call them harmonic intervals if two tones
sound simultaneously and melodic intervals if they sound successively.
</para>

<!-- translators: This paragraph is messy because the author is writing
in english, and english is not his mother language. Write this paragraph
so that is as clear and simple as possible, describing only what is relevant
for your language -->
<para>Interval names consist of two parts. Some examples are "major third" and
"perfect fifth". In Walter Piston's "Harmony" the two parts are called
<emphasis>the specific name</emphasis> and <emphasis>the general
name</emphasis> part. Wikipedia talks about <emphasis>interval
quality</emphasis> and <emphasis>interval number</emphasis>. I have seen people
talking about an interval's <emphasis>numerical size</emphasis>.</para>

<para>You find the
general name by counting the steps on the staff, ignoring any
accidentals. So if the interval you want to name goes from E to G#, then we count
to 3 (E F G) and see that the general name is <emphasis>third</emphasis>.</para>

<informalfigure>
    <mediaobject>
      <imageobject>
        <imagedata fileref="ly/theory-intervals-1.png" format="PNG"/>
      </imageobject>
    </mediaobject>
</informalfigure>

<para>
The specific name tells the exact size of the interval. Unisons, fourths, fifths
and octaves can be diminished, pure or augmented. Seconds, thirds, sixths and
sevenths can be minor, major, diminished or augmented. A minor interval is one
semitone smaller than a major interval. A diminished interval is one semitone
smaller than a pure or a minor interval, and an augmented interval is one
semitone larger than a pure or major interval.</para>

<para>Accidentals change the size of intervals. The interval becomes one
semitone larger if you add a sharp to the highest tone or a flat to the lowest
tone. And it becomes one semitone smaller if you add a flat to the highest tone
or a sharp to the lowest tone. In the following sections naming of the
intervals will be shown in greater detail.</para>
<!-- #################
          SECONDS
     ################# -->
<sect2 id='theory-seconds'>
<title>Seconds</title>
<para>Seconds are easy to recognise: the two notes are neighbours on the staff.
One note is on a staff line, and the other one is in the space above or below.
A minor second is one semitone step, also called a half step. A major second is
two semitone steps, also called a whole step.</para>

<para>To learn to identify seconds, you first have to learn which seconds there
are between the natural tones. As you can see in <xref
linkend='theory-intervals-seconds'/>, only the intervals E-F and B-C are minor
seconds. The rest are major intervals. You can check that <xref
linkend='theory-intervals-seconds'/> is correct by looking at a piano. You will
see that there are no black keys between E and F and between B and C.</para>

<figure id='theory-intervals-seconds'>
    <title></title>
    <mediaobject>
      <imageobject>
        <imagedata fileref="ly/theory-intervals-seconds.png" format="PNG"/>
      </imageobject>
    </mediaobject>
</figure>

<para>If the second has accidentals, then we have to examine them to find out
how they change the size of the interval. Let us identify a few intervals!
</para>

<figure id='theory-intervals-seconds-1'>
 <title></title>
 <mediaobject>
  <imageobject>
   <imagedata fileref="../C/ly/theory-intervals-seconds-1.png" format="PNG"/>
  </imageobject>
 </mediaobject>
</figure>

<para>We remove the accidental from the interval in <xref
linkend='theory-intervals-seconds-1'/> and see that the interval F-G is a major
second. When we add the flat to the highest tone, the interval becomes one
semitone smaller, turning into a minor second.</para>

<figure id='theory-intervals-seconds-2'>
 <title></title>
 <mediaobject>
  <imageobject>
   <imagedata fileref="../C/ly/theory-intervals-seconds-2.png" format="PNG"/>
  </imageobject>
 </mediaobject>
</figure>

<para>We remove the accidentals, and see that the interval A-B is a major
second. You still remember <xref linkend='theory-intervals-seconds'/>, don't
you? Then we add the flat to the A, and the interval becomes an augmented
second. And when we add the flat to the B, the interval becomes a major
second.</para>

<figure id='theory-intervals-seconds-3'>
 <title></title>
 <mediaobject>
  <imageobject>
   <imagedata fileref="../C/ly/theory-intervals-seconds-3.png" format="PNG"/>
  </imageobject>
 </mediaobject>
</figure>

<para>We remove the accidentals, and see that the interval E-F is a minor
second. When we add a flat to the lowest tone, the interval becomes one
semitone larger, turning into a major second. And when we add a sharp to the
highest tone, the interval becomes one semitone larger, turning into an
augmented second.</para>

</sect2>

<!-- #################
         THIRDS
     ################# -->

<sect2 id='theory-thirds'>
<title>Thirds</title>
<para>A minor third is one minor and one major second, or three semitones.  A
major third are two major seconds, or four semitone steps. <xref
linkend='theory-intervals-thirds'/> shows the thirds between all the natural
tones. You should memorise the major intervals, C-E, F-A and G-B. Then you know
that the other four intervals are minor.</para>

<figure id='theory-intervals-thirds'>
 <title></title>
 <mediaobject>
  <imageobject>
   <imagedata fileref="ly/theory-intervals-thirds.png" format="PNG"/>
  </imageobject>
 </mediaobject>
</figure>

<para>Then you examine the accidentals to see if they change the specific name.
This is done exactly the same way as for seconds.</para>

</sect2>
<!-- #################
          FOURTHS
     ################# -->
<sect2 id='theory-fourths'>
<title>Fourth</title>
<para>A pure fourth is 2½ steps, or two major seconds and a minor second.
<xref linkend='theory-intervals-fourths'/> shows all fourths between natural
tones. You should memorise that the fourth F-B is augmented, and that the other
six are pure.  </para>

<figure id='theory-intervals-fourths'>
    <title></title>
    <mediaobject>
      <imageobject>
        <imagedata fileref="ly/theory-intervals-fourths.png" format="PNG"/>
      </imageobject>
    </mediaobject>
</figure>
</sect2>

<!-- #################
          FIFTHS
     ################# -->
<sect2 id='theory-fifths'>
<title>Fifth</title>
<para>A pure fifth is 3½ steps, or three major seconds and a minor second.
<xref linkend='theory-intervals-fifths'/> shows all fifths between natural
tones. You should remember that all those intervals are pure, except B-F that
is diminished. </para>

<figure id='theory-intervals-fifths'>
    <title></title>
    <mediaobject>
      <imageobject>
        <imagedata fileref="ly/theory-intervals-fifths.png" format="PNG"/>
      </imageobject>
    </mediaobject>
</figure>

<para>If an interval has accidentals, then we must examine them to see how
they change the size of the interval. A diminished fifth is one semitone
smaller than a pure interval, and an augmented fifth is one semitone larger.
Below you will find a few examples:</para>

<figure id='theory-intervals-fifths-1'>
    <title></title>
    <mediaobject>
      <imageobject>
        <imagedata fileref="../C/ly/theory-intervals-fifths-1.png" format="PNG"/>
      </imageobject>
    </mediaobject>
</figure>

<para>We remember from <xref linkend='theory-intervals-fifths'/> that the
interval B-F is a diminished fifth. The lowest tone in <xref
linkend='theory-intervals-fifths-1'/> is preceded by a flat that makes the
interval one semitone larger and changes the interval from a diminished to a
pure fifth.</para>

<figure id='theory-intervals-fifths-2'>
    <title></title>
    <mediaobject>
      <imageobject>
        <imagedata fileref="../C/ly/theory-intervals-fifths-2.png" format="PNG"/>
      </imageobject>
    </mediaobject>
</figure>

<para>We know from <xref linkend='theory-intervals-fifths'/> that interval E-B
is a perfect fifth. In <xref linkend='theory-intervals-fifths-2'/> the E has a
flat in front of it, making the interval augmented. But then the B is preceded
by a double flat that makes the interval two semitone steps smaller and changes
the interval to a diminished fifth.</para>
</sect2>

<sect2 id='theory-sixths'>
<title>Sixths</title>
<para>Sixths are easiest identified by <link linkend='inverting-intervals'>
inverting the interval</link> and identifying the third. Then the following
rule applies:</para>

<itemizedlist>
<listitem><para>If the third is diminished, then the sixth is augmented</para></listitem>
<listitem><para>If the third is minor, then the sixth is major</para></listitem>
<listitem><para>If the third is major, then the sixth is minor</para></listitem>
<listitem><para>If the third is augmented, then the sixth is diminished</para></listitem>
</itemizedlist>

<para>If you find inverting intervals difficult, then you can memorise that the
intervals E-C, A-F and B-G are minor. The other four are major.  Then you
examine the accidentals to see if they change the specific name. This is done
exactly the same way as for seconds.</para>

<figure id='theory-intervals-sixths'>
    <title></title>
    <mediaobject>
      <imageobject>
        <imagedata fileref="ly/theory-intervals-sixths.png" format="PNG"/>
      </imageobject>
    </mediaobject>
</figure>

</sect2>

<sect2 id='theory-sevenths'>
<title>Sevenths</title>
<para>Sevenths are identified the same way as sixths. When you invert a
seventh, you get a second.</para>

<para>If you find inverting intervals difficult, then you
can memorise that the intervals C-B and F-E are major. The other five are
minor. Then you examine the accidentals to see if they change the specific
name. This is done exactly the same way as for seconds.</para>

<figure id='theory-intervals-sevenths'>
    <title></title>
    <mediaobject>
      <imageobject>
        <imagedata fileref="ly/theory-intervals-sevenths.png" format="PNG"/>
      </imageobject>
    </mediaobject>
</figure>


</sect2>

</sect1>

<sect1 id='inverting-intervals'>
<title>Inverting intervals</title>
<para>You invert an interval when you move the lowest tone of an interval one
octave higher or the highest tone one octave lower. The general name changes this way:</para>
<itemizedlist>
<listitem><para>Second becomes seventh.</para></listitem>
<listitem><para>Third becomes sixth.</para></listitem>
<listitem><para>Forth becomes fifth.</para></listitem>
<listitem><para>Fifth becomes fourth.</para></listitem>
<listitem><para>Sixth becomes third.</para></listitem>
<listitem><para>Seventh becomes second.</para></listitem>
</itemizedlist>

<para>The specific name changes this way:</para>
<itemizedlist>
<listitem><para>Diminished becomes augmented.</para></listitem>
<listitem><para>Minor becomes major.</para></listitem>
<listitem><para>Perfect stays perfect.</para></listitem>
<listitem><para>Major becomes minor.</para></listitem>
<listitem><para>Augmented becomes diminished.</para></listitem>
</itemizedlist>

<para>Below are two examples, a
major third is inverted and becomes a minor sixth, and a minor seventh is
inverted and becomes a major second.</para>

<figure id='music-theory-inverting-intervals-fig'>
    <title></title>
    <mediaobject>
      <imageobject>
        <imagedata fileref="ly/inverting-intervals.png" format="PNG"/>
      </imageobject>
    </mediaobject>
</figure>

</sect1>

</chapter>
