User:BudjarnLambeth/Sandbox: Difference between revisions

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'''This is a working out sandbox page, not a content page.'''
== Scales ==
; 12-tone 7edo&5edo
This scale is designed to be mapped to the key of C on a conventional piano keyboard, with 7edo on the white keys, and 5edo on black:
* 5 2 3 4 1 5 1 4 3 2 5 0


; 24-tone blackwood&greenwood
You can have two pianos/keyboards, one 68.6 [[cents]] sharp of the other, both tuned to the 12-tone 7edo&5edo scale. The combined black keys across both keyboards will be [[blackwood]][10] and the white keys will be [[greenwood]][14].
* 3 2 0 2 1 2 2 1 1 1 3 1 1 1 2 2 1 2 0 2 3 0 2 0


== Sandbox ==
; 20-tone blackwood&greenwood
Removing the duplicates from the previous scale (perhaps for use on other instruments beside keyboard) gives this 20-tone scale, which includes both blackwood[10] and greenwood[14] as subsets.
* 3 2 2 1 2 2 1 1 1 3 1 1 1 2 2 1 2 2 3 2


{| class="wikitable sortable"
; Muggles[19]
! rowspan="2" | Name of tuning !! rowspan="2" | Step size (cents) !! rowspan="2" | !! colspan="5" | Error (% step size) !! rowspan="2" | !! colspan="5" | Mapping (# steps)
Of all the regular temperaments available in 35edo, [[muggles]] approximates [[just intonation]] the most closely. Here is the muggles[19] [[MOS scale]]:
|-
* 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2
| Prime 2 || Prime 3 || Prime 5 || Prime 7 || Prime 11 || Prime 2 || Prime 3 || Prime 5 || Prime 7 || Prime 11
|-
! 154zpi
| 33.55 ||  || 23 || 31 || 5 || 41 || 27 ||  || 36 || 57 || 83 || 100 || 124
|-
! 36ed257/128
| 33.52 ||  || 20 || 26 || 12 || 50 || 15 ||  || 36 || 57 || 83 || 101 || 124
|-
! 36ed513/256
| 33.43 ||  || 10 || 11 || 35 || 23 || 18 ||  || 36 || 57 || 83 || 101 || 124
|-
! 57edt
| 33.37 ||  || 4 || 0 || 50 || 5 || 40 ||  || 36 || 57 || 83 || 101 || 124
|-
! 155zpi
| 33.35 ||  || 2 || 3 || 45 || 1 || 48 ||  || 36 || 57 || 84 || 101 || 124
|-
!
|  ||  ||  ||  ||  ||  ||  ||  ||  ||  ||  ||  ||
|-
! 36edo
| 33.33 ||  || 0 || 6 || 40 || 8 || 45 ||  || 36 || 57 || 84 || 101 || 125
|-
!
|  ||  ||  ||  ||  ||  ||  ||  ||  ||  ||  ||  ||
|-
! 36ed511/256
| 33.24 ||  || 10 || 22 || 18 || 35 || 11 ||  || 36 || 57 || 84 || 101 || 125
|-
! 156zpi
| 33.15 ||  || 20 || 37 || 5 || 38 || 23 ||  || 36 || 57 || 84 || 102 || 125
|-
! 36ed255/128
| 33.145 ||  || 21 || 38 || 6 || 36 || 25 ||  || 36 || 57 || 84 || 102 || 125
|}


; Ripple[23]
This [[modmos]] of ripple[12] sounds sort of like the familiar [[12edo]]:
* 3 3 3 2 3 3 3 4 2 3 3 3
And it can be extended out to the ripple[23] [MOS scale]] which adds many [[7-limit]] intervals:
* 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1


.
; [[MOS scale]]s
* [[Greenwood]][7]/[[whitewood]][7]: 5 5 5 5 5 5 5 (''a.k.a. [[7edo]]; an [[equiheptatonic]] scale'')
* [[Greenwood]][14]: 3 2 3 2 3 2 3 2 3 2 3 2 3 2
* [[Greenwood]][21]: 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2
* [[Muggles]][5] (a.k.a. sub-diatonic): 9 4 9 9 4
* [[Muggles]][13]: 2 2 5 2 2 2 5 2 2 2 5 2 2
* [[Muggles]][16]: 2 2 3 2 2 2 2 2 3 2 2 2 2 3 2 2
* [[Muggles]][19]: 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2
* [[Ripple]][12]: 3 3 3 3 3 3 3 3 2 3 3 3
* [[Ripple]][23]: 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1
* [[Secund]][17]: 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3
* [[Whitewood]][14]: 1 4 1 4 1 4 1 4 1 4 1 4 1 4
* [[Whitewood]][21]: 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1
* [[Blackwood]][5]: 7 7 7 7 7 (''a.k.a. [[5edo]]; an [[equipentatonic]] scale; [[slendro]]-like; works with all three blackwood tunings'')
* [[Blackwood|5/4-blackwood]][10]: 4 3 4 3 4 3 4 3 4 3
* [[Blackwood|5/4-blackwood]][15]: 3 1 3 3 1 3 3 1 3 3 1 3 3 1 3
* [[Blackwood|5/4-blackwood]][25]: 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1
* [[Blackwood|6/5-blackwood]][10]: 2 5 2 5 2 5 2 5 2 5
* [[Blackwood|6/5-blackwood]][15]: 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2
* [[Blackwood|6/5-blackwood]][20]: 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2
{| class="wikitable mw-collapsible mw-collapsed"
|+Secund[17] subsets
|''Contains [[Template:Idiosyncratic|idiosyncratic terms]].''


*[[Antipental blues]]: 8 7 1 4 8 7
* Antipental blues maj 6th: 8 7 1 4 7 1 7
* Antipental blues neutral 7th: 8 7 1 4 8 3 4
* Antipental blues maj 7th: 8 7 1 4 8 4 3
* Antipental blues harmonic: 8 7 1 4 3 9 3
* [[Pelog]]-like heptatonic: 3 5 7 5 3 8 4 (''Phrygian-like'')
* Pelog-like pentatonic: 3 5 12 3 12
* Secund chance ([[modmos]] of secund[8]): 4 7 4 1 4 4 7 4
* Secund-tempered rotated [[5afdo]]: 7 4 9 8 7
* Secund-tempered [[6afdo]]: 8 7 5 7 4 4
* Undecimal Mixolydian: 7 4 4 5 7 1 7
* Undecimal minor hexatonic: 7 1 7 5 8 7
* Undecimal quasi-equipentatonic: 7 8 5 8 7
* 12 from secund[17]: 7 1 3 4 1 4 3 4 1 3 1 3
|}


.
{| class="wikitable mw-collapsible mw-collapsed"
|+6/5-blackwood[20] subsets
|''Contains [[Template:Idiosyncratic|idiosyncratic terms]].''


*Blackwood meta-Hirajoshi: 2 3 4 2 5 7 2 12
** ''Blackwood pseudo-Akebono neutral: 5 9 7 2 12''
** ''Blackwood pseudo-Akebono supermajor: 7 7 7 2 12''
** ''Blackwood pseudo-Hirajoshi: 2 12 7 2 12''
** ''Blackwood pseudo-[[pelog]]: 5 4 12 2 12''
* Blackwood meta-partial: 4 3 2 2 3 7 7 7
** ''Blackwood-tempered [[5afdo]]: 7 4 10 7 7''
** ''Mechanical (from [[16afdo]]): 9 2 10 7 7''
** ''Starship (from [[68ifdo]]'', see [[ifdo]]''): 4 7 3 7 7 7''
** ''Volcanic (from [[16afdo]]): 4 7 10 7 7''
* Meta-monsoon: 7 4 3 2 5 9 5
** ''Monsoon (from [[47zpi]]): 7 7 7 9 5''
** ''Monsoon otonal: 7 9 5 9 5''
** ''Monsoon major: 11 5 5 9 5''
* Blackwood neutral nonatonic: 4 7 3 2 5 4 5 2 3
* Blackwood undecimal harmonic: 4 8 4 5 4 5 5
* Dungeon (from [[30afdo]]): 11 3 7 2 12
* Moonbeam (from [[16afdo]]): 7 2 12 12 2
* Underpass (from [[10afdo]]): 9 12 5 4 5
* 12 from 6/5-blackwood[20]: 4 3 2 2 3 7 2 3 2 2 3 2
|}


{{Harmonics in equal|1|8|7 |columns=18}}
{| class="wikitable mw-collapsible mw-collapsed"
{{Harmonics in equal|1|9|8 |columns=18}}
|+Ripple[23] subsets
|''Contains [[Template:Idiosyncratic|idiosyncratic terms]].''


* Clear pond (ripple[12] [[modmos]]): 3 3 3 2 3 3 3 4 2 3 3 3
** Lydian: 6 5 6 3 6 6 3
** Major: 6 5 3 6 6 6 3
** Mixolydian: 6 5 3 6 6 3 6
** Dorian: 6 3 5 6 6 3 6
** Minor: 6 3 5 6 4 5 6
** Phrygian: 3 6 5 6 4 5 6
** Locrian: 3 6 5 3 7 5 6
** Harmonic minor: 6 3 5 6 4 8 3
** Melodic minor: 6 3 5 6 6 6 3
** Major pentatonic: 6 8 6 6 9
** Minor pentatonic: 9 5 6 9 6
** Minor blues: 9 5 3 3 9 6
** Minor blues heptatonic: 9 5 3 3 6 3 6
** Akebono I: 6 3 11 6 9
* Hirajoshi: 6 3 11 3 12
* Subminor hexatonic: 6 2 6 6 9 6
* Subminor pentatonic: 8 6 6 9 6
* Subminor blues: 8 6 3 3 9 6
* Subminor blues heptatonic: 8 6 3 3 6 3 6
|}


.
; Other scales
 
* Amulet{{idiosyncratic}}, approximated from [[magic]] in [[25edo]]: 3 1 3 3 1 3 4 3 3 1 3 4 3
 
* Fourfourths{{idio}} ([[modmos]] of 7/6-blackwood[20]): 3 1 1 2 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4
.
* Near-just rotated [[5afdo]]: 6 5 9 8 7
 
* Near-just [[6afdo]]: 8 7 5 6 5 4
 
{{Harmonics in equal|1|10|9 |columns=18}}
{{Harmonics in equal|1|11|10 |columns=18}}
{{Harmonics in equal|1|12|11 |columns=18}}
{{Harmonics in equal|1|13|12 |columns=18}}
{{Harmonics in equal|1|14|13 |columns=18}}
{{Harmonics in equal|1|15|14 |columns=18}}
{{Harmonics in equal|1|16|15 |columns=18}}
{{Harmonics in equal|1|17|16 |columns=18}}
{{Harmonics in equal|1|18|17 |columns=18}}
{{Harmonics in equal|1|19|18 |columns=18}}
 
 
.
 
 
.
 
 
{{Harmonics in equal|1|20|19 |columns=18}}
{{Harmonics in equal|1|21|20 |columns=18}}
{{Harmonics in equal|1|22|21 |columns=18}}
{{Harmonics in equal|1|23|22 |columns=18}}
{{Harmonics in equal|1|24|23 |columns=18}}
{{Harmonics in equal|1|25|24 |columns=18}}
{{Harmonics in equal|1|26|25 |columns=18}}
{{Harmonics in equal|1|27|26 |columns=18}}
{{Harmonics in equal|1|28|27 |columns=18}}
{{Harmonics in equal|1|29|28 |columns=18}}
 
 
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{{Harmonics in equal|1|30|29 |columns=18}}
{{Harmonics in equal|1|31|30 |columns=18}}
{{Harmonics in equal|1|32|31 |columns=18}}
{{Harmonics in equal|1|33|32 |columns=18}}
{{Harmonics in equal|1|34|33 |columns=18}}
{{Harmonics in equal|1|35|34 |columns=18}}
{{Harmonics in equal|1|36|35 |columns=18}}
{{Harmonics in equal|1|37|36 |columns=18}}
{{Harmonics in equal|1|38|37 |columns=18}}
{{Harmonics in equal|1|39|38 |columns=18}}
 
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Page end.

Latest revision as of 07:16, 7 October 2025

Scales

12-tone 7edo&5edo

This scale is designed to be mapped to the key of C on a conventional piano keyboard, with 7edo on the white keys, and 5edo on black:

  • 5 2 3 4 1 5 1 4 3 2 5 0
24-tone blackwood&greenwood

You can have two pianos/keyboards, one 68.6 cents sharp of the other, both tuned to the 12-tone 7edo&5edo scale. The combined black keys across both keyboards will be blackwood[10] and the white keys will be greenwood[14].

  • 3 2 0 2 1 2 2 1 1 1 3 1 1 1 2 2 1 2 0 2 3 0 2 0
20-tone blackwood&greenwood

Removing the duplicates from the previous scale (perhaps for use on other instruments beside keyboard) gives this 20-tone scale, which includes both blackwood[10] and greenwood[14] as subsets.

  • 3 2 2 1 2 2 1 1 1 3 1 1 1 2 2 1 2 2 3 2
Muggles[19]

Of all the regular temperaments available in 35edo, muggles approximates just intonation the most closely. Here is the muggles[19] MOS scale:

  • 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2
Ripple[23]

This modmos of ripple[12] sounds sort of like the familiar 12edo:

  • 3 3 3 2 3 3 3 4 2 3 3 3

And it can be extended out to the ripple[23] [MOS scale]] which adds many 7-limit intervals:

  • 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1
MOS scales
Secund[17] subsets
Contains idiosyncratic terms.
  • Antipental blues: 8 7 1 4 8 7
  • Antipental blues maj 6th: 8 7 1 4 7 1 7
  • Antipental blues neutral 7th: 8 7 1 4 8 3 4
  • Antipental blues maj 7th: 8 7 1 4 8 4 3
  • Antipental blues harmonic: 8 7 1 4 3 9 3
  • Pelog-like heptatonic: 3 5 7 5 3 8 4 (Phrygian-like)
  • Pelog-like pentatonic: 3 5 12 3 12
  • Secund chance (modmos of secund[8]): 4 7 4 1 4 4 7 4
  • Secund-tempered rotated 5afdo: 7 4 9 8 7
  • Secund-tempered 6afdo: 8 7 5 7 4 4
  • Undecimal Mixolydian: 7 4 4 5 7 1 7
  • Undecimal minor hexatonic: 7 1 7 5 8 7
  • Undecimal quasi-equipentatonic: 7 8 5 8 7
  • 12 from secund[17]: 7 1 3 4 1 4 3 4 1 3 1 3
6/5-blackwood[20] subsets
Contains idiosyncratic terms.
  • Blackwood meta-Hirajoshi: 2 3 4 2 5 7 2 12
    • Blackwood pseudo-Akebono neutral: 5 9 7 2 12
    • Blackwood pseudo-Akebono supermajor: 7 7 7 2 12
    • Blackwood pseudo-Hirajoshi: 2 12 7 2 12
    • Blackwood pseudo-pelog: 5 4 12 2 12
  • Blackwood meta-partial: 4 3 2 2 3 7 7 7
    • Blackwood-tempered 5afdo: 7 4 10 7 7
    • Mechanical (from 16afdo): 9 2 10 7 7
    • Starship (from 68ifdo, see ifdo): 4 7 3 7 7 7
    • Volcanic (from 16afdo): 4 7 10 7 7
  • Meta-monsoon: 7 4 3 2 5 9 5
    • Monsoon (from 47zpi): 7 7 7 9 5
    • Monsoon otonal: 7 9 5 9 5
    • Monsoon major: 11 5 5 9 5
  • Blackwood neutral nonatonic: 4 7 3 2 5 4 5 2 3
  • Blackwood undecimal harmonic: 4 8 4 5 4 5 5
  • Dungeon (from 30afdo): 11 3 7 2 12
  • Moonbeam (from 16afdo): 7 2 12 12 2
  • Underpass (from 10afdo): 9 12 5 4 5
  • 12 from 6/5-blackwood[20]: 4 3 2 2 3 7 2 3 2 2 3 2
Ripple[23] subsets
Contains idiosyncratic terms.
  • Clear pond (ripple[12] modmos): 3 3 3 2 3 3 3 4 2 3 3 3
    • Lydian: 6 5 6 3 6 6 3
    • Major: 6 5 3 6 6 6 3
    • Mixolydian: 6 5 3 6 6 3 6
    • Dorian: 6 3 5 6 6 3 6
    • Minor: 6 3 5 6 4 5 6
    • Phrygian: 3 6 5 6 4 5 6
    • Locrian: 3 6 5 3 7 5 6
    • Harmonic minor: 6 3 5 6 4 8 3
    • Melodic minor: 6 3 5 6 6 6 3
    • Major pentatonic: 6 8 6 6 9
    • Minor pentatonic: 9 5 6 9 6
    • Minor blues: 9 5 3 3 9 6
    • Minor blues heptatonic: 9 5 3 3 6 3 6
    • Akebono I: 6 3 11 6 9
  • Hirajoshi: 6 3 11 3 12
  • Subminor hexatonic: 6 2 6 6 9 6
  • Subminor pentatonic: 8 6 6 9 6
  • Subminor blues: 8 6 3 3 9 6
  • Subminor blues heptatonic: 8 6 3 3 6 3 6
Other scales
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