Shoal17: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,282 edits
mNo edit summary
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,282 edits
m →Scala file: I don't know why I put a line break here
 
(33 intermediate revisions by 2 users not shown)
Line 1: Line 1:
17-tone [[MOS scale]] for the [[shoal]] temperament.
'''Shoal[17]''' is the 17-tone [[MOS scale]], [[11L 6s]], for the [[shoal]] temperament, which serves as an extremely accurate 2.3.13.23 [[subgroup]] detemper of [[17edo]].
 
== Scala file ==
This uses the symmetrical (LsLLsLLsLsLLsLLsL) mode of Shoal[17] with the [[CTE]] generator tuning of 212.261{{c}}.


<pre>
<pre>
Line 29: Line 32:
</pre>
</pre>


[[Category:17-tone scales]][[Category:Tempered scales]][[Category:23-limit]][[Category:Pages with Scala files]]
== Approximations of JI ==
These use the symmetrical mode of Shoal[17].
 
{| class="wikitable"
! Steps !! [[Cents]] !! 2.3.13.23 subgroup !! Others
|-
! 1
| 73.566 || 24/23 || 25/24, 23/22
|-
! 2
| 138.695 || 13/12 ||
|-
! 3
| 212.261 || 26/23 || 17/15
|-
! 4
| 285.827 || 46/39 || 7/6, 13/11
|-
! 5
| 350.956 || 207/169 || 11/9
|-
! 6
| 424.522 || 23/18 || 9/7
|-
! 7
| 498.088 || 4/3 ||
|-
! 8
| 563.217 || 18/13 || 11/8
|-
! 9
| 636.783 || 13/9 ||
|-
! 10
| 701.912 || 3/2 ||
|-
! 11
| 775.478 || 36/23 || 11/7, 25/16
|-
! 12
| 849.044 || 338/207 || 18/11
|-
! 13
| 914.173 || 39/23 || 17/10, 22/13
|-
! 14
| 987.739 || 23/13 || 7/4
|-
! 15
| 1061.305 || 24/13 || 11/6
|-
! 16
| 1126.434 || 23/12 || 21/11
|-
! 17
| 1200.000 || 2/1 ||
|}
<br>
 
== Subsets ==
 
=== Scales ===
==== Up to 10 tones/octave ====
Algal bloom scale (''shoal[17] is the original/default tuning for this scale'')
* 73.566
* 350.956
* 498.088
* 701.912
* 987.739
* 1200.000
 
 
[[Antipental blues]] scale (''approximated from [[dwarf17marv]]'')
* 285.827
* 498.088
* 563.217
* 701.912
* 987.739
* 1200.000
 
 
Diffractive scale (''shoal[17] is the original/default tuning for this scale'')
* 73.566
* 285.827
* 636.783
* 701.912
* 1200.000
 
 
Diffractive [[tetrad]] (''shoal[17] is the original/default tuning for this scale'')
* 285.827
* 636.783
* 701.912
* 1200.000
 
 
Driftwood scale (''shoal[17] is the original/default tuning for this scale'')
* 138.695
* 498.088
* 636.783
* 987.739
* 1200.000
 
 
Minor [[hexatonic]] scale (''approximated from [[12edo]]'')
* 212.261
* 285.827
* 498.088
* 701.912
* 987.739
* 1200.000
 
 
Minor [[pentatonic]] scale (''approximated from [[12edo]]'')
* 285.827
* 498.088
* 701.912
* 987.739
* 1200.000
 
 
Quasi-otonal [[pentad]] (''approximated from [[8afdo]]'')
* 424.522
* 563.217
* 701.912
* 987.739
* 1200.000
 
 
Refractive scale (''shoal[17] is the original/default tuning for this scale'')
* 285.827
* 701.912
* 775.478
* 1061.305
* 1200.000
 
 
Refractive tetrad (''shoal[17] is the original/default tuning for this scale'')
* 701.912
* 775.478
* 1061.305
* 1200.000
 
 
Roughened blues dorian pentatonic scale (''approximated from [[compton]] in [[96edo]]'')
* 285.827
* 701.912
* 914.173
* 987.739
* 1200.000
 
 
Sharpened blues dorian hexatonic scale (''approximated from [[compton]] in [[96edo]]'')
* 285.827
* 498.088
* 701.912
* 914.173
* 987.739
* 1200.000
 
 
Shoal17 over-9 tetrad (''shoal[17] is the original/default tuning for this scale'')
* 498.088
* 636.783
* 987.739
* 1200.000
<br>
 
==== Over 10 tones/octave ====
Shoal quasi-chromatic (''approximated from [[12edo]]; has 12 tones/octave so it maps nicely onto a [[:Category:Piano|piano]] keyboard'')
* 73.566
* 212.261
* 285.827
* 424.522
* 498.088
* 563.217
* 701.912
* 775.478
* 914.173
* 987.739
* 1126.434
* 1200.000
<br>
 
=== Triads ===
These can be used for a [[polytriadic]] approach. Any triad from ''shoal[17]'' can be used, so there are a huge number of possibilities, many more than can be listed here. These are just a small sampling of examples to start from.
 
These use the symmetrical mode of Shoal[17].
<br>
 
 
24/23-3/2-2/1 triad
* 73.566
* 701.912
* 1200.000
 
 
13/12-3/2-2/1 triad
* 138.695
* 701.912
* 1200.000
 
 
13/12-4/3-2/1 triad
* 138.695
* 498.088
* 1200.000
 
 
9/8 (26/23)-3/2-2/1 triad
* 212.261
* 701.912
* 1200.000
 
 
9/8 (26/23)-4/3-2/1 triad
* 212.261
* 498.088
* 1200.000
 
 
46/39-3/2-2/1 triad
* 285.827
* 701.912
* 1200.000
 
 
23/18-3/2-2/1 triad
* 424.522
* 701.912
* 1200.000
 
 
4/3-3/2-2/1 triad
* 498.088
* 701.912
* 1200.000
 
 
18/13-3/2-2/1 triad
* 563.217
* 701.912
* 1200.000
 
 
4/3-13/9-2/1 triad
* 498.088
* 636.783
* 1200.000
 
 
4/3-36/23-2/1 triad
* 498.088
* 775.478
* 1200.000
 
 
3/2-36/23-2/1 triad
* 701.912
* 775.478
* 1200.000
 
 
3/2-13/8-2/1 triad
* 701.912
* 849.044
* 1200.000
 
 
4/3-13/8-2/1 triad
* 498.088
* 849.044
* 1200.000
 
 
3/2-39/23-2/1 triad
* 701.912
* 914.173
* 1200.000
 
 
3/2-16/9 (23/13)-2/1 triad
* 701.912
* 987.739
* 1200.000
 
 
3/2-24/13-2/1 triad
* 701.912
* 1061.305
* 1200.000
 
 
3/2-23/12-2/1 triad
* 701.912
* 1126.434
* 1200.000
 
== Music ==
* [https://www.youtube.com/watch?v=bwGjN56iMM0 ''Moody Improvisation in the Shoal Temperament''] - [[Budjarn Lambeth]] (2025)
 
[[Category:17-tone scales]][[Category:Tempered scales]]
[[Category:Pages with mostly numerical content]][[Category:23-limit]][[Category:Pages with Scala files]][[Category:Listen]]

Latest revision as of 06:11, 29 September 2025

Shoal[17] is the 17-tone MOS scale, 11L 6s, for the shoal temperament, which serves as an extremely accurate 2.3.13.23 subgroup detemper of 17edo.

Scala file

This uses the symmetrical (LsLLsLLsLsLLsLLsL) mode of Shoal[17] with the CTE generator tuning of 212.261 ¢. 

! shoal17.scl
! Created using Scale Workshop 3.1.0
!
! https://scaleworkshop.plainsound.org/scale/i2oX3QRN_
!
Shoal17
 17
!
 73.566
 138.695
 212.261
 285.827
 350.956
 424.522
 498.088
 563.217
 636.783
 701.912
 775.478
 849.044
 914.173
 987.739
 1061.305
 1126.434
 2/1

Approximations of JI

These use the symmetrical mode of Shoal[17].

Steps Cents 2.3.13.23 subgroup Others
1 73.566 24/23 25/24, 23/22
2 138.695 13/12
3 212.261 26/23 17/15
4 285.827 46/39 7/6, 13/11
5 350.956 207/169 11/9
6 424.522 23/18 9/7
7 498.088 4/3
8 563.217 18/13 11/8
9 636.783 13/9
10 701.912 3/2
11 775.478 36/23 11/7, 25/16
12 849.044 338/207 18/11
13 914.173 39/23 17/10, 22/13
14 987.739 23/13 7/4
15 1061.305 24/13 11/6
16 1126.434 23/12 21/11
17 1200.000 2/1


Subsets

Scales

Up to 10 tones/octave

Algal bloom scale (shoal[17] is the original/default tuning for this scale)

  • 73.566
  • 350.956
  • 498.088
  • 701.912
  • 987.739
  • 1200.000


Antipental blues scale (approximated from dwarf17marv)

  • 285.827
  • 498.088
  • 563.217
  • 701.912
  • 987.739
  • 1200.000


Diffractive scale (shoal[17] is the original/default tuning for this scale)

  • 73.566
  • 285.827
  • 636.783
  • 701.912
  • 1200.000


Diffractive tetrad (shoal[17] is the original/default tuning for this scale)

  • 285.827
  • 636.783
  • 701.912
  • 1200.000


Driftwood scale (shoal[17] is the original/default tuning for this scale)

  • 138.695
  • 498.088
  • 636.783
  • 987.739
  • 1200.000


Minor hexatonic scale (approximated from 12edo)

  • 212.261
  • 285.827
  • 498.088
  • 701.912
  • 987.739
  • 1200.000


Minor pentatonic scale (approximated from 12edo)

  • 285.827
  • 498.088
  • 701.912
  • 987.739
  • 1200.000


Quasi-otonal pentad (approximated from 8afdo)

  • 424.522
  • 563.217
  • 701.912
  • 987.739
  • 1200.000


Refractive scale (shoal[17] is the original/default tuning for this scale)

  • 285.827
  • 701.912
  • 775.478
  • 1061.305
  • 1200.000


Refractive tetrad (shoal[17] is the original/default tuning for this scale)

  • 701.912
  • 775.478
  • 1061.305
  • 1200.000


Roughened blues dorian pentatonic scale (approximated from compton in 96edo)

  • 285.827
  • 701.912
  • 914.173
  • 987.739
  • 1200.000


Sharpened blues dorian hexatonic scale (approximated from compton in 96edo)

  • 285.827
  • 498.088
  • 701.912
  • 914.173
  • 987.739
  • 1200.000


Shoal17 over-9 tetrad (shoal[17] is the original/default tuning for this scale)

  • 498.088
  • 636.783
  • 987.739
  • 1200.000


Over 10 tones/octave

Shoal quasi-chromatic (approximated from 12edo; has 12 tones/octave so it maps nicely onto a piano keyboard)

  • 73.566
  • 212.261
  • 285.827
  • 424.522
  • 498.088
  • 563.217
  • 701.912
  • 775.478
  • 914.173
  • 987.739
  • 1126.434
  • 1200.000


Triads

These can be used for a polytriadic approach. Any triad from shoal[17] can be used, so there are a huge number of possibilities, many more than can be listed here. These are just a small sampling of examples to start from.

These use the symmetrical mode of Shoal[17].


24/23-3/2-2/1 triad

  • 73.566
  • 701.912
  • 1200.000


13/12-3/2-2/1 triad

  • 138.695
  • 701.912
  • 1200.000


13/12-4/3-2/1 triad

  • 138.695
  • 498.088
  • 1200.000


9/8 (26/23)-3/2-2/1 triad

  • 212.261
  • 701.912
  • 1200.000


9/8 (26/23)-4/3-2/1 triad

  • 212.261
  • 498.088
  • 1200.000


46/39-3/2-2/1 triad

  • 285.827
  • 701.912
  • 1200.000


23/18-3/2-2/1 triad

  • 424.522
  • 701.912
  • 1200.000


4/3-3/2-2/1 triad

  • 498.088
  • 701.912
  • 1200.000


18/13-3/2-2/1 triad

  • 563.217
  • 701.912
  • 1200.000


4/3-13/9-2/1 triad

  • 498.088
  • 636.783
  • 1200.000


4/3-36/23-2/1 triad

  • 498.088
  • 775.478
  • 1200.000


3/2-36/23-2/1 triad

  • 701.912
  • 775.478
  • 1200.000


3/2-13/8-2/1 triad

  • 701.912
  • 849.044
  • 1200.000


4/3-13/8-2/1 triad

  • 498.088
  • 849.044
  • 1200.000


3/2-39/23-2/1 triad

  • 701.912
  • 914.173
  • 1200.000


3/2-16/9 (23/13)-2/1 triad

  • 701.912
  • 987.739
  • 1200.000


3/2-24/13-2/1 triad

  • 701.912
  • 1061.305
  • 1200.000


3/2-23/12-2/1 triad

  • 701.912
  • 1126.434
  • 1200.000

Music

Retrieved from "https://en.xen.wiki/index.php?title=Shoal17&oldid=211468"