Tricesimoprimal Tetrachordal Tesseract
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenjacob and made on 2008-01-07 19:32:11 UTC.
- The original revision id was 14261691.
- 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:
//for AAH// This is not really a 4-dimensional cube, but a mere triangle. This is the table of tetrachord species in 31-edo, i.e. all of the ways that a perfect 4th (13 dieses) can be broken up into three steps. Numbers indicate intervals in degrees of 31. || 11-1-1 || 10-1-2 || 9-1-3 || 8-1-4 || 7-1-5 || 6-1-6 || 5-1-7 || 4-1-8 || 3-1-9 || 2-1-10 || 1-1-11 || || 10-2-1 || 9-2-2 || 8-2-3 || 7-2-4 || 6-2-5 || 5-2-6 || 4-2-7 || 3-2-8 || 2-2-9 || 1-2-10 || || || 9-3-1 || 8-3-2 || 7-3-3 || 6-3-4 || 5-3-5 || 4-3-6 || 3-3-7 || 2-3-8 || 1-3-9 || || || || 8-4-1 || 7-4-2 || 6-4-3 || 5-4-4 || 4-4-5 || 3-4-6 || 2-4-7 || 1-4-8 || || || || || 7-5-1 || 6-5-2 || 5-5-3 || 4-5-4 || 3-5-5 || 2-5-6 || 1-5-7 || || || || || || 6-6-1 || 5-6-2 || 4-6-3 || 3-6-4 || 2-6-5 || 1-6-6 || || || || || || || 5-7-1 || 4-7-2 || 3-7-3 || 2-7-4 || 1-7-5 || || || || || || || || 4-8-1 || 3-8-2 || 2-8-3 || 1-8-4 || || || || || || || || || 3-9-1 || 2-9-2 || 1-9-3 || || || || || || || || || || 2-10-1 || 1-10-2 || || || || || || || || || || || 1-11-1 || || || || || || || || || || || ===Pick an ostinato=== Have a rhythm and generalized contour that you use on each tetrachord. Using the 7-note scale made up of 2 "disjunct" tetrachords (separated by a major tone), my ostinato was 0-1-2-3-2-1-0-1-2-3, 4-5-6-7-6-5-4-5-6-7, 0-1-2-3-4-5-6-7. ===Pick a path=== I prefer a path that is complete (hits every square exactly once) and incremental (moves by exchanges of a single diesis; in the chart, single moves of up/down, left/right, or northeast/southwest only). The path used in the first recording begins at the upper-right of the chart and zigzags left-right-left-right to the bottom left. Another fun path yet untried is a spiral triangle. || link || ostinato || path || range || tempo || || [[media type="file" key="ttt 1.mp3"]] ([[http://xenharmonic.wikispaces.com/space/showimage/ttt%201.mp3|mp3]] [[http://xenharmonic.wikispaces.com/space/showimage/ttt0.mid|midi]]) || 0 1 2 3 2 1 0 1 2 3 4 5 6 7 6 5 4 5 6 7 0 1 2 3 4 5 6 7 || zigzag from 1-1-11 || Fd2 - Fd3 || eighth = 92 || ===Go!=== Start out just humming or singing along to the recording. Use the unretuned MIDI file if you want to change the tempo. Ask me for more renderings on my synth with different specifications, and I will make and upload them. I might add more renderings out of my own explorations too. ===Extra credit=== Sing the entire exercise with the shortspeak interval names. ===Next-assignment assignment=== Write a ditty in a specific or generalized tetrachord scale, and turn it into an assignment for me. [[user:xenjacob|1199752331]]
Original HTML content:
<html><head><title>Tricesimoprimal Tetrachordal Tesseract</title></head><body><em>for AAH</em><br />
<br />
This is not really a 4-dimensional cube, but a mere triangle. This is the table of tetrachord species in 31-edo, i.e. all of the ways that a perfect 4th (13 dieses) can be broken up into three steps. Numbers indicate intervals in degrees of 31.<br />
<br />
<table class="wiki_table">
<tr>
<td>11-1-1<br />
</td>
<td>10-1-2<br />
</td>
<td>9-1-3<br />
</td>
<td>8-1-4<br />
</td>
<td>7-1-5<br />
</td>
<td>6-1-6<br />
</td>
<td>5-1-7<br />
</td>
<td>4-1-8<br />
</td>
<td>3-1-9<br />
</td>
<td>2-1-10<br />
</td>
<td>1-1-11<br />
</td>
</tr>
<tr>
<td>10-2-1<br />
</td>
<td>9-2-2<br />
</td>
<td>8-2-3<br />
</td>
<td>7-2-4<br />
</td>
<td>6-2-5<br />
</td>
<td>5-2-6<br />
</td>
<td>4-2-7<br />
</td>
<td>3-2-8<br />
</td>
<td>2-2-9<br />
</td>
<td>1-2-10<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>9-3-1<br />
</td>
<td>8-3-2<br />
</td>
<td>7-3-3<br />
</td>
<td>6-3-4<br />
</td>
<td>5-3-5<br />
</td>
<td>4-3-6<br />
</td>
<td>3-3-7<br />
</td>
<td>2-3-8<br />
</td>
<td>1-3-9<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>8-4-1<br />
</td>
<td>7-4-2<br />
</td>
<td>6-4-3<br />
</td>
<td>5-4-4<br />
</td>
<td>4-4-5<br />
</td>
<td>3-4-6<br />
</td>
<td>2-4-7<br />
</td>
<td>1-4-8<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>7-5-1<br />
</td>
<td>6-5-2<br />
</td>
<td>5-5-3<br />
</td>
<td>4-5-4<br />
</td>
<td>3-5-5<br />
</td>
<td>2-5-6<br />
</td>
<td>1-5-7<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>6-6-1<br />
</td>
<td>5-6-2<br />
</td>
<td>4-6-3<br />
</td>
<td>3-6-4<br />
</td>
<td>2-6-5<br />
</td>
<td>1-6-6<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>5-7-1<br />
</td>
<td>4-7-2<br />
</td>
<td>3-7-3<br />
</td>
<td>2-7-4<br />
</td>
<td>1-7-5<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>4-8-1<br />
</td>
<td>3-8-2<br />
</td>
<td>2-8-3<br />
</td>
<td>1-8-4<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>3-9-1<br />
</td>
<td>2-9-2<br />
</td>
<td>1-9-3<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>2-10-1<br />
</td>
<td>1-10-2<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>1-11-1<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:1:<h3> --><h3 id="toc0"><a name="x--Pick an ostinato"></a><!-- ws:end:WikiTextHeadingRule:1 -->Pick an ostinato</h3>
Have a rhythm and generalized contour that you use on each tetrachord. Using the 7-note scale made up of 2 "disjunct" tetrachords (separated by a major tone), my ostinato was 0-1-2-3-2-1-0-1-2-3, 4-5-6-7-6-5-4-5-6-7, 0-1-2-3-4-5-6-7.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:3:<h3> --><h3 id="toc1"><a name="x--Pick a path"></a><!-- ws:end:WikiTextHeadingRule:3 -->Pick a path</h3>
I prefer a path that is complete (hits every square exactly once) and incremental (moves by exchanges of a single diesis; in the chart, single moves of up/down, left/right, or northeast/southwest only). The path used in the first recording begins at the upper-right of the chart and zigzags left-right-left-right to the bottom left. Another fun path yet untried is a spiral triangle.<br />
<br />
<table class="wiki_table">
<tr>
<td>link<br />
</td>
<td>ostinato<br />
</td>
<td>path<br />
</td>
<td>range<br />
</td>
<td>tempo<br />
</td>
</tr>
<tr>
<td><!-- ws:start:WikiTextMediaRule:0:<img src="http://www.wikispaces.com/site/embedthumbnail/file-audio/ttt%201.mp3?h=20&w=240" class="WikiMedia WikiMediaFile" id="wikitext@@media@@type=&quot;file&quot; key=&quot;ttt 1.mp3&quot;" title="Local Media File"height="20" width="240"/> --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fttt%252B1.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:0 --><br />
(<a class="wiki_link_ext" href="http://xenharmonic.wikispaces.com/space/showimage/ttt%201.mp3" rel="nofollow">mp3</a> <a class="wiki_link_ext" href="http://xenharmonic.wikispaces.com/space/showimage/ttt0.mid" rel="nofollow">midi</a>)<br />
</td>
<td>0 1 2 3 2 1<br />
0 1 2 3<br />
4 5 6 7 6 5<br />
4 5 6 7<br />
0 1 2 3 4 5 6 7<br />
</td>
<td>zigzag from 1-1-11<br />
</td>
<td>Fd2 - Fd3<br />
</td>
<td>eighth = 92<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:5:<h3> --><h3 id="toc2"><a name="x--Go!"></a><!-- ws:end:WikiTextHeadingRule:5 -->Go!</h3>
Start out just humming or singing along to the recording. Use the unretuned MIDI file if you want to change the tempo. Ask me for more renderings on my synth with different specifications, and I will make and upload them. I might add more renderings out of my own explorations too.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:7:<h3> --><h3 id="toc3"><a name="x--Extra credit"></a><!-- ws:end:WikiTextHeadingRule:7 -->Extra credit</h3>
Sing the entire exercise with the shortspeak interval names.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:9:<h3> --><h3 id="toc4"><a name="x--Next-assignment assignment"></a><!-- ws:end:WikiTextHeadingRule:9 -->Next-assignment assignment</h3>
Write a ditty in a specific or generalized tetrachord scale, and turn it into an assignment for me.<br />
<br />
<!-- ws:start:WikiTextUserlinkRule:00:[[user:xenjacob|1199752331]] --><span class="membersnap">- <a class="userLink" href="http://www.wikispaces.com/user/view/xenjacob" style="outline: none;"><img src="http://www.wikispaces.com/user/pic/xenjacob-lg.jpg" width="16" height="16" alt="xenjacob" class="userPicture" /></a> <a class="userLink" href="http://www.wikispaces.com/user/view/xenjacob" style="outline: none;">xenjacob</a> <small>Jan 7, 2008</small></span><!-- ws:end:WikiTextUserlinkRule:00 --></body></html>