17edo tetrachords: Difference between revisions

Revision as of 04:31, 19 September 2014

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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 || phrygian || diatonic (phrygian) ||
|| 1-4-2 || do ra mu fa ||   ||   ||
|| 1-5-1 || do ra mi fa || balkan, Hijaz (arabic) ||   ||
|| 2-2-3 || do ru me fa || Bayyati (arabic) || [[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 || Rast (arabic) || [[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 ||   ||   ||

See also: [[tetrachord]], [[22edo tetrachords]], [[Tricesimoprimal Tetrachordal Tesseract]].

Original HTML content:

<html><head><title>17edo tetrachords</title></head><body>Let a &quot;17edo primary <a class="wiki_link" href="/tetrachord">tetrachord</a>&quot; mean a set of four pitches in <a class="wiki_link" href="/17edo">17edo</a> that span a <a class="wiki_link" href="/perfect%20fourth">perfect fourth</a> (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>phrygian<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, Hijaz (arabic)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2-2-3<br />
</td>
        <td>do ru me fa<br />
</td>
        <td>Bayyati (arabic)<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>Rast (arabic)<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>

<br />
See also: <a class="wiki_link" href="/tetrachord">tetrachord</a>, <a class="wiki_link" href="/22edo%20tetrachords">22edo tetrachords</a>, <a class="wiki_link" href="/Tricesimoprimal%20Tetrachordal%20Tesseract">Tricesimoprimal Tetrachordal Tesseract</a>.</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:xenwolf|xenwolf]] and made on <tt>2010-06-10 17:47:29 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2014-09-19 04:31:36 UTC</tt>.<br>
-: The original revision id was <tt>148249533</tt>.<br>
+: The original revision id was <tt>522925744</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>
@@ Line 41: / Line 41: @@
 || tetrachord notation || solfege || name (suggestions?) || used in ||
-|| 1-3-3 || do ra me fa || phyrgian || diatonic (phrygian) ||
+|| 1-3-3 || do ra me fa || phrygian || diatonic (phrygian) ||
 || 1-4-2 || do ra mu fa ||   ||   ||
-|| 1-5-1 || do ra mi fa || balkan ||   ||
+|| 1-5-1 || do ra mi fa || balkan, Hijaz (arabic) ||   ||
-|| 2-2-3 || do ru me fa ||   || [[17edo neutral scale]] (led) ||
+|| 2-2-3 || do ru me fa || Bayyati (arabic) || [[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) ||
+|| 3-2-2 || do re mu fa || Rast (arabic) || [[17edo neutral scale]] (dril, gil, kleeth) ||
 || 3-3-1 || do re mi fa || ionian || diatonic (ionian, mixolydian) ||
@@ Line 211: / Line 211: @@
          &lt;td&gt;do ra me fa&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;phyrgian&lt;br /&gt;
+         &lt;td&gt;phrygian&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;diatonic (phrygian)&lt;br /&gt;
@@ Line 231: / Line 231: @@
          &lt;td&gt;do ra mi fa&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;balkan&lt;br /&gt;
+         &lt;td&gt;balkan, Hijaz (arabic)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 241: / Line 241: @@
          &lt;td&gt;do ru me fa&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;Bayyati (arabic)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;a class="wiki_link" href="/17edo%20neutral%20scale"&gt;17edo neutral scale&lt;/a&gt; (led)&lt;br /&gt;
@@ Line 281: / Line 281: @@
          &lt;td&gt;do re mu fa&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;Rast (arabic)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;a class="wiki_link" href="/17edo%20neutral%20scale"&gt;17edo neutral scale&lt;/a&gt; (dril, gil, kleeth)&lt;br /&gt;

17edo tetrachords: Difference between revisions

Revision as of 04:31, 19 September 2014

IMPORTED REVISION FROM WIKISPACES

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Original HTML content:

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