35edo: Difference between revisions

BudjarnLambeth (talk | contribs)
BudjarnLambeth (talk | contribs)
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== Scales ==
== Scales ==


=== Ripple scales ===
; Ripple[23]
; Ripple[23]
The ''[[ripple]][23]'' [[MOS scale]] makes maximum use of 35edo's dual-fifth nature, with both its sizes of fifth and fourth occurring frequently throughout the whole scale:
The ''[[ripple]][23]'' [[MOS scale]] makes maximum use of 35edo's dual-fifth nature, with both its sizes of fifth and fourth occurring frequently throughout the whole scale:
* Symmetrical mode (has the most consonances): 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
* Symmetrical mode (has the most consonances): 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
* Clear pond mode{{idio}} (includes the clear pond modmos{{idio}}): 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1
* Mode that includes the clear pond{{idio}} modmos: 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1
 
; Clear pond{{idio}}
The ''clear pond scale''{{idio}}, a [[modmos]] of ripple[12], tries to sound close to the familiar [[12edo]]:
* 3 3 3 2 3 3 3 4 2 3 3 3
 
; 12-tone 7edo&5edo
The ''12-tone 7edo&5edo 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
 
; [[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"
{| class="wikitable mw-collapsible mw-collapsed"
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* Underpass: 9 11 7 3 5
* Underpass: 9 11 7 3 5
|}
|}
; Clear pond{{idio}}
The ''clear pond scale''{{idio}}, a [[modmos]] of ripple[12], tries to sound close to the familiar [[12edo]]:
* 3 3 3 2 3 3 3 4 2 3 3 3


{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
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|''Contains [[Template:Idiosyncratic|idiosyncratic terms]].''
|''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
** Lydian: 6 5 6 3 6 6 3
* Major: 6 5 3 6 6 6 3
** Major: 6 5 3 6 6 6 3
* Mixolydian: 6 5 3 6 6 3 6
** Mixolydian: 6 5 3 6 6 3 6
* Dorian: 6 3 5 6 6 3 6
** Dorian: 6 3 5 6 6 3 6
* Minor: 6 3 5 6 4 5 6
** Minor: 6 3 5 6 4 5 6
* Phrygian: 3 6 5 6 4 5 6
** Phrygian: 3 6 5 6 4 5 6
* Locrian: 3 6 5 3 7 5 6
** Locrian: 3 6 5 3 7 5 6
* Harmonic minor: 6 3 5 6 4 8 3
** Harmonic minor: 6 3 5 6 4 8 3
* Melodic minor: 6 3 5 6 6 6 3
** Melodic minor: 6 3 5 6 6 6 3
* Major pentatonic: 6 8 6 6 9
** Major pentatonic: 6 8 6 6 9
* Minor pentatonic: 9 5 6 9 6
** Minor pentatonic: 9 5 6 9 6
* Minor blues: 9 5 3 3 9 6
** Minor blues: 9 5 3 3 9 6
* Minor blues heptatonic: 9 5 3 3 6 3 6
** Minor blues heptatonic: 9 5 3 3 6 3 6
* Akebono I: 6 3 11 6 9
** Akebono I: 6 3 11 6 9
|}
|}


; 12-tone 7edo&5edo
The ''12-tone 7edo&5edo 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
=== MOS scales ===
; 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
; Other [[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
=== Secund scales ===
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+Secund[17] subsets
|+Secund[17] subsets
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|}
|}


=== Blackwood scales ===
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+6/5-blackwood[20] subsets
|+6/5-blackwood[20] subsets
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|}
|}


; Other scales
=== Other scales ===
* Amulet{{idiosyncratic}}, approximated from [[magic]] in [[25edo]]: 3 1 3 3 1 3 4 3 3 1 3 4 3
* 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
* 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