17edo tetrachords
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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 || aeolian || 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 "17edo primary <a class="wiki_link" href="/tetrachord">tetrachord</a>" 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:<h3> --><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:<h3> --><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:<h3> --><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>aeolian<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:<h3> --><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>