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36edo is also notable for being the smallest multiple of 12edo to be [[distinctly consistent]] in the [[7-odd-limit]] (that is, all 7-odd-limit just intervals are represented by different steps).
36edo is also notable for being the smallest multiple of 12edo to be [[distinctly consistent]] in the [[7-odd-limit]] (that is, all 7-odd-limit just intervals are represented by different steps).
36edo has almost 50% relative error on harmonics 5/1 and 11/1. This means that whether one [[octave stretch|stretches]] or [[octave shrinking|compresses]] the octave, either way it will improve 36edo's approximations of [[JI]], but in opposite directions, as long as it is done by the right amount, as discussed in more detail in [[36edo #Octave stretch or compression|octave stretch or compression]].
{{Harmonics in equal|36|intervals=odd|prec=2|columns=14}}
{{Harmonics in equal|36|intervals=odd|prec=2|columns=14}}
{{Harmonics in equal|36|intervals=odd|columns=14|prec=2|start=15|collapsed=true|title=Approximation of odd harmonics in 36edo (continued)}}
{{Harmonics in equal|36|intervals=odd|columns=14|prec=2|start=15|collapsed=true|title=Approximation of odd harmonics in 36edo (continued)}}


=== Mappings ===
=== Mappings ===
''See [[regular temperament]] for more about what all this means and how to use it.''
36edo's patent val, like 12, tempers out [[81/80]], [[128/125]], and [[648/625]] in the 5-limit. It departs from 12 in the 7-limit, tempering out [[686/675]] and [[1029/1000]], and as a no-fives temperament, [[1029/1024]] and [[118098/117649]]. The no-fives temperament tempering out 1029/1024, [[slendric]], is well supported by 36edo, its generator of ~8/7 represented by 7 steps of 36edo. In the 11-limit, the patent val tempers out [[56/55]], [[245/242]], and [[540/539]], and is the [[optimal patent val]] for the rank four temperament tempering out [[56/55]], as well as the rank-3 temperament [[melpomene]] tempering out 81/80 and 56/55. In the 13-limit, it tempers out [[78/77]] and [[91/90]], in the 17-limit [[51/50]], and in the 19-limit [[76/75]] and [[96/95]].
 
36edo's patent val, like 12, tempers out 81/80, 128/125, and 648/625 in the 5-limit. It departs from 12 in the 7-limit, tempering out 686/675 and 1029/1000, and as a no-fives temperament, 1029/1024 and 118098/117649. The no-fives temperament tempering out 1029/1024, [[slendric]], is well supported by 36edo, its generator of ~8/7 represented by 7 steps of 36edo. In the 11-limit, the patent val tempers out 56/55, 245/242, and 540/539, and is the [[optimal patent val]] for the rank four temperament tempering out 56/55, as well as the rank three temperament [[Didymus rank three family|melpomene]] tempering out 81/80 and 56/55. In the 13-limit, it tempers out 78/77 and 91/90, in the 17-limit 51/50, and in the 19-limit 76/75 and 96/95.


As a 5-limit temperament, the patent val for 36edo is [[contorted]], meaning there are notes of it which cannot be reached from the unison using only 5-limit intervals.
As a 5-limit temperament, the patent val for 36edo is [[contorted]], meaning there are notes of it which cannot be reached from the unison using only 5-limit intervals.
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=== Additional properties ===
=== Additional properties ===
36edo also offers a good approximation to the [[acoustic phi|acoustic golden ratio]], as 25\36. [[Heinz Bohlen]] proposed 36edo as a suitable temperament for approximating his 833-cents scale. The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 36edo could be treated as a 2.3.7.ϕ.17 temperament.
36edo offers a good approximation to the [[acoustic phi|acoustic golden ratio]], as 25\36. [[Heinz Bohlen]] proposed 36edo as a suitable temperament for approximating his 833-cents scale. The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 36edo could be treated as a 2.3.7.ϕ.17 temperament.
 
The [[edonoi]] scales of [[57edt]] and [[101ed7]] are almost exactly the same as 36edo. It is 36edo with the [[stretched octave|octave stretched]] by less than 1{{c}}. Its main usage is to optimise 36edo for use as a [[dual-n|dual-5]] tuning, while also making slight improvements to 3/1 and 7/1 as well. So if one intends to use both 36edo’s vals for 5/1 at once, 101ed7 may be worth considering.


Thanks to its sevenths, 36edo is an ideal tuning for its size for [[metallic harmony]].
Thanks to its sevenths, 36edo is an ideal tuning for its size for [[metallic harmony]].
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! Additional ratios<br>of 2.3.7.13.17.19<ref group="note" name="subg" />
! Additional ratios<br>of 2.3.7.13.17.19<ref group="note" name="subg" />
! Additional ratios<br>of 2.3.5.7<ref group="note" name="incons">Inconsistent intervals are in ''italics.''</ref>
! Additional ratios<br>of 2.3.5.7<ref group="note" name="incons">Inconsistent intervals are in ''italics.''</ref>
! colspan="3" | [[ups and downs notation|Ups and downs<br />notation]]
! colspan="3" | [[Ups and downs notation]]
([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>3</sup>A1 and d2)
|-
|-
| 0
| 0
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| 17
| 17
| 566.7
| 566.7
|  
| [[112/81]]
| [[18/13]]
| [[18/13]]
| [[7/5]]
| [[7/5]]
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| 18
| 18
| 600.0
| 600.0
|  
| [[729/512]], [[1024/729]]
| [[17/12]], [[24/17]]
| [[17/12]], [[24/17]]
| [[45/32]], [[64/45]]
| [[45/32]], [[64/45]]
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| 19
| 19
| 633.3
| 633.3
|  
| 81/56
| [[13/9]]
| [[13/9]]
| [[10/7]]
| [[10/7]]
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| 20
| 20
| 666.7
| 666.7
| 72/49
| [[72/49]]
|  
|  
|  
|  
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| D
| D
|}
|}
<references group="note" />


Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chords and chord progressions]].
Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chords and chord progressions]].


== Notation ==
== Notation ==
=== Colored notes ===
=== Stein–Zimmermann–Gould notation ===
One way of notating 36edo (at least for people who aren't colorblind) is to use colors. For example, {{colored note|blue|A}} is 33{{frac|3}}{{c}} below {{colored note|A}} and {{colored note|red|A}} is 33{{frac|3}} cents above {{colored note|A}}. Or, the colors could be written out (red A, blue C♯, etc.) or abbreviated as rA, bC♯, etc. This use of red and blue is consistent with [[Kite's_color_notation|color notation]] (ru and zo).
[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
{{Sharpness-sharp3-szg|36}}
 
If the arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best denoted using double arrows.


=== Ups and downs notation ===
=== Kite's ups and downs notation ===
Spoken as up, downsharp, sharp, upsharp, etc. Note that downsharp can be respelled as dup (double-up), and upflat as dud.
Spoken as up, downsharp, sharp, upsharp, etc. Note that downsharp can be respelled as dup (double-up), and upflat as dud.
{{sharpness-sharp3a|36}}
{{Ups and downs sharpness}}


Alternatively, one can use sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
=== Colored notes ===
{{Sharpness-sharp3|36}}
One way of notating 36edo (at least for people who are not colorblind) is to use colors. For example, {{colored note|blue|A}} is 33{{frac|3}}{{c}} below {{colored note|A}} and {{colored note|red|A}} is 33{{frac|3}} cents above {{colored note|A}}. Or, the colors could be written out (red A, blue C♯, etc.) or abbreviated as rA, bC♯, etc. This use of red and blue is consistent with [[Kite's_color_notation|color notation]] (ru and zo).
 
If the arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best denoted using double arrows.


=== Sagittal notation ===
=== Sagittal notation ===
This notation uses the same sagittal sequence as [[43edo#Sagittal notation|43-EDO]], is a subset of the notation for [[72edo#Sagittal notation|72-EDO]], and is a superset of the notations for EDOs [[18edo#Sagittal notation|18]], [[12edo#Sagittal notation|12]], and [[6edo#Sagittal notation|6]].
This notation uses the same sagittal sequence as [[43edo #Sagittal notation|43edo]], is a subset of the notation for [[72edo #Sagittal notation|72edo]], and is a superset of the notations for edos [[18edo #Sagittal notation|18]], [[12edo #Sagittal notation|12]], and [[6edo #Sagittal notation|6]].


==== Evo flavor ====
==== Evo flavor ====
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== Approximation to JI ==
== Approximation to JI ==
[[File:36ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 19-limit intervals approximated in 36edo]]
[[File:36ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 19-limit intervals approximated in 36edo]]
=== Interval mappings ===
{{Q-odd-limit intervals|36}}
{{Q-odd-limit intervals|35.98|apx=val|header=none|tag=none|title=15-odd-limit intervals by 36e val mapping}}


=== 3-limit (Pythagorean) approximations (same as 12edo): ===
=== 3-limit (Pythagorean) approximations (same as 12edo): ===
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63/32 = 1172.736... cents; 35 degrees of 36edo = 1166.666... cents.
63/32 = 1172.736... cents; 35 degrees of 36edo = 1166.666... cents.


{{clear}}
=== 15-odd-limit approximations ===
{{Q-odd-limit intervals|36}}
{{Q-odd-limit intervals|35.9|apx=val|header=none|tag=none|title=15-odd-limit intervals by 36ce val mapping}}


=== Zeta peak index ===
{{Clear}}
{{ZPI
| zpi = 155
| steps = 35.9823877000425
| step size = 33.3496490006021
| tempered height = 6.027497
| pure height = 5.885059
| integral = 1.028887
| gap = 14.706508
| octave = 1200.58736402167
| consistent = 8
| distinct = 8
}}


== Regular temperament properties ==
== Regular temperament properties ==
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=== Uniform maps ===
=== Uniform maps ===
{{Uniform map|edo=36}}
{{Uniform map|min=35.8|max=36.2}}


=== Commas ===
=== Commas ===
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| 0.42
| 0.42
| Sathurugu
| Sathurugu
| Schismina
| Minisma
|-
|-
| 17
| 17
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| Go comma
| Go comma
|}
|}
<references group="note" />


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
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| 166.67
| 166.67
| 10/9
| 10/9
| [[Squirrel]] (36), [[coendou]] (36c)  
| [[Squirrel]] (36) / [[coendou]] (36c)  
| [[1L&nbsp;6s]], [[7L&nbsp;1s]], [[7L&nbsp;8s]], [[7L&nbsp;15s]], [[7L&nbsp;22s]]
| [[1L&nbsp;6s]], [[7L&nbsp;1s]], [[7L&nbsp;8s]], [[7L&nbsp;15s]], [[7L&nbsp;22s]]
|-
|-
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| 233.33
| 233.33
| 8/7
| 8/7
| [[Slendric]] / [[mothra]] / [[guiron]]
| [[Slendric]] (36) / [[guiron]] (36e) / [[mothra]]
| [[1L&nbsp;4s]], [[1L&nbsp;5s]], [[5L&nbsp;1s]], [[5L&nbsp;6s]], [[5L&nbsp;11s]], [[5L&nbsp;16s]], [[5L&nbsp;21s]], [[5L&nbsp;26s]]
| [[1L&nbsp;4s]], [[1L&nbsp;5s]], [[5L&nbsp;1s]], [[5L&nbsp;6s]], [[5L&nbsp;11s]], [[5L&nbsp;16s]], [[5L&nbsp;21s]], [[5L&nbsp;26s]]
|-
|-
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| 566.67
| 566.67
| 7/5
| 7/5
| [[Liese]], [[pycnic]] (36c)
| [[Liese]] (36) / [[pycnic]] (36c)
| [[2L&nbsp;1s]], [[2L&nbsp;3s]], [[2L&nbsp;5s]], [[2L&nbsp;7s]], [[2L&nbsp;9s]], …, [[2L&nbsp;15s]], [[17L&nbsp;2s]]
| [[2L&nbsp;1s]], [[2L&nbsp;3s]], [[2L&nbsp;5s]], [[2L&nbsp;7s]], [[2L&nbsp;9s]], …, [[2L&nbsp;15s]], [[17L&nbsp;2s]]
|-
|-
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| 166.67
| 166.67
| 10/9
| 10/9
| [[Hedgehog]] (36ceff), [[echidna]] (36)
| [[Echidna]] (36) / [[hedgehog]] (36ceff)
| [[2L&nbsp;4s]], [[6L&nbsp;2s]], [[8L&nbsp;6s]], [[14L&nbsp;8s]]
| [[2L&nbsp;4s]], [[6L&nbsp;2s]], [[8L&nbsp;6s]], [[14L&nbsp;8s]]
|-
|-
Line 974: Line 962:
| 233.33
| 233.33
| 8/7
| 8/7
| [[Baladic]] / [[echidnic]]
| [[Baladic]] (36) / [[echidnic]] (36e)
| [[4L&nbsp;2s]], [[6L&nbsp;4s]], [[10L&nbsp;6s]], [[10L&nbsp;16s]]
| [[4L&nbsp;2s]], [[6L&nbsp;4s]], [[10L&nbsp;6s]], [[10L&nbsp;16s]]
|-
|-
Line 1,009: Line 997:
| 500.00<br>(33.33)
| 500.00<br>(33.33)
| 4/3<br>(36/35)
| 4/3<br>(36/35)
| [[Niner]]
| [[Niner]] (36)
| [[9L&nbsp;9s]]
| [[9L&nbsp;9s]]
|-
|-
Line 1,016: Line 1,004:
| 233.33<br>(33.33)
| 233.33<br>(33.33)
| 8/7<br>(64/63)
| 8/7<br>(64/63)
| [[Catler]]
| [[Catnip]] (36) / [[catler]] (36e) / [[compton]] (36ce)
| [[12L&nbsp;12s]]
| [[12L&nbsp;12s]]
|-
|-
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|  
|  
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
 
== Octave stretch or compression ==
If one intends to use both 36edo's vals for 5/1 at once, stretching the octave of 36edo by about 1{{c}} optimises 36edo for that dual-5 usage, while also making slight improvements to primes 3, 7, 11, and 13. This approximates all harmonics up to 16 within 16.6{{c}}. Several almost-identical tunings do this: [[57edt]], [[93ed6]], [[101ed7]], [[zpi|155zpi]], and the 2.3.7.13-subgroup [[TE]] and [[WE]] tunings of 36et.
 
Compressing the octave of 36edo by 1–2{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. The 11- and 13-limit [[TE]] tunings of 36et both do this, as do their respective [[WE]] tunings.
 
{| class="wikitable sortable center-all mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | Comparison of stretched and compressed tunings
|-
! rowspan="2" | Tuning !! rowspan="2" | Octave size<br>(cents) !! colspan="6" | Prime error (cents)
! rowspan="2" | Mapping of primes 2–13 (steps)
|-
! 2 !! 3 !! 5 !! 7 !! 11 !! 13
|-
! 21edf
| 1203.351
| +3.3 || +3.3 || −12.0 || +7.2 || −6.5 || +5.1
| 36, 57, 83, 101, 124, 133
|-
! 57edt
| 1201.235
| +1.2 || 0.0 || +16.6 || +1.3 || −13.7 || −2.6
| 36, 57, 84, 101, 124, 133
|-
! 155zpi
| 1200.587
| +0.6 || −1.0 || +15.1 || −0.5 || −16.0|| −5.0
| 36, 57, 84, 101, 124, 133
|-
! 36edo
| '''1200.000'''
| '''0.0''' || '''−2.0''' || '''+13.7''' || '''−2.2''' || '''+15.3''' || '''−7.2'''
| '''36, 57, 84, 101, 125, 133'''
|-
! 13-limit TE
| 1198.929
| −1.1 || −3.7 || +11.2 || −5.2 || +11.6 || −11.1
| 36, 57, 84, 101, 125, 133
|-
! 11-limit TE
| 1198.330
| −1.7 || −4.6 || +9.8 || −6.8 || +9.5 || −13.4
| 36, 57, 84, 101, 125, 133
|}


== Scales ==
== Scales ==
{{main|List of MOS scales in 36edo}}
''See also: [[List of MOS scales in 36edo]]''
{{Idiosyncratic terms}}
 
; [[Polymicrotonal]] scales
* [[Werntz Nocturne scale]]: 4 2 2 4 4 2 2 4 4 2 2 4
* 12-tone 4&9edo scale: 4 4 1 3 4 2 2 4 3 1 4 4
* 12-tone 9&12edo scale: 4 2 2 4 3 3 3 3 3 3 2 4
* 12-tone 12&18edo scale: 4 4 2 2 3 3 3 3 2 4 2 4
* 18-tone 9&12edo scale: 3 1 2 2 1 3 3 1 2 2 1 3 3 1 2 2 1 3
* 24-tone 12&18edo 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]][16] subsets
Baladic[16] MOS: 3 1 3 1 3 3 1 3 3 1 3 1 3 3 1 3
* 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
* 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 [[5afdo]]: 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
** 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
** 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
* 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
** 12edo plus 1 extra maj7 note: 3 3 3 3 3 3 3 3 3 3 1 2 3
** 12edo plus 1 extra maj2 note: 3 3 1 2 3 3 3 3 3 3 3 3 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
** 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
** 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
** 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
** 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 (from catnip[24] in [[60edo]])
*** Sharpened minor: 7 3 5 6 4 6 5
*** Sharpened minor pentatonic: 10 5 6 10 5
*** Sharpened minor harmonic pentatonic I: 7 3 11 12 3
*** Sharpened Phyrgian pentatonic: 4 6 11 4 11
*** Sharpened blues Aeolian pentatonic I: 10 5 6 4 11
*** Sharpened blues Aeolian hexatonic: 10 5 3 3 4 11
*** Sharpened blues Dorian hexatonic: 10 5 6 6 4 5
*** Sharpened blues pentachordal I: 6 4 5 3 3 15
*** Sharpened akebono I: 6 4 11 6 9
*** Sharpened hirajoshi: 6 4 11 4 11
*** Extra sharpened hirajoshi: 7 3 11 4 11
*** Catnip Deja Vu: 10 11 4 6 5
*** Catnip underpass: 10 11 6 4 5
** 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


'''Catler'''
; [[Echidna]][22] subsets
* [[Lost spirit]] (approximated from [[Meantone]] in [[31edo]]): '''9 6 2 4 7 2 6'''
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
* Fennec ''(approx. from [[14edo]])'': 5 5 5 6 2 11 2
* Echidna[14] MOS: 3 2 3 2 3 2 3 3 2 3 2 3 2 3
** ''(the squirrel[6] & [7] MOSes occur as subsets of Echidna[14])''
** 12-tone subset: 3 2 3 2 5 3 3 5 2 3 2 3


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


'''Hedgehog'''
; [[Slendric]][21] subsets
* [[Hedgehog]][14] MOS: '''3 2 3 2 3 2 3 3 2 3 2 3 2 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
* Palace (subset of Hedgehog[14]): '''5 5 5 6 5 5 5'''
* Slendric[16] MOS: 1 5 1 1 5 1 1 1 5 1 1 5 1 1 5 1
** 12-tone subset: 6 1 1 5 2 6 2 5 1 1 5 1
** Slendric[11] MOS: 1 6 1 6 1 6 1 6 1 6 1


[[833 Cent Golden Scale (Bohlen)]]: '''3 4 4 3 4 4 3'''
; [[Squirrel]][22] subsets
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[15] MOS: 1 4 1 4 1 4 1 4 1 4 1 4 1 4 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


833 Cent Golden Scale MOS [11]: '''3 1 3 3 1 3 1 3 3 1 3'''
; Other scales
* 833 Cent Golden Scale MOS[11]: 3 1 3 3 1 3 1 3 3 1 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 ==
Line 1,049: Line 1,155:


== 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 ==
Line 1,060: Line 1,168:
; [[Ivan Bratt]]
; [[Ivan Bratt]]
* [http://micro.soonlabel.com/gene_ward_smith/36edo/boomers.mp3 ''Boomers'']
* [http://micro.soonlabel.com/gene_ward_smith/36edo/boomers.mp3 ''Boomers'']
; [[Stevie Boyes]]
* [https://youtu.be/CUWZfomL-DQ ''Getting in the rhythm]'' (2016)
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/SXspsdNtxQg ''36edo''] (2023)
* [https://www.youtube.com/watch?v=psvrsa10-Wo ''36edo jam''] (2025)
* [https://www.youtube.com/shorts/3la1W-_-ceA ''36edo cowbell''] (2025)
* [https://www.youtube.com/shorts/MjUdMnUA-2k ''18 tone unequal improv''] (2026) (this is tuned as two rings of [[9edo]] offset by 35{{c}}, to make a good approximation of [[3/2]] available, for a tuning that is an 18 note subset of a well-tempered derivative of 36edo)
* [https://www.youtube.com/shorts/KCtEYSkEK8U ''36edo improv''] (2026)


; [[E8 Heterotic]]
; [[E8 Heterotic]]
* [https://youtu.be/VRbXae4L00A?si=YLuyLAP6mxzbBC45 "Elements - Lightning"] from ''Elements'' (2020)
* [https://youtu.be/VRbXae4L00A?si=YLuyLAP6mxzbBC45 ''Lightning''] from ''Elements'' (2020)


; [[User:Francium|Francium]]
; [[User:Francium|Francium]]
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; [[Herman Klein]]
; [[Herman Klein]]
* [http://micro.soonlabel.com/gene_ward_smith/36edo/something.mp3 ''Something''] (2022)
* [http://micro.soonlabel.com/gene_ward_smith/36edo/something.mp3 ''Something''] (2022)
; [[Budjarn Lambeth]]
* [https://youtu.be/XZKafk-PkPc ''Improvisation in zeta-stretched 36edo (catnip24 scale)''] (2025)


; [[Claudi Meneghin]]
; [[Claudi Meneghin]]
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; [[Joseph Monzo]]
; [[Joseph Monzo]]
* [https://m.youtube.com/watch?v=7t79lBI_4_s ''African Rhythms in 36-ET''] (2005)
* [https://m.youtube.com/watch?v=7t79lBI_4_s ''African Rhythms in 36-ET''] (2005)
; [[Norokusi]]
* [https://www.youtube.com/watch?v=JPpjYzddGSg&t=495s ''Symphony for String Orchestra''] (2024)
** [https://www.youtube.com/watch?v=l5SQOI1kTHc ''Arranged for orchestra''] (2026)


; [[NullPointerException Music]]
; [[NullPointerException Music]]
* [https://www.youtube.com/watch?v=i5Pa5R7PKu4 ''Jungle Hillocks''] (2020)
* [https://www.youtube.com/watch?v=i5Pa5R7PKu4 ''Jungle Hillocks''] (2020)
; [[Juhani Nuorvala]]
* [https://m.youtube.com/watch?v=wy3qlby0Yiw ''Prelude from 'Suite 36' for Lumatone and piano''] (2025)
; [[Chris Orphal]]
* [https://www.youtube.com/watch?v=qbOOzC4360M ''Vademecum - Vadetecum (36-EDO) - Perf. New Music New Mexico''] (2023) (Saxophone: Edwin Anthony; Horn: Samuel Lutz; Trumpet: Doug Falk; Guitar: Carlos Arellano; Guitar tuned -31¢: Chris Orphal; Piano: Axel Retif)


; {{W|Henri Pousseur}}
; {{W|Henri Pousseur}}
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; [[Stephen Weigel]]
; [[Stephen Weigel]]
* [https://soundcloud.com/overtoneshock/exponentially-more-lost-and-forgetful-36-edo ''Exponentially More Lost and Forgetful''] (2017) played by flautists Orlando Cela and Wei Zhao
* [https://soundcloud.com/overtoneshock/exponentially-more-lost-and-forgetful-36-edo ''Exponentially More Lost and Forgetful''] (2017) played by flautists Orlando Cela and Wei Zhao
== Notes ==
<references group="note" />


[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/36edo"