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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro}}
{{ED intro}}


== Theory ==
== 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 & composite [[55edo]] as an approximation). It is indistinguishable from 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 [[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.


It is 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 and an orgone temperament ([[26edo]] could be called meantone, but it is more of a [[flattone]]). 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. 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]].
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]].


=== Prime harmonics ===
=== Prime harmonics ===
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67edo is the 19th [[prime edo]], following [[61edo]] and before [[71edo]].
67edo is the 19th [[prime edo]], following [[61edo]] and before [[71edo]].


== Intervals==
== Intervals ==
{{Interval table}}
{{Interval table}}
== Notation ==
=== Stein–Zimmermann–Gould notation ===
[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
{{Sharpness-sharp5-szg}}
=== 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}}
=== 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>
==== 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>
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.


== Scales ==
== Scales ==
{{Idiosyncratic terms}}
=== Mos scales ===
=== Mos scales ===
* Meantone[5]: 11 11 17 11 17
* Meantone[5]: 11 11 17 11 17
* Meantone[7]: 11 11 6 11 11 11 6
* Meantone[7]: 11 11 6 11 11 11 6
* Barbados[5], Bustling Docks (original/default tuning): 14 14 11 14 14
* Barbados[5], Bustling Docks (original/default tuning): 14 14 11 14 14
* Barbados[9]: 11 3 11 3 11 3 11 3 11


=== Modmos scales ===
=== Modmos scales ===
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=== Others ===
=== Others ===
* Approximation of [[Pelog]] lima: 6 10 22 7 22
* 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
* Arcade (approximated from [[32afdo]]): 22 4 13 15 13
* Cosmic (approximated from [[32afdo]]): 29 10 6 11 11
* Cosmic (approximated from [[32afdo]]): 29 10 6 11 11
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* Sourgummy (approximated from [[51afdo]]): 14 12 14 14 13
* Sourgummy (approximated from [[51afdo]]): 14 12 14 14 13
* Bubblegum/Cola (approximated from [[60afdo]]/[[99afdo]]): 14 13 13 13 14
* Bubblegum/Cola (approximated from [[60afdo]]/[[99afdo]]): 14 13 13 13 14
* Spearmint/Whitechocolate (approximated from [[62afdo]]/[[90afdo]]): 13 14 13 14 13
* Tropicalpunch/Whitechocolate (approximated from [[62afdo]]/[[90afdo]]): 13 14 13 14 13
* Lemonade (approximated from [[79afdo]]): 14 13 13 14 13
* Lemonade (approximated from [[79afdo]]): 14 13 13 14 13
* Candycorn (approximated from [[91afdo]]): 11 12 11 10 12 11
* Candycorn (approximated from [[91afdo]]): 11 12 11 10 12 11
* Trailmix (approximated from [[97afdo]]): 11 11 11 12 11 11
* Trailmix (approximated from [[97afdo]]): 11 11 11 12 11 11
* Liquorice (approximated from [[101afdo]]): 11 11 12 10 12 11
* Liquorice (approximated from [[101afdo]]): 11 11 12 10 12 11
* Apple Mint (approximated from [[80afdo]]): 9 11 9 9 10 9 10
* Fishcracker (approximated from [[80afdo]]): 9 11 9 9 10 9 10
 
== Instruments ==
* [[Lumatone mapping for 67edo]]
 
== 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)
 
; [[Delta Quartz]]
* [https://youtu.be/WOguarC1lEI ''Making microtonality accessible - "Keep It Tight"''] (2026) (also has a small amount of 24edo)
 
; [[Dolores Catherino]]
* [https://youtu.be/AYHpxeM6o_g ''Moments of Unexpected Beauty''] (2026)
 
; [[Peter Kosmorsky]]
* [http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/67-edo.mp3 Beginning of a piece in 67 tone] (2011) {{dead link}}


==Music==
; [[Budjarn Lambeth]]
* [http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/67-edo.mp3 Beginning of a piece in 67 tone], [[Peter Kosmorsky]] {{dead link}}
* [https://youtu.be/xeOjzyXJl_M 67edo Negri8 MODMOS Improvisation] (2024)
* [https://youtu.be/xeOjzyXJl_M 67edo Negri8 MODMOS Improvisation], [[Budjarn Lambeth]]


[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Meantone]]
[[Category:Meantone]]
[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/67edo"