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<b>67 equal divisions of the octave</b> or <b>67-EDO</b> divides the octave into 67 equal parts of 17.910 cents each. It tempers out 81/80, supporting meantone temperament, with a tuning which is approximately 1/6 comma (the tuning favored by Mozart and contemporaries), or 0.16 comma, meantone. In the 7-limit the patent val tempers out 1029/1024 and 1728/1715, so that it supports [[Meantone_family|mothra temperament]]. In the 11-limit it tempers out 176/175 and 540/539, supporting mosura, an alternative 11-limit mothra. In the 13-limit it tempers out 144/143 and 196/195, supporting 13-limit mosura. It tempers out the orgonisma, and on the 2.7.11 subgroup it supports [[Orgonia|orgone temperament]].
{{Infobox ET}}
{{ED intro}}


A promising tuning which has, as many relatively large equal temperaments do, a variety of tonal resources: it is the first edo to have both meantone (26 could be called meantone, but it's more of a flattone) and an orgone temperament. It has relatively good approximations of the 3rd, 7th, 11th, 13th, 15th, 17th harmonics, although the 5th, 9th, and 19th as well as certain higher ones are workable as well. 33+34 can be used to construct this temperament explaining some of its properties.
== Theory ==
67edo [[tempering out|tempers out]] [[81/80]], [[support]]ing [[meantone]], with a tuning which is slightly sharp of [[1/6-comma meantone|1/6-comma]] (the tuning favored by {{w|Wolfgang Amadeus Mozart|Mozart}} and contemporaries, though they suggested the flatter and composite [[55edo]] as an approximation). It is indistinguishable from {{nowrap|{{frac|4|25}} {{=}} 0.16-comma}} meantone. In the 7-limit the [[patent val]] tempers out [[1029/1024]] and [[1728/1715]], so that it supports [[mothra]]. In the 11-limit it tempers out [[176/175]] and [[540/539]], supporting [[mosura]], an alternative 11-limit mothra. In the 13-limit it tempers out [[144/143]] and [[196/195]], supporting 13-limit mosura. It tempers out the [[orgonisma]], and on the 2.7.11 subgroup it supports the [[orgone]] temperament.


67edo is the 19th [[prime EDO]].
It is a promising tuning which has, as many relatively large equal temperaments do, a variety of tonal resources: it is the second edo after [[26edo]] to have both meantone and an orgone temperament. It has relatively good approximations of the [[3/1|3rd]], [[7/1|7th]], [[11/1|11th]], [[13/1|13th]], [[15/1|15th]], [[17/1|17th]] [[harmonic]]s, although the [[5/1|5th]], [[9/1|9th]], and [[19/1|19th]] as well as certain higher ones are workable as well. {{nowrap|33 + 34}} can be used to construct this temperament explaining some of its properties. It does well on the 2.3.7.11.13.17.23.31.37.41 [[subgroup]].


Music:
=== Prime harmonics ===
{{Harmonics in equal|67|columns=13}}


[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/67-edo.mp3 Beginning of a piece in 67 tone], [[Peter_Kosmorsky|Peter Kosmorsky]]
=== Subsets and supersets ===
67edo is the 19th [[prime edo]], following [[61edo]] and before [[71edo]].


Cents
== Intervals ==
{{Interval table}}


0: 1/1 0.000 unison, perfect prime
== Notation ==
=== Stein–Zimmermann–Gould notation ===
[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
{{Sharpness-sharp5-szg}}


1: 17.910 cents 17.910
=== Kite's ups and downs notation ===
67edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
{{Sharpness-sharp5a}}


2: 35.821 cents 35.821
=== Sagittal notation ===
==== Evo flavor ====
<imagemap>
File:67-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 735 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 160 106 [[896/891]]
rect 160 80 280 106 [[36/35]]
rect 280 80 440 106 [[1053/1024]]
default [[File:67-EDO_Evo_Sagittal.svg]]
</imagemap>


3: 53.731 cents 53.731
==== Revo flavor ====
<imagemap>
File:67-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 759 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 160 106 [[896/891]]
rect 160 80 280 106 [[36/35]]
rect 280 80 440 106 [[1053/1024]]
default [[File:67-EDO_Revo_Sagittal.svg]]
</imagemap>


4: 71.642 cents 71.642
In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation #Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this edo.


5: 89.552 cents 89.552
== Scales ==
{{Idiosyncratic terms}}


6: 107.463 cents 107.463
=== Mos scales ===
* Meantone[5]: 11 11 17 11 17
* Meantone[7]: 11 11 6 11 11 11 6
* Barbados[5], Bustling Docks (original/default tuning): 14 14 11 14 14
* Barbados[9]: 11 3 11 3 11 3 11 3 11


7: 125.373 cents 125.373
=== Modmos scales ===
* Cavernous (original/default tuning): 14 14 11 21 7
* Formicarium (original/default tuning): 14 7 18 14 14
* Negri Blues (original/default tuning): 14 14 3 8 14 14
* Negri Blues Septatonic (original/default tuning): 14 14 3 8 11 3 14
* Negri Blues Octatonic (original/default tuning): 7 14 7 11 7 11 3 7
* Understory (original/default tuning): 14 7 18 7 21
* Meantone Ionian Pentatonic: 22 6 11 22 6
* Meantone Minor Melodic: 11 6 11 11 11 11 6
* Meantone Minor Harmonic: 11 6 11 11 6 16 6
* Meantone Minor Hexatonic: 11 6 11 11 17 11
* Meantone Dorian Harmonic: 11 6 16 6 11 6 11
* Meantone Mixolydian Pentatonic: 22 6 11 17 11
* Meantone Phrygian Dominant: 6 16 6 11 6 11 11
* Meantone Phrygian Dominant Hexatonic: 6 16 6 11 6 22
* Meantone Phrygian Dominant Pentatonic: 22 6 11 6 22
* Meantone Phrygian Pentatonic: 6 11 22 6 22
* Meantone Double Harmonic: 6 16 6 11 6 16 6


8: 143.284 cents 143.284
=== Blues scales ===
* [[Lost spirit]]  (approximated from [[31edo]]): 17 11 6 5 13 4 11
* [[Blackened skies]] (approximated from [[72edo]]): 18 10 5 6 5 18 5
* Blues Aeolian Hexatonic: 17 11 6 5 6 22
* Blues Aeolian Pentatonic I: 17 11 11 6 22
* Blues Aeolian Pentatonic II: 17 22 6 11 11
* Blues Bright Double Harmonic: 6 16 6 11 6 11 6 5
* Blues Dark Double Harmonic: 11 6 11 6 5 6 16 6
* Blues Dorian Hexatonic: 17 11 11 11 6 11
* Blues Dorian Pentatonic: 17 22 11 6 11
* Blues Dorian Septatonic: 17 11 6 5 11 6 11
* Blues Harmonic Hexatonic: 11 6 11 11 22 6
* Blues Harmonic Septatonic: 17 11 6 5 6 11 5 6
* Blues Leading: 17 11 6 5 17 6 5
* Blues Minor: 17 11 6 5 17 11
* Blues Minor Maj7: 17 11 6 5 22 6
* Blues Pentachordal: 11 6 11 5 6 28
* Greyed Skies (approximated from [[91edo]]): 17 11 5 6 6 17 5
* Akebono I: 11 6 11 11 17
* Augmented: 17 6 16 6 16 6
* Dominant Pentatonic: 11 11 17 17 11
* Hirajoshi: 11 6 12 6 22
* Javanese Pentachordal: 6 11 17 4 29


9: 161.194 cents 161.194
=== Others ===
* Approximation of ''[[Pelog]] lima'': 6 10 22 7 22
* [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic|Gutierrez-Lambeth quasi-subharmonic pentatonic]] ''(octave-reduced: 9 6 23 16 13)''
* Arcade (approximated from [[32afdo]]): 22 4 13 15 13
* Cosmic (approximated from [[32afdo]]): 29 10 6 11 11
* Mechanical (approximated from [[16afdo]]): 17 5 17 15 13
* Moonbeam (approximated from [[16afdo]]): 11 6 12 22 6
* Springwater (approximated from [[8afdo]]): 11 11 17 15 13
* Volcanic (approximated from [[16afdo]]): 6 16 17 15 13
* Deja Vu (approximated from [[101afdo]]): 18 21 6 12 10
* Freeway (approximated from [[6afdo]]): 15 12 11 11 9 8
* Mushroom (approximated from [[30afdo]]): 15 12 11 4 24
* Underpass (approximated from [[10afdo]]): 18 21 12 6 10
* Sourgummy (approximated from [[51afdo]]): 14 12 14 14 13
* Bubblegum/Cola (approximated from [[60afdo]]/[[99afdo]]): 14 13 13 13 14
* Tropicalpunch/Whitechocolate (approximated from [[62afdo]]/[[90afdo]]): 13 14 13 14 13
* Lemonade (approximated from [[79afdo]]): 14 13 13 14 13
* Candycorn (approximated from [[91afdo]]): 11 12 11 10 12 11
* Trailmix (approximated from [[97afdo]]): 11 11 11 12 11 11
* Liquorice (approximated from [[101afdo]]): 11 11 12 10 12 11
* Fishcracker (approximated from [[80afdo]]): 9 11 9 9 10 9 10


10: 179.104 cents 179.104
== Instruments ==
* [[Lumatone mapping for 67edo]]


11: 197.015 cents 197.015
== Music ==
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/uwxey9_jINA ''microtonal improvisation in 67edo''] (2025)
* [https://www.youtube.com/shorts/L6BXGZyvK8Y ''67edo prelude''] (2025)
* [https://www.youtube.com/shorts/za_Ov95HbjQ ''improv in 67edo''] (2025)


12: 214.925 cents 214.925
; [[Delta Quartz]]
* [https://youtu.be/WOguarC1lEI ''Making microtonality accessible - "Keep It Tight"''] (2026) (also has a small amount of 24edo)


13: 232.836 cents 232.836
; [[Dolores Catherino]]
* [https://youtu.be/AYHpxeM6o_g ''Moments of Unexpected Beauty''] (2026)


14: 250.746 cents 250.746
; [[Peter Kosmorsky]]
* [http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/67-edo.mp3 Beginning of a piece in 67 tone] (2011) {{dead link}}


15: 268.657 cents 7/6
; [[Budjarn Lambeth]]
* [https://youtu.be/xeOjzyXJl_M 67edo Negri8 MODMOS Improvisation] (2024)


16: 286.567 cents 286.567
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
 
17: 304.478 cents 304.478
 
18: 322.388 cents 322.388
 
19: 340.299 cents 340.299
 
20: 358.209 cents 358.209
 
21: 376.119 cents 5/4 -
 
22: 394.030 cents 5/4 +
 
23: 411.940 cents 411.940
 
24: 429.851 cents 429.851
 
25: 447.761 cents 447.761
 
26: 465.672 cents 21/16
 
27: 483.582 cents 483.582
 
28: 501.493 cents 501.493
 
29: 519.403 cents 519.403
 
30: 537.313 cents 537.313
 
31: 555.224 cents 11/8
 
32: 573.134 cents 573.134
 
33: 591.045 cents 591.045
 
34: 608.955 cents 608.955
 
35: 626.866 cents 626.866
 
36: 644.776 cents 644.776
 
37: 662.687 cents 662.687
 
38: 680.597 cents 680.597
 
39: 698.507 cents 3/2
 
40: 716.418 cents 716.418
 
41: 734.328 cents 734.328
 
42: 752.239 cents 752.239
 
43: 770.149 cents 770.149
 
44: 788.060 cents 788.060
 
45: 805.970 cents 805.970
 
46: 823.881 cents 823.881
 
47: 841.791 cents 841.791
 
48: 859.701 cents 859.701
 
49: 877.612 cents 877.612
 
50: 895.522 cents 895.522
 
51: 913.433 cents 913.433
 
52: 931.343 cents 931.343
 
53: 949.254 cents 949.254
 
54: 967.164 cents 7/4
 
55: 985.075 cents 985.075
 
56: 1002.985 cents 1002.985
 
57: 1020.896 cents 1020.896
 
58: 1038.806 cents 1038.806
 
59: 1056.716 cents 1056.716
 
60: 1074.627 cents 1074.627
 
61: 1092.537 cents 1092.537
 
62: 1110.448 cents 1110.448
 
63: 1128.358 cents 1128.358
 
64: 1146.269 cents 1146.269
 
65: 1164.179 cents 1164.179
 
66: 1182.090 cents 1182.090
 
67: 2/1 1200.000 octave
 
[[Category:Edo]]
[[Category:Prime EDO]]
[[Category:Meantone]]
[[Category:Meantone]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/67edo"