<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE document PUBLIC "-//CNX//DTD CNXML 0.5 plus MathML//EN" "http://cnx.rice.edu/cnxml/0.5/DTD/cnxml_mathml.dtd">
<document xmlns="http://cnx.rice.edu/cnxml" xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="m10877">
  <name>Triads</name>
  <metadata>
  <md:version>2.14</md:version>
  <md:created>2002/10/03</md:created>
  <md:revised>2007/03/02 15:53:03.440 US/Central</md:revised>
  <md:authorlist>
      <md:author id="Catherine">
      <md:firstname>Catherine</md:firstname>
      <md:othername>A.</md:othername>
      <md:surname>Schmidt-Jones</md:surname>
      <md:email>casjones@soltec.net</md:email>
    </md:author>
  </md:authorlist>

  <md:maintainerlist>
    <md:maintainer id="Catherine">
      <md:firstname>Catherine</md:firstname>
      <md:othername>A.</md:othername>
      <md:surname>Schmidt-Jones</md:surname>
      <md:email>casjones@soltec.net</md:email>
    </md:maintainer>
  </md:maintainerlist>
  
  <md:keywordlist>
    <md:keyword>chord</md:keyword>
    <md:keyword>first inversion</md:keyword>
    <md:keyword>inversions</md:keyword>
    <md:keyword>root position</md:keyword>
    <md:keyword>second inversion</md:keyword>
    <md:keyword>triad</md:keyword>
  </md:keywordlist>

  <md:abstract>Triads are basic three-note chords built of thirds. They can be in root position, first inversion, or second inversion.</md:abstract>
</metadata>



  <content>

    <para id="p0a">
<cnxn document="m11654" strength="9">Harmony</cnxn> in <cnxn document="m11421" strength="7">Western music</cnxn> is based on triads. <term>Triads</term> are simple three-note <cnxn document="m11654" target="l0b" strength="9">chords</cnxn> built of <cnxn document="m10867" target="p1b" strength="9">thirds</cnxn>.
    </para>

    <section id="s1">	
    <name>Triads in Root Position</name>

   	<figure id="fig18a"><name>Triads in Root Position</name>
		<media type="application/postscript" src="roottriads-0.eps">
		  <media type="image/png" src="roottriads.png"/>
		</media>
	</figure>
 
      <para id="p1a">The chords in <cnxn target="fig18a"/> are written in root position, which is the most basic way to write a triad. In <term>root position</term>, the <term>root</term>, which is the note that names the chord, is the lowest note. The <term>third of the chord</term> is written a <cnxn document="m10867" target="fig7c" strength="8">third</cnxn> higher than the root, and the <term>fifth of the chord</term> is written a <cnxn document="m10867" target="fig7c" strength="8">fifth</cnxn> higher than the root (which is also a third higher than the third of the chord). So the simplest way to write a triad is as a stack of thirds, in root position.<note>The type of interval or chord - major, minor, diminished, etc., is not important when you are determining the position of the chord. To simplify things, all notes in the examples and exercises below are natural, but it would not change their position at all if some notes were sharp or flat. It would, however, change the name of the triad - see <cnxn document="m10890" strength="9">Naming Triads</cnxn>.</note>
     </para>

     <exercise id="exer1a">
      <problem>
       <para id="prob1a">
Write a triad in root position using each root given. If you need some staff paper for exercises you can print this <link src="staffpaper1.pdf">PDF file</link>.
       </para>

	<figure id="fig18e"><media type="application/postscript" src="triadprob1-0.eps">
		  <media type="image/png" src="triadprob1.png"/>
		</media>
	</figure>
      </problem>

      <solution>
		<figure id="fig18f"><media type="application/postscript" src="Triadsolv1-0.eps">
			  <media type="image/png" src="Triadsolv1.png"/>
			</media>
		</figure>
      </solution>

     </exercise>


    </section> 
    <section id="s2">	<name>First and Second Inversions</name>
     <para id="p2a">
Any other chord that has the same-named notes as a root position chord is considered to be essentially the same chord in a different <term>position</term>. In other words, all chords that have only D naturals, F sharps, and A naturals, are considered D major chords. <note><emphasis>But</emphasis> if you change the <cnxn document="m10943" strength="7">pitch</cnxn> or <cnxn document="m11641" strength="7">spelling</cnxn> of any note in the triad, you have changed the chord (see <cnxn document="m10890" strength="9">Naming Triads</cnxn>). For example, if the F sharps are written as G flats, or if the A's are sharp instead of natural, you have a different chord, not an inversion of the same chord. If you add notes, you have also changed the name of the chord (see <cnxn document="m11995" strength="8">Beyond Triads</cnxn>). <emphasis>You cannot call one chord the inversion of another if either one of them has a note that does not share a name (for example "F sharp" or "B natural") with a note in the other chord.</emphasis></note> If the third of the chord is the lowest note, the chord is in <term>first inversion</term>. If the fifth of the chord is the lowest note, the chord is in <term>second inversion</term>. A chord in second inversion may also be called a <term>six-four chord</term>, because the <cnxn document="m10867" strength="8">intervals</cnxn> in it are a sixth and a fourth.
     </para>

	<figure id="fig18b"><media type="application/postscript" src="triadpositions-0.eps">
		  <media type="image/png" src="triadpositions.png"/>
		</media>
	</figure>

     <para id="p2b">
It does not matter how far the higher notes are from the lowest note, or how many of each note there are (at different octaves or on different instruments); all that matters is which note is lowest. (In fact, one of the notes may not even be written, only implied by the context of the chord in a piece of music. A practiced ear will tell you what the missing note is; we won't worry about that here.) To decide what position a chord is in, move the notes to make a stack of thirds and identify the root.
     </para>


     <example id="examp2a">
		<figure id="fig18c"><media type="application/postscript" src="triadex1-0.eps">
			  <media type="image/png" src="triadex1.png"/>
			</media>
		</figure>

     </example>

     <example id="examp2b">
		<figure id="fig18cc"><media type="application/postscript" src="Triadex2-0.eps">
			  <media type="image/png" src="Triadex2.png"/>
			</media>
		</figure>

     </example>


     <exercise id="exer2a">

      <problem>
                <para id="prob2a">
Rewrite each chord in root position, and name the original position of the chord.
                </para>
		<figure id="fig18d"><media type="application/postscript" src="TriadProb2-0.eps">
			<media type="image/png" src="TriadProb2.png"/>
			</media>
		</figure>
      </problem>

      <solution>
		<figure id="fig18g"><media type="application/postscript" src="TriadSolv2-0.eps">
			  <media type="image/png" src="TriadSolv2.png"/>
			</media>
		</figure>
      </solution>
     </exercise>

    </section> 
  </content>
  
</document>
