Tricesimoprimal Tetrachordal Tesseract: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>FREEZE
No edit summary
Fredg999 category edits (talk | contribs)
autopatrolled, Bots, emailconfirmed
4,457 edits
m Removing from Category:Practice using Cat-a-lot
 
(3 intermediate revisions by 3 users not shown)
Line 27: Line 27:
| | [[31edo_Tetra_2-2-9|2-2-9]]
| | [[31edo_Tetra_2-2-9|2-2-9]]
| | [[31edo_Tetra_1-2-10|1-2-10]]
| | [[31edo_Tetra_1-2-10|1-2-10]]
| |  
| |
|-
|-
| | [[31edo_Tetra_9-3-1|9-3-1]]
| | [[31edo_Tetra_9-3-1|9-3-1]]
Line 38: Line 38:
| | [[31edo_Tetra_2-3-8|2-3-8]]
| | [[31edo_Tetra_2-3-8|2-3-8]]
| | [[31edo_Tetra_1-3-9|1-3-9]]
| | [[31edo_Tetra_1-3-9|1-3-9]]
| |  
| |
| |  
| |
|-
|-
| | [[31edo_Tetra_8-4-1|8-4-1]]
| | [[31edo_Tetra_8-4-1|8-4-1]]
Line 49: Line 49:
| | [[31edo_Tetra_2-4-7|2-4-7]]
| | [[31edo_Tetra_2-4-7|2-4-7]]
| | [[31edo_Tetra_1-4-8|1-4-8]]
| | [[31edo_Tetra_1-4-8|1-4-8]]
| |  
| |
| |  
| |
| |  
| |
|-
|-
| | [[31edo_Tetra_7-5-1|7-5-1]]
| | [[31edo_Tetra_7-5-1|7-5-1]]
Line 60: Line 60:
| | [[31edo_Tetra_2-5-6|2-5-6]]
| | [[31edo_Tetra_2-5-6|2-5-6]]
| | [[31edo_Tetra_1-5-7|1-5-7]]
| | [[31edo_Tetra_1-5-7|1-5-7]]
| |  
| |
| |  
| |
| |  
| |
| |  
| |
|-
|-
| | [[31edo_Tetra_6-6-1|6-6-1]]
| | [[31edo_Tetra_6-6-1|6-6-1]]
Line 71: Line 71:
| | [[31edo_Tetra_2-6-5|2-6-5]]
| | [[31edo_Tetra_2-6-5|2-6-5]]
| | [[31edo_Tetra_1-6-6|1-6-6]]
| | [[31edo_Tetra_1-6-6|1-6-6]]
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
|-
|-
| | [[31edo_Tetra_5-7-1|5-7-1]]
| | [[31edo_Tetra_5-7-1|5-7-1]]
Line 82: Line 82:
| | [[31edo_Tetra_2-7-4|2-7-4]]
| | [[31edo_Tetra_2-7-4|2-7-4]]
| | [[31edo_Tetra_1-7-5|1-7-5]]
| | [[31edo_Tetra_1-7-5|1-7-5]]
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
|-
|-
| | [[31edo_Tetra_4-8-1|4-8-1]]
| | [[31edo_Tetra_4-8-1|4-8-1]]
Line 93: Line 93:
| | [[31edo_Tetra_2-8-3|2-8-3]]
| | [[31edo_Tetra_2-8-3|2-8-3]]
| | [[31edo_Tetra_1-8-4|1-8-4]]
| | [[31edo_Tetra_1-8-4|1-8-4]]
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
|-
|-
| | [[31edo_Tetra_3-9-1|3-9-1]]
| | [[31edo_Tetra_3-9-1|3-9-1]]
| | [[31edo_Tetra_2-9-2|2-9-2]]
| | [[31edo_Tetra_2-9-2|2-9-2]]
| | [[31edo_Tetra_1-9-3|1-9-3]]
| | [[31edo_Tetra_1-9-3|1-9-3]]
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
|-
|-
| | [[31edo_Tetra_2-10-1|2-10-1]]
| | [[31edo_Tetra_2-10-1|2-10-1]]
| | [[31edo_Tetra_1-10-2|1-10-2]]
| | [[31edo_Tetra_1-10-2|1-10-2]]
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
|-
|-
| | [[31edo_Tetra_1-11-1|1-11-1]]
| | [[31edo_Tetra_1-11-1|1-11-1]]
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
|}
|}


Line 199: Line 199:
| | leto leto nudi
| | leto leto nudi
| | gosu leto jadi
| | gosu leto jadi
| |  
| |
|-
|-
| | nudi mito gosu
| | nudi mito gosu
Line 210: Line 210:
| | leto mito midi
| | leto mito midi
| | gosu mito nudi
| | gosu mito nudi
| |  
| |
| |  
| |
|-
|-
| | midi nuto gosu
| | midi nuto gosu
Line 221: Line 221:
| | leto nuto ledi
| | leto nuto ledi
| | gosu nuto midi
| | gosu nuto midi
| |  
| |
| |  
| |
| |  
| |
|-
|-
| | ledi jato gosu
| | ledi jato gosu
Line 232: Line 232:
| | leto jato goto
| | leto jato goto
| | gosu jato ledi
| | gosu jato ledi
| |  
| |
| |  
| |
| |  
| |
| |  
| |
|-
|-
| | goto goto gosu
| | goto goto gosu
Line 243: Line 243:
| | leto goto jato
| | leto goto jato
| | gosu goto goto
| | gosu goto goto
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
|-
|-
| | jato ledi gosu
| | jato ledi gosu
Line 254: Line 254:
| | leto ledi nuto
| | leto ledi nuto
| | gosu ledi jato
| | gosu ledi jato
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
|-
|-
| | nuto midi gosu
| | nuto midi gosu
Line 265: Line 265:
| | leto midi mito
| | leto midi mito
| | gosu midi nuto
| | gosu midi nuto
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
|-
|-
| | mito nudi gosu
| | mito nudi gosu
| | leto nudi leto
| | leto nudi leto
| | gosu nudi mito
| | gosu nudi mito
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
|-
|-
| | leto jadi gosu
| | leto jadi gosu
| | gosu jadi leto
| | gosu jadi leto
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
|-
|-
| | gosu godi gosu
| | gosu godi gosu
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
| |  
| |
|}
|}


Line 313: Line 313:
Write a ditty in a specific or generalized tetrachord scale, and turn it into an assignment for me.
Write a ditty in a specific or generalized tetrachord scale, and turn it into an assignment for me.


<span style="">- [[http://www.wikispaces.com/user/view/xenjacob
- [[User:Xenjacob|xenjacob]] <small>Jan 7, 2008</small>


<div class='external-image-warning' style='background-color:#f8f9fa; border: 1px solid #eaecf0; padding-left: 0.5em; padding-right:0.5em; display:inline-block'>
[[Category:31edo]]
External image: files/external-6bc0030f5a26941b1c6d9ebefe5111aa<br>
[[Category:Listen]]
: <small><b>WARNING</b>: MediaWiki doesn't have very good support for external images.</small><br>
[[Category:Tetrachords]]
: <small>Furthermore, since external images can break, we recommend that you replace the above with a local copy of the image.</small><br>
: <small>The file name files/external-6bc0030f5a26941b1c6d9ebefe5111aa was autogenerated by Wikispaces from its cache, but is not in this import because Mediawiki requires filenames to have extensions.</small><br>
: <small>However, you can get the original external URL for this image by clicking "View history", going to the last pre-import history revision, and looking at the original code for this image tag.</small><br>
: <small>The cached image is available for reference in the original xenharmonic export, available [https://archive.org/details/xenwikiultimatebackup here].</small>
</div>
[[Category:IMPORTDEBUG - Change External Images]]
 
]] [http://www.wikispaces.com/user/view/xenjacob xenjacob] <small>Jan 7, 2008</small></span>      [[Category:31edo]]
[[Category:listen]]
[[Category:practice]]
[[Category:tetrachord]]

Latest revision as of 05:42, 21 February 2023

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

(mp3 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. This chart should help:

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.

- xenjacob Jan 7, 2008

Retrieved from "https://en.xen.wiki/index.php?title=Tricesimoprimal_Tetrachordal_Tesseract&oldid=103529"