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36edo: Difference between revisions

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{{Harmonics in cet|33.287|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11lim TE-tuned 36edo (continued)}}
{{Harmonics in cet|33.287|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11lim TE-tuned 36edo (continued)}}


Compressing the octave of 36edo by about 2{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all primes up to 11 within 9.7{{c}}. The 11- and 13-limit TE tunings of 36edo both do this, as do their respective WE tunings.
Compressing the octave of 36edo by about 2{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all primes up to 16 within 13.4{{c}}. The 11- and 13-limit TE tunings of 36edo both do this, as do their respective WE tunings.


{| class="wikitable sortable center-all mw-collapsible mw-collapsed"
{| class="wikitable sortable center-all mw-collapsible mw-collapsed"
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{{Idiosyncratic terms}}
{{Idiosyncratic terms}}


; Polymicrotonal scales
; [[Polymicrotonal]] scales
* 12-tone 4&9edo polymicrotonal scale: 4 4 1 3 4 2 2 4 3 1 4 4
* 12-tone 4&9edo polymicrotonal scale: 4 4 1 3 4 2 2 4 3 1 4 4
* 12-tone 6&9edo polymicrotonal scale: 4 2 2 4 4 2 2 4 4 2 2 4
* 12-tone 6&9edo polymicrotonal scale: 4 2 2 4 4 2 2 4 4 2 2 4
Line 1,100: Line 1,100:
* 24-tone 12&18edo polymicrotonal scale: 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2
* 24-tone 12&18edo polymicrotonal scale: 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2


; [[Baladic]][26] subsets
; [[Baladic]][16] subsets
* Baladic[16] [[MOS]]: 3 1 3 1 3 3 1 3 3 1 3 1 3 3 1 3
Baladic[16] MOS: 3 1 3 1 3 3 1 3 3 1 3 1 3 3 1 3
* Baladic[26] MOS: 1 2 1 2 1 1 2 1 1 2 1 2 1 1 2 1 2 1 1 2 1 1 2 1 2 1
* 12-tone subset: 3 4 1 3 4 3 3 4 1 3 4 3
* 12-tone subset: 4 3 1 3 4 3 3 4 1 3 3 4


; [[Catnip]][24] subsets
{| class="wikitable mw-collapsible mw-collapsed"
|+[[Catnip]][24] subsets
|Bright catnip[24] MOS: 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
• 12edo plus 1 extra min7 note: 3 3 3 3 3 3 3 3 3 2 1 3 3
 
• 12edo with 7/4 replacing 9/5: 3 3 3 3 3 3 3 3 3 2 4 3
 
• 12edo with 7/4 replacing 9/5 & 7/6 replacing 6/5 3 3 2 4 3 3 3 3 3 2 4 3
 
• 12-tone chord 30:34:35:36:37:38:40:35:47:52:53:56 approximated from [[30afdo]]^: 6 2 1 2 1 3 6 2 6 1 2 4
 
　　　　•  Rotated [[6afdo]]: 6 6 9 8 7
 
　　　　• Flattened Ionian pentatonic: 11 4 6 11 4
 
　　　　• Flattened blues Aeolian pentatonic I: 8 7 6 2 13
 
　　　　• Flattened cosmic: 15 6 2 7 6
 
　　　　• Catnip moonbeam: 6 3 12 11 4


* Bright catnip[24] [[MOS]]: 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
• 12-tone chord 24:25:27:28:30:32:33:36:38:39:42:45 approximated from [[24afdo]]: 2 4 2 4 3 2 4 3 2 3 4 3
** ''subsets thereof'':
*** 3 3 3 3 3 3 3 3 3 2 1 3 3 (12edo plus 1 extra note)
*** 3 3 3 3 3 3 3 3 3 2 4 3 (like 12edo with 7/4 replacing 9/5)
*** 3 3 2 4 3 3 3 3 3 2 4 3 (like 12edo with 7/4 replacing 9/5 & 7/6 replacing 6/5)
*** 3 3 4 3 2 4 2 4 3 2 4 2 (12-tone, approximates the chord 18:19:20:22:23:24:26:27:29:31:32:35 from [[18afdo]])
*** 2 4 2 4 3 2 4 3 2 3 4 3 (12-tone, approximates the chord 24:25:27:28:30:32:33:36:38:39:42:45 from [[24afdo]])
{| class="wikitable mw-collapsible mw-collapsed"
|+''approximated from bright catnip[24] in [[60edo]]''
|Flattened Ionian pentatonic: 11 7 6 8 4
Flattened major: 6 2 7 6 5 6 4


Flattened major pentatonic: 5 6 10 5 10
• 12-tone chord 18:19:20:22:23:24:26:27:29:31:32:35 approximated from [[18afdo]]: 3 3 4 3 2 4 2 4 3 2 4 2


Flattened minor hexatonic: 5 4 6 6 8 7


Flattened phyrgian: 2 6 7 6 2 6 10
Dark catnip[24] MOS: 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2  


Flattened phyrgian dominant: 2 10 3 6 2 6 10
• 12edo plus 1 extra maj7 note: 3 3 3 3 3 3 3 3 3 3 1 2 3


Flattened blues aeolian pentatonic I: 8 7 6 2 13
• 12edo plus 1 extra maj2 note: 3 3 1 2 3 3 3 3 3 3 3 3 3


Flattened blues minor maj7: 8 7 3 3 12 3
• 12edo but 6/5, 8/5 & 9/5 are sharp not flat: 3 3 4 2 3 3 3 4 2 4 2 3


Flattened cosmic: 15 6 2 6 13
• 12edo but 6/5, 8/5 & 9/5 are sharp not flat, with 10/7 replacing 7/5: 3 3 4 2 3 4 2 4 2 4 2 3


Flattened Javanese pentachordal: 2 7 9 3 15
• 12edo but 16/15, 6/5, 8/5 & 9/5 are sharp not flat: 4 2 4 2 3 3 3 4 2 4 2 3


Catnip moonbeam: 6 3 12 11 4
• 12edo but 16/15, 6/5, 8/5 & 9/5 are sharp not flat, with 10/7 replacing 7/5: 4 2 4 2 3 4 2 4 2 4 2 3
|}


* Dark catnip[24] MOS: 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
• 12-tone, approximates the chord 42:45:47:48:51:56:59:63:68:71:76:78 from [[42afdo]]^: 4 2 1 3 5 3 3 4 2 4 2 3
** ''subsets thereof'':
*** 3 3 4 2 3 3 3 4 2 4 2 3 (like 12edo but 6/5, 8/5 & 9/5 are sharp not flat)
*** 3 3 4 2 3 4 2 4 2 4 2 3 (like 12edo but 6/5, 8/5 & 9/5 are sharp not flat, with 10/7 replacing 7/5)
*** 4 2 4 2 3 3 3 4 2 4 2 3 (like 12edo but 16/15, 6/5, 8/5 & 9/5 are sharp not flat)
*** 4 2 4 2 3 4 2 4 2 4 2 3 (like 12edo but 16/15, 6/5, 8/5 & 9/5 are sharp not flat, with 10/7 replacing 7/5)
*** 3 3 2 3 4 2 4 2 3 4 3 3 (12-tone, approximates the chord 18:19:20:21:22:24:25:27:28:30:32:34 from [[18afdo]])
{| class="wikitable mw-collapsible mw-collapsed"
|+''approximated from dark catnip[24] in [[60edo]]''
|Sharpened minor: 6 4 5 6 4 6 5
Sharpened minor hexatonic: 7 3 5 6 10 5


Sharpened minor pentatonic: 10 5 6 10 5
　　　　• Sharpened minor: 7 3 5 6 4 6 5


Sharpened minor harmonic: 7 3 5 6 4 9 2
　　　　• Sharpened minor pentatonic: 10 5 6 10 5


Sharpened minor harmonic pentatonic II: 7 3 11 13 2
　　　　• Sharpened minor harmonic pentatonic I: 7 3 11 12 3


Sharpened minor harmonic pentatonic II: 10 5 6 13 2
　　　　• Sharpened Phyrgian pentatonic: 4 6 11 4 11


Sharpened Dorian: 7 3 5 6 7 3 5
　　　　• Sharpened blues Aeolian pentatonic I: 10 5 6 4 11


Sharpened Dorian harmonic: 7 3 6 2 7 3 5
　　　　• Sharpened blues Aeolian hexatonic: 10 5 3 3 4 11


Sharpened Phyrgian pentatonic: 3 7 11 4 11
　　　　• Sharpened blues Dorian hexatonic: 10 5 6 6 4 5


Sharpened blues Aeolian hexatonic: 10 5 3 3 3 12
　　　　• Sharpened blues pentachordal I: 6 4 5 3 3 15


Sharpened blues Aeolian pentatonic I: 10 11 6 6 6
　　　　• Sharpened akebono I: 6 4 11 6 9


Sharpened blues Dorian hexatonic: 10 11 6 9 4 5
　　　　• Sharpened hirajoshi: 6 4 11 4 11


Sharpened blues harmonic septatonic: 10 5 4 2 7 9 2
　　　　• Extra sharpened hirajoshi: 7 3 11 4 11


Sharpened blues pentachordal: 7 3 5 4 2 15
　　　　• Catnip Deja Vu: 10 11 4 6 5


Sharpened hirajoshi: 6 4 11 4 11
　　　　• Catnip underpass: 10 11 6 4 5


Sharpened akebono I: 6 4 11 6 9
• 12-tone chord 18:19:20:21:22:24:25:27:28:30:32:34 approximated from [[18afdo]]: 3 3 2 3 4 2 4 2 3 4 3 3


Catnip Deja Vu: 10 11 4 6 5


Catnip underpass: 10 11 7 3 5
^ ''its subsets listed here come from catnip[24] in [[60edo]]''
|}
|}


; [[Echidna]][22] subsets
; [[Echidna]][22] subsets
* Echidna[14] [[MOS]]: 3 2 3 2 3 2 3 3 2 3 2 3 2 3
Echidna[22] MOS: 2 1 2 2 1 2 1 2 2 1 2 2 1 2 2 1 2 1 2 2 1 2
** ''subsets thereof'':
* Fennec ''(approx. from [[14edo]])'': 5 5 5 6 2 11 2
*** Palace (''quasi-[[equiheptatonic]]''): 5 5 5 6 5 5 5
* Echidna[14] MOS: 3 2 3 2 3 2 3 3 2 3 2 3 2 3
* Echidna[22] MOS: 2 1 2 2 1 2 1 2 2 1 2 2 1 2 2 1 2 1 2 2 1 2
** ''(the squirrel[6] & [7] MOSes occur as subsets of Echidna[14])''
** ''subsets thereof'':
** 12-tone subset: 3 2 3 2 5 3 3 5 2 3 2 3
*** Fennec ''(approx. from [[14edo]])'': 5 5 5 6 2 11 2


; [[Liese]][19] subsets
; [[Liese]][19] subsets
* Liese[7] [[MOS]]: 2 13 2 2 2 13 2
Liese[19] MOS: 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2
* Liese[9] MOS: 2 2 11 2 2 2 11 2 2
* [[Lost spirit]]: 9 6 2 4 7 2 6
* Liese[11] MOS: 2 2 9 2 2 2 2 2 9 2 2
* Liese[13] MOS: 2 2 2 7 2 2 2 2 2 7 2 2 2
* Liese[15] MOS: 2 2 2 5 2 2 2 2 2 2 2 5 2 2 2
* Liese[17] MOS: 2 2 2 2 3 2 2 2 2 2 2 2 3 2 2 2 2
* Liese[17] MOS: 2 2 2 2 3 2 2 2 2 2 2 2 3 2 2 2 2
* Liese[19] MOS: 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2
** Liese[15] MOS: 2 2 2 5 2 2 2 2 2 2 2 5 2 2 2
** ''subsets thereof'':
*** Liese[13] MOS: 2 2 2 7 2 2 2 2 2 7 2 2 2
*** [[Lost spirit]]: 9 6 2 4 7 2 6
**** Liese[11] MOS: 2 2 9 2 2 2 2 2 9 2 2
***** Liese[9] MOS: 2 2 11 2 2 2 11 2 2


; [[Niner]][27] subsets
; [[Slendric]][21] subsets
* Niner[18] [[MOS]]: 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3
Slendric[21] MOS: 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1
* Niner[27] MOS: 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1
 
; [[Slendric]][26] subsets
* Slendric[11] [[MOS]]: 1 6 1 6 1 6 1 6 1 6 1
** ''subsets thereof'':
*** Quasi-[[equipentatonic]]: 7 8 6 8 7
* Slendric[16] MOS: 1 5 1 1 5 1 1 1 5 1 1 5 1 1 5 1
* Slendric[16] MOS: 1 5 1 1 5 1 1 1 5 1 1 5 1 1 5 1
* Slendric[21] MOS: 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1
** 12-tone subset: 6 1 1 5 2 6 2 5 1 1 5 1
* Slendric[26] MOS: 1 1 3 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1
** Slendric[11] MOS: 1 6 1 6 1 6 1 6 1 6 1
** ''subsets thereof'':
*** [[Lost spirit]]: 9 6 2 4 7 2 6


; [[Squirrel]][22] subsets
; [[Squirrel]][22] subsets
* Squirrel[6] [[MOS]]: 5 5 11 5 5 5
Squirrel[22] MOS: 1 3 1 1 3 1 1 3 1 1 1 3 1 1 3 1 1 3 1 1 3 1
* Squirrel[7] MOS: 5 5 5 6 5 5 5
* Squirrel[8] MOS: 5 5 5 1 5 5 5 5
* Squirrel[15] MOS: 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1
* Squirrel[15] MOS: 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1
* Squirrel[22] MOS: 1 3 1 1 3 1 1 3 1 1 1 3 1 1 3 1 1 3 1 1 3 1  
** 12-tone subset: 5 1 4 1 4 6 4 1 4 1 4 1
** Squirrel[8] MOS: 5 5 5 1 5 5 5 5
*** Squirrel[7] MOS: 5 5 5 6 5 5 5
**** Squirrel[6] MOS: 5 5 11 5 5 5


; Other scales
; Other scales
* 833 Cent Golden Scale [[MOS]] [11]: 3 1 3 3 1 3 1 3 3 1 3
* 833 Cent Golden Scale MOS[11]: 3 1 3 3 1 3 1 3 3 1 3
** ''subsets thereof'':
** [[833 Cent Golden Scale (Bohlen)]]: 3 4 4 3 4 4 3
*** [[833 Cent Golden Scale (Bohlen)]]: 3 4 4 3 4 4 3
* Niner[18] MOS: 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 (''9/18 keys have a 3/2, 0/18 keys have both a 4/3 and a 3/2'')
* Niner[18] [[modmos]]: 1 1 3 1 3 5 1 1 1 3 1 3 1 1 3 1 3 3  (''11/18 keys have a 3/2, 6/18 keys have both a 4/3 and a 3/2'')


== Tuning by ear ==
== Tuning by ear ==
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== Instruments ==
== Instruments ==
36edo can be played on the [[Lumatone]] (see [[Lumatone mapping for 36edo]]) and using three instruments tuned to 12edo with different root notes (that is, a sixth-tone apart).
36edo can be played on the [[Lumatone]]: see [[Lumatone mapping for 36edo]].
 
36edo can also be played using three instruments tuned to 12edo with different root notes (that is, a sixth-tone apart).


== Music ==
== Music ==
Retrieved from "https://en.xen.wiki/w/36edo"