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Tricesimoprimal Tetrachordal Tesseract: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
''for AAH''
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2008-01-05 21:29:20 UTC</tt>.<br>
: The original revision id was <tt>14171685</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 work in progress//


This is the table of tetrachord species in 31-edo. Numbers indicate intervals in degrees of 31. We will use them in ascending order.
This is not really a 4-dimensional cube, but a mere triangle. This is the table of [[tetrachord|tetrachord]] species in [[31edo|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 ||
{| class="wikitable"
|| 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 ||   ||   ||
| | [[31edo_Tetra_11-1-1|11-1-1]]
|| 8-4-1 || 7-4-2 || 6-4-3 || 5-4-4 || 4-4-5 || 3-4-6 || 2-4-7 || 1-4-8 ||   ||   ||   ||
| | [[31edo_Tetra_10-1-2|10-1-2]]
|| 7-5-1 || 6-5-2 || 5-5-3 || 4-5-4 || 3-5-5 || 2-5-6 || 1-5-7 ||   ||   ||   ||   ||
| | [[31edo_Tetra_9-1-3|9-1-3]]
|| 6-6-1 || 5-6-2 || 4-6-3 || 3-6-4 || 2-6-5 || 1-6-6 ||   ||   ||   ||   ||   ||
| | [[31edo_Tetra_8-1-4|8-1-4]]
|| 5-7-1 || 4-7-2 || 3-7-3 || 2-7-4 || 1-7-5 ||   ||   ||   ||   ||   ||   ||
| | [[31edo_Tetra_7-1-5|7-1-5]]
|| 4-8-1 || 3-8-2 || 2-8-3 || 1-8-4 ||   ||   ||   ||   ||   ||   ||   ||
| | [[31edo_Tetra_6-1-6|6-1-6]]
|| 3-9-1 || 2-9-2 || 1-9-3 ||   ||   ||   ||   ||   ||   ||   ||   ||
| | [[31edo_Tetra_5-1-7|5-1-7]]
|| 2-10-1 || 1-10-2 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
| | [[31edo_Tetra_4-1-8|4-1-8]]
|| 1-11-1 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
| | [[31edo_Tetra_3-1-9|3-1-9]]
| | [[31edo_Tetra_2-1-10|2-1-10]]
| | [[31edo_Tetra_1-1-11|1-1-11]]
|-
| | [[31edo_Tetra_10-2-1|10-2-1]]
| | [[31edo_Tetra_9-2-2|9-2-2]]
| | [[31edo_Tetra_8-2-3|8-2-3]]
| | [[31edo_Tetra_7-2-4|7-2-4]]
| | [[31edo_Tetra_6-2-5|6-2-5]]
| | [[31edo_Tetra_5-2-6|5-2-6]]
| | [[31edo_Tetra_4-2-7|4-2-7]]
| | [[31edo_Tetra_3-2-8|3-2-8]]
| | [[31edo_Tetra_2-2-9|2-2-9]]
| | [[31edo_Tetra_1-2-10|1-2-10]]
| |
|-
| | [[31edo_Tetra_9-3-1|9-3-1]]
| | [[31edo_Tetra_8-3-2|8-3-2]]
| | [[31edo_Tetra_7-3-3|7-3-3]]
| | [[31edo_Tetra_6-3-4|6-3-4]]
| | [[31edo_Tetra_5-3-5|5-3-5]]
| | [[31edo_Tetra_4-3-6|4-3-6]]
| | [[31edo_Tetra_3-3-7|3-3-7]]
| | [[31edo_Tetra_2-3-8|2-3-8]]
| | [[31edo_Tetra_1-3-9|1-3-9]]
| |
| |
|-
| | [[31edo_Tetra_8-4-1|8-4-1]]
| | [[31edo_Tetra_7-4-2|7-4-2]]
| | [[31edo_Tetra_6-4-3|6-4-3]]
| | [[31edo_Tetra_5-4-4|5-4-4]]
| | [[31edo_Tetra_4-4-5|4-4-5]]
| | [[31edo_Tetra_3-4-6|3-4-6]]
| | [[31edo_Tetra_2-4-7|2-4-7]]
| | [[31edo_Tetra_1-4-8|1-4-8]]
| |
| |
| |
|-
| | [[31edo_Tetra_7-5-1|7-5-1]]
| | [[31edo_Tetra_6-5-2|6-5-2]]
| | [[31edo_Tetra_5-5-3|5-5-3]]
| | [[31edo_Tetra_4-5-4|4-5-4]]
| | [[31edo_Tetra_3-5-5|3-5-5]]
| | [[31edo_Tetra_2-5-6|2-5-6]]
| | [[31edo_Tetra_1-5-7|1-5-7]]
| |
| |
| |
| |
|-
| | [[31edo_Tetra_6-6-1|6-6-1]]
| | [[31edo_Tetra_5-6-2|5-6-2]]
| | [[31edo_Tetra_4-6-3|4-6-3]]
| | [[31edo_Tetra_3-6-4|3-6-4]]
| | [[31edo_Tetra_2-6-5|2-6-5]]
| | [[31edo_Tetra_1-6-6|1-6-6]]
| |
| |
| |
| |
| |
|-
| | [[31edo_Tetra_5-7-1|5-7-1]]
| | [[31edo_Tetra_4-7-2|4-7-2]]
| | [[31edo_Tetra_3-7-3|3-7-3]]
| | [[31edo_Tetra_2-7-4|2-7-4]]
| | [[31edo_Tetra_1-7-5|1-7-5]]
| |
| |
| |
| |
| |
| |
|-
| | [[31edo_Tetra_4-8-1|4-8-1]]
| | [[31edo_Tetra_3-8-2|3-8-2]]
| | [[31edo_Tetra_2-8-3|2-8-3]]
| | [[31edo_Tetra_1-8-4|1-8-4]]
| |
| |
| |
| |
| |
| |
| |
|-
| | [[31edo_Tetra_3-9-1|3-9-1]]
| | [[31edo_Tetra_2-9-2|2-9-2]]
| | [[31edo_Tetra_1-9-3|1-9-3]]
| |
| |
| |
| |
| |
| |
| |
| |
|-
| | [[31edo_Tetra_2-10-1|2-10-1]]
| | [[31edo_Tetra_1-10-2|1-10-2]]
| |
| |
| |
| |
| |
| |
| |
| |
| |
|-
| | [[31edo_Tetra_1-11-1|1-11-1]]
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
|}


details at eleven. </pre></div>
===Pick an ostinato===
<h4>Original HTML content:</h4>
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.
<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;Tricesimoprimal Tetrachordal Tesseract&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;a work in progress&lt;/em&gt;&lt;br /&gt;
&lt;br /&gt;
This is the table of tetrachord species in 31-edo. Numbers indicate intervals in degrees of 31. We will use them in ascending order.&lt;br /&gt;
&lt;br /&gt;


===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.


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td&gt;11-1-1&lt;br /&gt;
| | link
&lt;/td&gt;
| | ostinato
        &lt;td&gt;10-1-2&lt;br /&gt;
| | path
&lt;/td&gt;
| | range
        &lt;td&gt;9-1-3&lt;br /&gt;
| | tempo
&lt;/td&gt;
|-
        &lt;td&gt;8-1-4&lt;br /&gt;
| | [[File:ttt_1.mp3]]
&lt;/td&gt;
        &lt;td&gt;7-1-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6-1-6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-1-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4-1-8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-1-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-1-10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-1-11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10-2-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9-2-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8-2-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7-2-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6-2-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-2-6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4-2-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-2-8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-2-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-2-10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9-3-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8-3-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7-3-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6-3-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-3-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4-3-6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-3-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-3-8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3-9&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;8-4-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7-4-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6-4-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-4-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4-4-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-4-6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-4-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-4-8&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;7-5-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6-5-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-5-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4-5-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-5-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-5-6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5-7&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;tr&gt;
        &lt;td&gt;6-6-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-6-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4-6-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-6-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-6-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6-6&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;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5-7-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4-7-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-7-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-7-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7-5&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;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;4-8-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-8-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-8-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-8-4&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;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;3-9-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-9-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-9-3&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;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;tr&gt;
        &lt;td&gt;2-10-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-10-2&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;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;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1-11-1&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;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;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
([[:File:ttt_1.mp3|mp3]] [[:File:ttt0.mid|midi]])
details at eleven.&lt;/body&gt;&lt;/html&gt;</pre></div>
| | 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|shortspeak]] interval names. This chart should help:
 
{| class="wikitable"
|-
| | godi gosu gosu
| | jadi gosu leto
| | nudi gosu mito
| | midi gosu nuto
| | ledi gosu jato
| | goto gosu goto
| | jato gosu ledi
| | nuto gosu midi
| | mito gosu nudi
| | leto gosu jadi
| | gosu gosu godi
|-
| | jadi leto gosu
| | nudi leto leto
| | midi leto mito
| | ledi leto nuto
| | goto leto jato
| | jato leto goto
| | nuto leto ledi
| | mito leto midi
| | leto leto nudi
| | gosu leto jadi
| |
|-
| | nudi mito gosu
| | midi mito leto
| | ledi mito mito
| | goto mito nuto
| | jato mito jato
| | nuto mito goto
| | mito mito ledi
| | leto mito midi
| | gosu mito nudi
| |
| |
|-
| | midi nuto gosu
| | ledi nuto leto
| | goto nuto mito
| | jato nuto nuto
| | nuto nuto jato
| | mito nuto goto
| | leto nuto ledi
| | gosu nuto midi
| |
| |
| |
|-
| | ledi jato gosu
| | goto jato leto
| | jato jato mito
| | nuto jato nuto
| | mito jato jato
| | leto jato goto
| | gosu jato ledi
| |
| |
| |
| |
|-
| | goto goto gosu
| | jato goto leto
| | nuto goto mito
| | mito goto nuto
| | leto goto jato
| | gosu goto goto
| |
| |
| |
| |
| |
|-
| | jato ledi gosu
| | nuto ledi leto
| | mito ledi mito
| | leto ledi nuto
| | gosu ledi jato
| |
| |
| |
| |
| |
| |
|-
| | nuto midi gosu
| | mito midi leto
| | leto midi mito
| | gosu midi nuto
| |
| |
| |
| |
| |
| |
| |
|-
| | mito nudi gosu
| | leto nudi leto
| | gosu nudi mito
| |
| |
| |
| |
| |
| |
| |
| |
|-
| | leto jadi gosu
| | gosu jadi leto
| |
| |
| |
| |
| |
| |
| |
| |
| |
|-
| | gosu godi gosu
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
|}
 
===Next-assignment assignment===
Write a ditty in a specific or generalized tetrachord scale, and turn it into an assignment for me.
 
- [[User:Xenjacob|xenjacob]] <small>Jan 7, 2008</small>
 
[[Category:31edo]]
[[Category:Listen]]
[[Category:Tetrachords]]
Retrieved from "https://en.xen.wiki/w/Tricesimoprimal_Tetrachordal_Tesseract"