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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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=== Subsets and supersets ===
=== Subsets and supersets ===
67edo is the 19th [[prime edo]], following [[61edo]] and before [[71edo]].
67edo is the 19th [[prime edo]], following [[61edo]] and before [[71edo]].
== Intervals ==
{{Interval table}}


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


===Sagittal notation===
=== Kite's ups and downs notation ===
In the following diagrams, 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.
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).
====Evo flavor====
{{Sharpness-sharp5a}}


=== Sagittal notation ===
==== Evo flavor ====
<imagemap>
<imagemap>
File:67-EDO_Evo_Sagittal.svg
File:67-EDO_Evo_Sagittal.svg
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</imagemap>
</imagemap>


====Revo flavor====
==== Revo flavor ====
 
<imagemap>
<imagemap>
File:67-EDO_Revo_Sagittal.svg
File:67-EDO_Revo_Sagittal.svg
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default [[File:67-EDO_Revo_Sagittal.svg]]
default [[File:67-EDO_Revo_Sagittal.svg]]
</imagemap>
</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"