17edo tetrachords: Difference between revisions

Revision as of 01:22, 30 April 2009

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author Andrew_Heathwaite and made on 2009-04-30 01:22:48 UTC.

The original revision id was 70554107.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

Let a "17edo primary tetrachord" mean a set of four pitches in [[17edo]] that span a perfect fourth (seven degrees) and include one of each of the following:

# the unison - 0 (degrees of 17edo) - solfege name 'do'.
# a second - includes 1 (ra, a minor second), 2 (ru, a neutral second), and 3 (re, a major second).
# a third - includes 4 (me, a minor third), 5 (mu, a neutral third), and 6 (mi, a major third).
# the perfect fourth - 7 (fa).

===correspondance:=== 
|| degrees || cents || name || solfege ||
|| 0 || 0 || unison || do ||
|| 1 || 71 || minor second (a.k.a third-tone) || ra ||
|| 2 || 141 || neutral second (a.k.a. two-thirds-tone) || ru ||
|| 3 || 212 || major second (a.k.a. tone) || re ||
|| 4 || 282 || minor third (a.k.a. subminor third) || me ||
|| 5 || 353 || neutral third || mu ||
|| 6 || 424 || major third (a.k.a. supermajor third) || mi ||
|| 7 || 494 || perfect fourth || fa ||

===tetrachord notation=== 

Tetrachord notation will show three scalar steps (as degrees of 17edo) separated by hyphens.

For instance, tetrachord 3-3-1 consists of
0 (do), the unison;
3 (re), a major second, 3 degrees up from 0;
6 (mi), a major third, 3 degrees up from 3; and
7 (fa), the perfect fourth, 1 degree up from 6.

The numbers in a tetrachord name will always add to 7.

===17edo primary tetrachords=== 

We have 9 primary tetrachords in 17edo.

|| tetrachord notation || solfege || name (suggestions?) || used in ||
|| 1-3-3 || do ra me fa || phyrgian || diatonic (phrygian) ||
|| 1-4-2 || do ra mu fa ||   ||   ||
|| 1-5-1 || do ra mi fa || balkan ||   ||
|| 2-2-3 || do ru me fa ||   || [[17edo neutral scale]] (led) ||
|| 2-3-2 || do ru mu fa ||   || [[17edo neutral scale]] (bish, fish, jwl) ||
|| 2-4-1 || do ru mi fa ||   ||   ||
|| 3-1-3 || do re me fa || aolian || diatonic (aolian, dorian) ; [[scorp]] (mode 3) ||
|| 3-2-2 || do re mu fa ||   || [[17edo neutral scale]] (dril, gil, kleeth) ||
|| 3-3-1 || do re mi fa || ionian || diatonic (ionian, mixolydian) ||

Another way of showing them:
||   || ra || ru || re ||
|| me || 1-3-3 || 2-2-3 || 3-1-3 ||
|| mu || 1-4-2 || 2-3-2 || 3-2-2 ||
|| mi || 1-5-1 || 2-4-1 || 3-3-1 ||

===17edo tetrachords complete=== 
A more generalized tetrachord system would allow multiple seconds or multiple thirds: for instance, 1-1-5 or 5-1-1. Thus, a complete chart of 17edo tetrachords looks like this (with primary tetrachords in bold):

|| 1-1-5 || 2-1-4 || **3-1-3** || 4-1-2 || 5-1-1 ||
|| 1-2-4 || **2-2-3** || **3-2-2** || 4-2-1 ||   ||
|| **1-3-3** || **2-3-2** || **3-3-1** ||   ||   ||
|| **1-4-2** || **2-4-1** ||   ||   ||   ||
|| **1-5-1** ||   ||   ||   ||   ||
Thus, by allowing multiples seconds or multiple thirds, we add 6 new tetrachords to our 9 primary tetrachords, for a total of 15. Our new ones:

|| tetrachord notation || solfege || name (suggestions?) || used in ||
|| 1-1-5 || do ra ru fa ||   ||   ||
|| 1-2-4 || do ra re fa ||   ||   ||
|| 2-1-4 || do ru re fa ||   ||   ||
|| 4-1-2 || do me mu fa ||   ||   ||
|| 4-2-1 || do me mi fa ||   ||   ||
|| 5-1-1 || do mu mi fa ||   ||   ||

Original HTML content:

<html><head><title>17edo tetrachords</title></head><body>Let a &quot;17edo primary tetrachord&quot; mean a set of four pitches in <a class="wiki_link" href="/17edo">17edo</a> that span a perfect fourth (seven degrees) and include one of each of the following:<br />
<br />
<ol><li>the unison - 0 (degrees of 17edo) - solfege name 'do'.</li><li>a second - includes 1 (ra, a minor second), 2 (ru, a neutral second), and 3 (re, a major second).</li><li>a third - includes 4 (me, a minor third), 5 (mu, a neutral third), and 6 (mi, a major third).</li><li>the perfect fourth - 7 (fa).</li></ol><br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--correspondance:"></a><!-- ws:end:WikiTextHeadingRule:0 -->correspondance:</h3>
 

<table class="wiki_table">
    <tr>
        <td>degrees<br />
</td>
        <td>cents<br />
</td>
        <td>name<br />
</td>
        <td>solfege<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
        <td>unison<br />
</td>
        <td>do<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>71<br />
</td>
        <td>minor second (a.k.a third-tone)<br />
</td>
        <td>ra<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>141<br />
</td>
        <td>neutral second (a.k.a. two-thirds-tone)<br />
</td>
        <td>ru<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>212<br />
</td>
        <td>major second (a.k.a. tone)<br />
</td>
        <td>re<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>282<br />
</td>
        <td>minor third (a.k.a. subminor third)<br />
</td>
        <td>me<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>353<br />
</td>
        <td>neutral third<br />
</td>
        <td>mu<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>424<br />
</td>
        <td>major third (a.k.a. supermajor third)<br />
</td>
        <td>mi<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>494<br />
</td>
        <td>perfect fourth<br />
</td>
        <td>fa<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x--tetrachord notation"></a><!-- ws:end:WikiTextHeadingRule:2 -->tetrachord notation</h3>
 <br />
Tetrachord notation will show three scalar steps (as degrees of 17edo) separated by hyphens.<br />
<br />
For instance, tetrachord 3-3-1 consists of<br />
0 (do), the unison;<br />
3 (re), a major second, 3 degrees up from 0;<br />
6 (mi), a major third, 3 degrees up from 3; and<br />
7 (fa), the perfect fourth, 1 degree up from 6.<br />
<br />
The numbers in a tetrachord name will always add to 7.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x--17edo primary tetrachords"></a><!-- ws:end:WikiTextHeadingRule:4 -->17edo primary tetrachords</h3>
 <br />
We have 9 primary tetrachords in 17edo.<br />
<br />


<table class="wiki_table">
    <tr>
        <td>tetrachord notation<br />
</td>
        <td>solfege<br />
</td>
        <td>name (suggestions?)<br />
</td>
        <td>used in<br />
</td>
    </tr>
    <tr>
        <td>1-3-3<br />
</td>
        <td>do ra me fa<br />
</td>
        <td>phyrgian<br />
</td>
        <td>diatonic (phrygian)<br />
</td>
    </tr>
    <tr>
        <td>1-4-2<br />
</td>
        <td>do ra mu fa<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-5-1<br />
</td>
        <td>do ra mi fa<br />
</td>
        <td>balkan<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2-2-3<br />
</td>
        <td>do ru me fa<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/17edo%20neutral%20scale">17edo neutral scale</a> (led)<br />
</td>
    </tr>
    <tr>
        <td>2-3-2<br />
</td>
        <td>do ru mu fa<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/17edo%20neutral%20scale">17edo neutral scale</a> (bish, fish, jwl)<br />
</td>
    </tr>
    <tr>
        <td>2-4-1<br />
</td>
        <td>do ru mi fa<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3-1-3<br />
</td>
        <td>do re me fa<br />
</td>
        <td>aolian<br />
</td>
        <td>diatonic (aolian, dorian) ; <a class="wiki_link" href="/scorp">scorp</a> (mode 3)<br />
</td>
    </tr>
    <tr>
        <td>3-2-2<br />
</td>
        <td>do re mu fa<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/17edo%20neutral%20scale">17edo neutral scale</a> (dril, gil, kleeth)<br />
</td>
    </tr>
    <tr>
        <td>3-3-1<br />
</td>
        <td>do re mi fa<br />
</td>
        <td>ionian<br />
</td>
        <td>diatonic (ionian, mixolydian)<br />
</td>
    </tr>
</table>

<br />
Another way of showing them:<br />


<table class="wiki_table">
    <tr>
        <td><br />
</td>
        <td>ra<br />
</td>
        <td>ru<br />
</td>
        <td>re<br />
</td>
    </tr>
    <tr>
        <td>me<br />
</td>
        <td>1-3-3<br />
</td>
        <td>2-2-3<br />
</td>
        <td>3-1-3<br />
</td>
    </tr>
    <tr>
        <td>mu<br />
</td>
        <td>1-4-2<br />
</td>
        <td>2-3-2<br />
</td>
        <td>3-2-2<br />
</td>
    </tr>
    <tr>
        <td>mi<br />
</td>
        <td>1-5-1<br />
</td>
        <td>2-4-1<br />
</td>
        <td>3-3-1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x--17edo tetrachords complete"></a><!-- ws:end:WikiTextHeadingRule:6 -->17edo tetrachords complete</h3>
 A more generalized tetrachord system would allow multiple seconds or multiple thirds: for instance, 1-1-5 or 5-1-1. Thus, a complete chart of 17edo tetrachords looks like this (with primary tetrachords in bold):<br />
<br />


<table class="wiki_table">
    <tr>
        <td>1-1-5<br />
</td>
        <td>2-1-4<br />
</td>
        <td><strong>3-1-3</strong><br />
</td>
        <td>4-1-2<br />
</td>
        <td>5-1-1<br />
</td>
    </tr>
    <tr>
        <td>1-2-4<br />
</td>
        <td><strong>2-2-3</strong><br />
</td>
        <td><strong>3-2-2</strong><br />
</td>
        <td>4-2-1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>1-3-3</strong><br />
</td>
        <td><strong>2-3-2</strong><br />
</td>
        <td><strong>3-3-1</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>1-4-2</strong><br />
</td>
        <td><strong>2-4-1</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>1-5-1</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

Thus, by allowing multiples seconds or multiple thirds, we add 6 new tetrachords to our 9 primary tetrachords, for a total of 15. Our new ones:<br />
<br />


<table class="wiki_table">
    <tr>
        <td>tetrachord notation<br />
</td>
        <td>solfege<br />
</td>
        <td>name (suggestions?)<br />
</td>
        <td>used in<br />
</td>
    </tr>
    <tr>
        <td>1-1-5<br />
</td>
        <td>do ra ru fa<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-2-4<br />
</td>
        <td>do ra re fa<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2-1-4<br />
</td>
        <td>do ru re fa<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4-1-2<br />
</td>
        <td>do me mu fa<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4-2-1<br />
</td>
        <td>do me mi fa<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5-1-1<br />
</td>
        <td>do mu mi fa<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-04-29 15:52:49 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-04-30 01:22:48 UTC</tt>.<br>
-: The original revision id was <tt>70461943</tt>.<br>
+: The original revision id was <tt>70554107</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">A "17edo tetrachord," for the purposes of this naming system, will mean a set of four pitches in [[17edo]] that span a perfect fourth (seven degrees) and include one of each of these:
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Let a "17edo primary tetrachord" mean a set of four pitches in [[17edo]] that span a perfect fourth (seven degrees) and include one of each of the following:
-# 'The unison' in 17edo means 0 (degrees of 17edo) and has the solfege name 'do'.
+# the unison - 0 (degrees of 17edo) - solfege name 'do'.
-# 'Seconds' in 17edo include 1 (ra, a minor second), 2 (ru, a neutral second), and 3 (re, a major second).
+# a second - includes 1 (ra, a minor second), 2 (ru, a neutral second), and 3 (re, a major second).
-# 'Thirds' in 17edo include 4 (me, a minor third), 5 (mu, a neutral third), and 6 (mi, a major third).
+# a third - includes 4 (me, a minor third), 5 (mu, a neutral third), and 6 (mi, a major third).
-# 'The perfect fourth' in 17edo means 7 (fa).
+# the perfect fourth - 7 (fa).
-===Correspondance:===
+===correspondance:===
 || degrees || cents || name || solfege ||
 || 0 || 0 || unison || do ||
@@ Line 24: / Line 24: @@
 || 7 || 494 || perfect fourth || fa ||
-===Tetrachord notation===
+===tetrachord notation===
-Tetrachord notation will show three steps (as degrees of 17edo) separated by hyphens.
+Tetrachord notation will show three scalar steps (as degrees of 17edo) separated by hyphens.
 For instance, tetrachord 3-3-1 consists of
-(do), the unison, a given;
+(do), the unison;
-(re), a note 3 degrees up from 0 (do), a second;
+(re), a major second, 3 degrees up from 0;
-(mi), a note 3 degrees up from 3 (mi), a third; and
+(mi), a major third, 3 degrees up from 3; and
-(fa), the perfect fourth.
+(fa), the perfect fourth, 1 degree up from 6.
 The numbers in a tetrachord name will always add to 7.
-===The tetrachords===
+===17edo primary tetrachords===
+We have 9 primary tetrachords in 17edo.
 || tetrachord notation || solfege || name (suggestions?) || used in ||
@@ Line 53: / Line 55: @@
 || me || 1-3-3 || 2-2-3 || 3-1-3 ||
 || mu || 1-4-2 || 2-3-2 || 3-2-2 ||
-|| mi || 1-5-1 || 2-4-1 || 3-3-1 ||</pre></div>
+|| mi || 1-5-1 || 2-4-1 || 3-3-1 ||
+===17edo tetrachords complete===
+A more generalized tetrachord system would allow multiple seconds or multiple thirds: for instance, 1-1-5 or 5-1-1. Thus, a complete chart of 17edo tetrachords looks like this (with primary tetrachords in bold):
+|| 1-1-5 || 2-1-4 || **3-1-3** || 4-1-2 || 5-1-1 ||
+|| 1-2-4 || **2-2-3** || **3-2-2** || 4-2-1 ||   ||
+|| **1-3-3** || **2-3-2** || **3-3-1** ||   ||   ||
+|| **1-4-2** || **2-4-1** ||   ||   ||   ||
+|| **1-5-1** ||   ||   ||   ||   ||
+Thus, by allowing multiples seconds or multiple thirds, we add 6 new tetrachords to our 9 primary tetrachords, for a total of 15. Our new ones:
+|| tetrachord notation || solfege || name (suggestions?) || used in ||
+|| 1-1-5 || do ra ru fa ||   ||   ||
+|| 1-2-4 || do ra re fa ||   ||   ||
+|| 2-1-4 || do ru re fa ||   ||   ||
+|| 4-1-2 || do me mu fa ||   ||   ||
+|| 4-2-1 || do me mi fa ||   ||   ||
+|| 5-1-1 || do mu mi fa ||   ||   ||</pre></div>
 <h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;17edo tetrachords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &amp;quot;17edo tetrachord,&amp;quot; for the purposes of this naming system, will mean a set of four pitches in &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt; that span a perfect fourth (seven degrees) and include one of each of these:&lt;br /&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;17edo tetrachords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Let a &amp;quot;17edo primary tetrachord&amp;quot; mean a set of four pitches in &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt; that span a perfect fourth (seven degrees) and include one of each of the following:&lt;br /&gt;
 &lt;br /&gt;
-&lt;ol&gt;&lt;li&gt;'The unison' in 17edo means 0 (degrees of 17edo) and has the solfege name 'do'.&lt;/li&gt;&lt;li&gt;'Seconds' in 17edo include 1 (ra, a minor second), 2 (ru, a neutral second), and 3 (re, a major second).&lt;/li&gt;&lt;li&gt;'Thirds' in 17edo include 4 (me, a minor third), 5 (mu, a neutral third), and 6 (mi, a major third).&lt;/li&gt;&lt;li&gt;'The perfect fourth' in 17edo means 7 (fa).&lt;/li&gt;&lt;/ol&gt;&lt;br /&gt;
+&lt;ol&gt;&lt;li&gt;the unison - 0 (degrees of 17edo) - solfege name 'do'.&lt;/li&gt;&lt;li&gt;a second - includes 1 (ra, a minor second), 2 (ru, a neutral second), and 3 (re, a major second).&lt;/li&gt;&lt;li&gt;a third - includes 4 (me, a minor third), 5 (mu, a neutral third), and 6 (mi, a major third).&lt;/li&gt;&lt;li&gt;the perfect fourth - 7 (fa).&lt;/li&gt;&lt;/ol&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Correspondance:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Correspondance:&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--correspondance:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;correspondance:&lt;/h3&gt;
@@ Line 155: / Line 175: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--Tetrachord notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Tetrachord notation&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--tetrachord notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;tetrachord notation&lt;/h3&gt;
   &lt;br /&gt;
-Tetrachord notation will show three steps (as degrees of 17edo) separated by hyphens.&lt;br /&gt;
+Tetrachord notation will show three scalar steps (as degrees of 17edo) separated by hyphens.&lt;br /&gt;
 &lt;br /&gt;
 For instance, tetrachord 3-3-1 consists of&lt;br /&gt;
-(do), the unison, a given;&lt;br /&gt;
+(do), the unison;&lt;br /&gt;
-(re), a note 3 degrees up from 0 (do), a second;&lt;br /&gt;
+(re), a major second, 3 degrees up from 0;&lt;br /&gt;
-(mi), a note 3 degrees up from 3 (mi), a third; and&lt;br /&gt;
+(mi), a major third, 3 degrees up from 3; and&lt;br /&gt;
-(fa), the perfect fourth.&lt;br /&gt;
+(fa), the perfect fourth, 1 degree up from 6.&lt;br /&gt;
 &lt;br /&gt;
 The numbers in a tetrachord name will always add to 7.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x--The tetrachords"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;The tetrachords&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x--17edo primary tetrachords"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;17edo primary tetrachords&lt;/h3&gt;
   &lt;br /&gt;
+We have 9 primary tetrachords in 17edo.&lt;br /&gt;
+&lt;br /&gt;
@@ Line 317: / Line 339: @@
 &lt;/td&gt;
          &lt;td&gt;3-3-1&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x--17edo tetrachords complete"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;17edo tetrachords complete&lt;/h3&gt;
+ A more generalized tetrachord system would allow multiple seconds or multiple thirds: for instance, 1-1-5 or 5-1-1. Thus, a complete chart of 17edo tetrachords looks like this (with primary tetrachords in bold):&lt;br /&gt;
+&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1-1-5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2-1-4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;3-1-3&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4-1-2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5-1-1&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1-2-4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;2-2-3&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;3-2-2&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4-2-1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;strong&gt;1-3-3&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;2-3-2&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;3-3-1&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;strong&gt;1-4-2&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;2-4-1&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;strong&gt;1-5-1&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+Thus, by allowing multiples seconds or multiple thirds, we add 6 new tetrachords to our 9 primary tetrachords, for a total of 15. Our new ones:&lt;br /&gt;
+&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;tetrachord notation&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;solfege&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;name (suggestions?)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;used in&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1-1-5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;do ra ru fa&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1-2-4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;do ra re fa&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;2-1-4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;do ru re fa&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;4-1-2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;do me mu fa&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;4-2-1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;do me mi fa&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;5-1-1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;do mu mi fa&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

17edo tetrachords: Difference between revisions

Revision as of 01:22, 30 April 2009

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

Navigation menu

Search