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

~~{{Harmonics in equal|21|9|4|intervals=prime|columns=6}}~~

; Muggles[19]

~~{{Harmonics in equal|23|9|4|intervals=prime|columns=6}}~~

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

~~{{Harmonics in equal|25|9|4|intervals=prime|columns=6}}~~

* 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2

~~{{Harmonics~~ in ~~equal|27|9|4|intervals=prime|columns=6}}~~

~~{{Harmonics in equal|29|9|4|intervals=prime|columns=6}}~~

; 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

~~{{Harmonics in equal~~|31|9|4|~~intervals=prime~~|~~columns=~~6}}

; [[MOS scale]]s

{~~{Harmonics in equal~~|33|9|4|~~intervals~~=~~prime~~|~~columns=~~6}}

* [[Greenwood]][7]/[[whitewood]][7]: 5 5 5 5 5 5 5 (''a.k.a. [[7edo]]; an [[equiheptatonic]] scale'')

~~{{Harmonics in equal~~|35|9|4|~~intervals=prime~~|~~columns~~=~~6}}~~

* [[Greenwood]][14]: 3 2 3 2 3 2 3 2 3 2 3 2 3 2

~~{{Harmonics in equal~~|37|9|4|~~intervals=prime|columns=6}~~}

* [[Greenwood]][21]: 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2

{{~~Harmonics~~ in ~~equal|39|9|~~4~~|intervals=prime|columns=6~~}}

* [[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

~~Page end.~~

* [[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

|}

{| class="wikitable mw-collapsible mw-collapsed"

|+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

@@ Line 1: / Line 1: @@
-'''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
-{{Harmonics in equal|21|9|4|intervals=prime|columns=6}}
+; Muggles[19]
-{{Harmonics in equal|23|9|4|intervals=prime|columns=6}}
+Of all the regular temperaments available in 35edo, [[muggles]] approximates [[just intonation]] the most closely. Here is the muggles[19] [[MOS scale]]:
-{{Harmonics in equal|25|9|4|intervals=prime|columns=6}}
+* 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2
-{{Harmonics in equal|27|9|4|intervals=prime|columns=6}}
-{{Harmonics in equal|29|9|4|intervals=prime|columns=6}}
+; 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
-{{Harmonics in equal|31|9|4|intervals=prime|columns=6}}
+; [[MOS scale]]s
-{{Harmonics in equal|33|9|4|intervals=prime|columns=6}}
+* [[Greenwood]][7]/[[whitewood]][7]: 5 5 5 5 5 5 5 (''a.k.a. [[7edo]]; an [[equiheptatonic]] scale'')
-{{Harmonics in equal|35|9|4|intervals=prime|columns=6}}
+* [[Greenwood]][14]: 3 2 3 2 3 2 3 2 3 2 3 2 3 2
-{{Harmonics in equal|37|9|4|intervals=prime|columns=6}}
+* [[Greenwood]][21]: 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2
-{{Harmonics in equal|39|9|4|intervals=prime|columns=6}}
+* [[Muggles]][5] (a.k.a. sub-diatonic): 9 4 9 9 4
-<br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br>
+* [[Muggles]][13]: 2 2 5 2 2 2 5 2 2 2 5 2 2
-<br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br>
+* [[Muggles]][16]: 2 2 3 2 2 2 2 2 3 2 2 2 2 3 2 2
-<br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br>
+* [[Muggles]][19]: 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2
-<br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br>
+* [[Ripple]][12]: 3 3 3 3 3 3 3 3 2 3 3 3
-Page end.
+* [[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
+|}
+{| class="wikitable mw-collapsible mw-collapsed"
+|+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