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<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Intervals</title><link rel="stylesheet" href="../style.css" type="text/css"><meta name="generator" content="DocBook XSL Stylesheets V1.75.2"><link rel="home" href="index.html" title="GNU Solfege 3.16.4 User Manual"><link rel="up" href="music-theory.html" title="Chapter 3. Music theory"><link rel="prev" href="music-theory.html" title="Chapter 3. Music theory"><link rel="next" href="inverting-intervals.html" title="Inverting intervals"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Intervals</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="music-theory.html">Prev</a> </td><th width="60%" align="center">Chapter 3. Music theory</th><td width="20%" align="right"> <a accesskey="n" href="inverting-intervals.html">Next</a></td></tr></table><hr></div><div class="sect1" title="Intervals"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="theory-intervals"></a>Intervals</h2></div></div></div><p>In music theory we use the word interval when we talk about the pitch
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<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Intervals</title><link rel="stylesheet" href="../style.css" type="text/css"><meta name="generator" content="DocBook XSL Stylesheets V1.75.2"><link rel="home" href="index.html" title="GNU Solfege 3.19.6 User Manual"><link rel="up" href="music-theory.html" title="Chapter 3. Music theory"><link rel="prev" href="music-theory.html" title="Chapter 3. Music theory"><link rel="next" href="inverting-intervals.html" title="Inverting intervals"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Intervals</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="music-theory.html">Prev</a> </td><th width="60%" align="center">Chapter 3. Music theory</th><td width="20%" align="right"> <a accesskey="n" href="inverting-intervals.html">Next</a></td></tr></table><hr></div><div class="sect1" title="Intervals"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="theory-intervals"></a>Intervals</h2></div></div></div><p>In music theory we use the word interval when we talk about the pitch
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difference between two notes. We call them harmonic intervals if two tones
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sound simultaneosly and melodic intervals if they sound successively.
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sound simultaneously and melodic intervals if they sound successively.
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</p><p>Interval names consist of two parts. Some examples are "major third" and
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"perfect fifth". In Walter Pistons "Harmony" the two parts are called
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"perfect fifth". In Walter Piston's "Harmony" the two parts are called
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<span class="emphasis"><em>the specific name</em></span> and <span class="emphasis"><em>the general
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name</em></span> part. Wikipedia talk about <span class="emphasis"><em>interval
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name</em></span> part. Wikipedia talks about <span class="emphasis"><em>interval
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quality</em></span> and <span class="emphasis"><em>interval number</em></span>. I have seen people
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talk about an intervals <span class="emphasis"><em>numerical size</em></span>.</p><p>You find the
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talking about an interval's <span class="emphasis"><em>numerical size</em></span>.</p><p>You find the
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general name by counting the steps on the staff, ignoring any
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accidentals. So if the inteval you want to name goes from E to G#, then we count
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to 3 (E F G) and see that the general name is <span class="emphasis"><em>third</em></span>.</p><div class="informalfigure"><div class="mediaobject"><img src="../C/ly/theory-intervals-1.png"></div></div><p>
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The specific name say the exact size of the interval. Unisons, fourths, fifths
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accidentals. So if the interval you want to name goes from E to G#, then we count
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to 3 (E F G) and see that the general name is <span class="emphasis"><em>third</em></span>.</p><div class="informalfigure"><div class="mediaobject"><img src="ly/theory-intervals-1.png"></div></div><p>
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The specific name tells the exact size of the interval. Unisons, fourths, fifths
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and octaves can be diminished, pure or augmented. Seconds, thirds, sixths and
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sevenths can be minor, major, diminished or augmented. A minor interval is one
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semitone smaller than a major interval. A diminished interval is one semitone
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smaller than a pure or a minor interval, and a augmented interval is one
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smaller than a pure or a minor interval, and an augmented interval is one
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semitone larger than a pure or major interval.</p><p>Accidentals change the size of intervals. The interval becomes one
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semitone larger if you add a sharp to the highest tone or a flat to the lowest
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tone. And it becomes one semitone smaller if you add a flat to the highest tone
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two semitone steps, also called a whole step.</p><p>To learn to identify seconds, you first have to learn which seconds there
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are between the natural tones. As you can see in <a class="xref" href="theory-intervals.html#theory-intervals-seconds" title="Figure 3.1. ">Figure 3.1</a>, only the intervals E-F and B-C are minor
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seconds. The rest are major intervals. You can check that <a class="xref" href="theory-intervals.html#theory-intervals-seconds" title="Figure 3.1. ">Figure 3.1</a> is correct by looking at a piano. You will
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see that there are no black keys between E and F and between B and C.</p><div class="figure"><a name="theory-intervals-seconds"></a><p class="title"><b>Figure 3.1. </b></p><div class="figure-contents"><div class="mediaobject"><img src="../C/ly/theory-intervals-seconds.png"></div></div></div><br class="figure-break"><p>If the second has accidentals, then we have to examine them to find out
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see that there are no black keys between E and F and between B and C.</p><div class="figure"><a name="theory-intervals-seconds"></a><p class="title"><b>Figure 3.1. </b></p><div class="figure-contents"><div class="mediaobject"><img src="ly/theory-intervals-seconds.png"></div></div></div><br class="figure-break"><p>If the second has accidentals, then we have to examine them to find out
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how they change the size of the interval. Let us identify a few intervals!
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</p><div class="figure"><a name="theory-intervals-seconds-1"></a><p class="title"><b>Figure 3.2. </b></p><div class="figure-contents"><div class="mediaobject"><img src="../C/ly/theory-intervals-seconds-1.png"></div></div></div><br class="figure-break"><p>We remove the accidental from the interval in <a class="xref" href="theory-intervals.html#theory-intervals-seconds-1" title="Figure 3.2. ">Figure 3.2</a> and see that the interval F-G is a major
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second. When we add the flat to the highest tone, the interval becomes one
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semitone smaller, and becomes a minor second.</p><div class="figure"><a name="theory-intervals-seconds-2"></a><p class="title"><b>Figure 3.3. </b></p><div class="figure-contents"><div class="mediaobject"><img src="../C/ly/theory-intervals-seconds-2.png"></div></div></div><br class="figure-break"><p>We remove the accidentals, and see that the interval A-B is a major
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second. You still do remember <a class="xref" href="theory-intervals.html#theory-intervals-seconds" title="Figure 3.1. ">Figure 3.1</a>, don't
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you? Then we add the flat to the A, and the interval become a augmented
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second. And when we add the flat to the B, and the interval becomes a major
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semitone smaller, turning into a minor second.</p><div class="figure"><a name="theory-intervals-seconds-2"></a><p class="title"><b>Figure 3.3. </b></p><div class="figure-contents"><div class="mediaobject"><img src="../C/ly/theory-intervals-seconds-2.png"></div></div></div><br class="figure-break"><p>We remove the accidentals, and see that the interval A-B is a major
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second. You still remember <a class="xref" href="theory-intervals.html#theory-intervals-seconds" title="Figure 3.1. ">Figure 3.1</a>, don't
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you? Then we add the flat to the A, and the interval becomes an augmented
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second. And when we add the flat to the B, the interval becomes a major
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second.</p><div class="figure"><a name="theory-intervals-seconds-3"></a><p class="title"><b>Figure 3.4. </b></p><div class="figure-contents"><div class="mediaobject"><img src="../C/ly/theory-intervals-seconds-3.png"></div></div></div><br class="figure-break"><p>We remove the accidentals, and see that the interval E-F is a minor
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second. When we add a flat to the lowest tone, the interval becomes one
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semitone larger, and becomes a major second. And when we add a sharp to the
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highest tone, the interval becomes one semitone larger, and becomes an
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semitone larger, turning into a major second. And when we add a sharp to the
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highest tone, the interval becomes one semitone larger, turning into an
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augmented second.</p></div><div class="sect2" title="Thirds"><div class="titlepage"><div><div><h3 class="title"><a name="theory-thirds"></a>Thirds</h3></div></div></div><p>A minor third is one minor and one major second, or three semitones. A
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major third are two major seconds, or four semitone steps. <a class="xref" href="theory-intervals.html#theory-intervals-thirds" title="Figure 3.5. ">Figure 3.5</a> show the thirds between all the natural
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major third are two major seconds, or four semitone steps. <a class="xref" href="theory-intervals.html#theory-intervals-thirds" title="Figure 3.5. ">Figure 3.5</a> shows the thirds between all the natural
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tones. You should memorise the major intervals, C-E, F-A and G-B. Then you know
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that the other four intervals are minor.</p><div class="figure"><a name="theory-intervals-thirds"></a><p class="title"><b>Figure 3.5. </b></p><div class="figure-contents"><div class="mediaobject"><img src="../C/ly/theory-intervals-thirds.png"></div></div></div><br class="figure-break"><p>Then you examine the accidentals to see if they change the specific name.
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that the other four intervals are minor.</p><div class="figure"><a name="theory-intervals-thirds"></a><p class="title"><b>Figure 3.5. </b></p><div class="figure-contents"><div class="mediaobject"><img src="ly/theory-intervals-thirds.png"></div></div></div><br class="figure-break"><p>Then you examine the accidentals to see if they change the specific name.
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This is done exactly the same way as for seconds.</p></div><div class="sect2" title="Fourth"><div class="titlepage"><div><div><h3 class="title"><a name="theory-fourths"></a>Fourth</h3></div></div></div><p>A pure fourth is 2½ steps, or two major seconds and a minor second.
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<a class="xref" href="theory-intervals.html#theory-intervals-fourths" title="Figure 3.6. ">Figure 3.6</a> show all fourths between natural
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<a class="xref" href="theory-intervals.html#theory-intervals-fourths" title="Figure 3.6. ">Figure 3.6</a> shows all fourths between natural
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tones. You should memorise that the fourth F-B is augmented, and that the other
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six are pure. </p><div class="figure"><a name="theory-intervals-fourths"></a><p class="title"><b>Figure 3.6. </b></p><div class="figure-contents"><div class="mediaobject"><img src="../C/ly/theory-intervals-fourths.png"></div></div></div><br class="figure-break"></div><div class="sect2" title="Fifth"><div class="titlepage"><div><div><h3 class="title"><a name="theory-fifths"></a>Fifth</h3></div></div></div><p>A pure fifth is 3½ steps, or three major seconds and a minor second.
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<a class="xref" href="theory-intervals.html#theory-intervals-fifths" title="Figure 3.7. ">Figure 3.7</a> show all fifths between natural
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six are pure. </p><div class="figure"><a name="theory-intervals-fourths"></a><p class="title"><b>Figure 3.6. </b></p><div class="figure-contents"><div class="mediaobject"><img src="ly/theory-intervals-fourths.png"></div></div></div><br class="figure-break"></div><div class="sect2" title="Fifth"><div class="titlepage"><div><div><h3 class="title"><a name="theory-fifths"></a>Fifth</h3></div></div></div><p>A pure fifth is 3½ steps, or three major seconds and a minor second.
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<a class="xref" href="theory-intervals.html#theory-intervals-fifths" title="Figure 3.7. ">Figure 3.7</a> shows all fifths between natural
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tones. You should remember that all those intervals are pure, except B-F that
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is diminished. </p><div class="figure"><a name="theory-intervals-fifths"></a><p class="title"><b>Figure 3.7. </b></p><div class="figure-contents"><div class="mediaobject"><img src="../C/ly/theory-intervals-fifths.png"></div></div></div><br class="figure-break"><p>If the interval has accidentals, then we must examine them to see how
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is diminished. </p><div class="figure"><a name="theory-intervals-fifths"></a><p class="title"><b>Figure 3.7. </b></p><div class="figure-contents"><div class="mediaobject"><img src="ly/theory-intervals-fifths.png"></div></div></div><br class="figure-break"><p>If an interval has accidentals, then we must examine them to see how
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they change the size of the interval. A diminished fifth is one semitone
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smaller than a pure interval, and a augmented fifth is one semitone larger.
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smaller than a pure interval, and an augmented fifth is one semitone larger.
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Below you will find a few examples:</p><div class="figure"><a name="theory-intervals-fifths-1"></a><p class="title"><b>Figure 3.8. </b></p><div class="figure-contents"><div class="mediaobject"><img src="../C/ly/theory-intervals-fifths-1.png"></div></div></div><br class="figure-break"><p>We remember from <a class="xref" href="theory-intervals.html#theory-intervals-fifths" title="Figure 3.7. ">Figure 3.7</a> that the
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interval B-F is a diminished fifth. The lowest tone in <a class="xref" href="theory-intervals.html#theory-intervals-fifths-1" title="Figure 3.8. ">Figure 3.8</a> is preceded by a flat that makes the
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interval one semitone larger and changes the interval from a diminished to a
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pure fifth.</p><div class="figure"><a name="theory-intervals-fifths-2"></a><p class="title"><b>Figure 3.9. </b></p><div class="figure-contents"><div class="mediaobject"><img src="../C/ly/theory-intervals-fifths-2.png"></div></div></div><br class="figure-break"><p>We know from <a class="xref" href="theory-intervals.html#theory-intervals-fifths" title="Figure 3.7. ">Figure 3.7</a> that interval E-B
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is a perfect fifth. In <a class="xref" href="theory-intervals.html#theory-intervals-fifths-2" title="Figure 3.9. ">Figure 3.9</a> the E has a
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flat in front of it, making the interval augmented. But then the B is preceded
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by a doble flat that makes the interval two semitone steps smaller and changes
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by a double flat that makes the interval two semitone steps smaller and changes
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the interval to a diminished fifth.</p></div><div class="sect2" title="Sixths"><div class="titlepage"><div><div><h3 class="title"><a name="theory-sixths"></a>Sixths</h3></div></div></div><p>Sixths are easiest identified by <a class="link" href="inverting-intervals.html" title="Inverting intervals">
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inverting the interval</a> and identifying the third. Then the following
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rule apply:</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"><p>If the third is diminished, then the sixth is augmented</p></li><li class="listitem"><p>If the third is minor, then the sixth is major</p></li><li class="listitem"><p>If the third is major, then the sixth is minor</p></li><li class="listitem"><p>If the third is augmented, then the sixth is diminished</p></li></ul></div><p>If you find inverting intervals difficult, then you can memorise that the
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rule applies:</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"><p>If the third is diminished, then the sixth is augmented</p></li><li class="listitem"><p>If the third is minor, then the sixth is major</p></li><li class="listitem"><p>If the third is major, then the sixth is minor</p></li><li class="listitem"><p>If the third is augmented, then the sixth is diminished</p></li></ul></div><p>If you find inverting intervals difficult, then you can memorise that the
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intervals E-C, A-F and B-G are minor. The other four are major. Then you
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examine the accidentals to see if they change the specific name. This is done
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exactly the same way as for seconds.</p><div class="figure"><a name="theory-intervals-sixths"></a><p class="title"><b>Figure 3.10. </b></p><div class="figure-contents"><div class="mediaobject"><img src="../C/ly/theory-intervals-sixths.png"></div></div></div><br class="figure-break"></div><div class="sect2" title="Sevenths"><div class="titlepage"><div><div><h3 class="title"><a name="theory-sevenths"></a>Sevenths</h3></div></div></div><p>Sevenths are identified the same way as sixths. When you invert a
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exactly the same way as for seconds.</p><div class="figure"><a name="theory-intervals-sixths"></a><p class="title"><b>Figure 3.10. </b></p><div class="figure-contents"><div class="mediaobject"><img src="ly/theory-intervals-sixths.png"></div></div></div><br class="figure-break"></div><div class="sect2" title="Sevenths"><div class="titlepage"><div><div><h3 class="title"><a name="theory-sevenths"></a>Sevenths</h3></div></div></div><p>Sevenths are identified the same way as sixths. When you invert a
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seventh, you get a second.</p><p>If you find inverting intervals difficult, then you
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can memorise that the intervals C-B and F-E are major. The other five are
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minor. Then you examine the accidentals to see if they change the specific
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name. This is done exactly the same way as for seconds.</p><div class="figure"><a name="theory-intervals-sevenths"></a><p class="title"><b>Figure 3.11. </b></p><div class="figure-contents"><div class="mediaobject"><img src="../C/ly/theory-intervals-sevenths.png"></div></div></div><br class="figure-break"></div></div><div class="navfooter"><hr><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="music-theory.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="music-theory.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="inverting-intervals.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 3. Music theory </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Inverting intervals</td></tr></table></div></body></html>
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name. This is done exactly the same way as for seconds.</p><div class="figure"><a name="theory-intervals-sevenths"></a><p class="title"><b>Figure 3.11. </b></p><div class="figure-contents"><div class="mediaobject"><img src="ly/theory-intervals-sevenths.png"></div></div></div><br class="figure-break"></div></div><div class="navfooter"><hr><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="music-theory.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="music-theory.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="inverting-intervals.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 3. Music theory </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Inverting intervals</td></tr></table></div></body></html>
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