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34edo supports the [[diatonic scale]], both the simpler 5L 2s [[Moment-of-symmetry scale|moment-of-symmetry]] form and a more complex [[nicetone]] scale representing the [[zarlino]] diatonic. This can be extended into a 12-note chromatic scale of [[10L 2s]] by stacking the two different varieties of semitones, with an intuitive non-MOS form appearing at LLsLLLLLLsLL (created by first subdividing 34edo into the standard [[pentic]] scale and then splitting that into further smaller steps).  
34edo supports the [[diatonic scale]], both the simpler 5L 2s [[Moment-of-symmetry scale|moment-of-symmetry]] form and a more complex [[nicetone]] scale representing the [[zarlino]] diatonic. This can be extended into a 12-note chromatic scale of [[10L 2s]] by stacking the two different varieties of semitones, with an intuitive non-MOS form appearing at LLsLLLLLLsLL (created by first subdividing 34edo into the standard [[pentic]] scale and then splitting that into further smaller steps).  
[[Stephen Weigel]] recommends [https://youtu.be/NWLbdwFeYrk in this video] the use of 34edo to notate [[Music of Georgia|Georgian music]].


=== Odd harmonics ===
=== Odd harmonics ===
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| 1
| 1
| 35.294
| 35.294
| [[81/80]], [[128/125]], [[51/50]]
| [[81/80]], [[128/125]], [[40/39]], [[45/44]],<br>[[51/50]], [[52/51]], [[55/54]], [[65/64]]
| [[28/27]], [[64/63]]
| [[28/27]], [[64/63]]
| [[36/35]]
| [[36/35]]
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| 2
| 2
| 70.588
| 70.588
| [[25/24]], [[26/25]], [[24/23]], [[27/26]], [[23/22]], [[648/625]], [[33/32]]
| [[23/22]], [[24/23]], [[25/24]], [[26/25]],<br>[[27/26]], [[648/625]], [[33/32]]
| [[21/20]], [[36/35]], [[50/49]]
| [[21/20]], [[36/35]], [[50/49]]
| [[28/27]], [[49/48]]
| [[28/27]], [[49/48]]
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| [[15/14]], [[21/20]]
| [[15/14]], [[21/20]]
| vA1, ^m2
| vA1, ^m2
| downaug 1sn,<br />upminor 2nd
| downaug 1sn, upminor 2nd
| vD#, ^Eb
| vD#, ^Eb
| fru
| fru
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|  
|  
| ^M2, vm3
| ^M2, vm3
| upmajor 2nd,<br />downminor 3rd
| upmajor 2nd, downminor 3rd
| ^E, vF
| ^E, vF
| ru/no
| ru/no
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| 32
| 32
| 1129.412
| 1129.412
| [[48/25]], [[25/13]], [[23/12]], [[625/324]],  [[64/33]]
| [[48/25]], [[25/13]], [[23/12]],  [[64/33]]
| [[40/21]], [[35/18]], [[49/25]]
| [[40/21]], [[35/18]], [[49/25]]
| [[27/14]], [[96/49]]
| [[27/14]], [[96/49]]
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| do
| do
|}
|}
<references group="note" />


Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chord names in other EDOs]].
Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chord names in other EDOs]].


== Notation ==
== Notation ==
=== Ups and downs notation ===
=== Stein–Zimmermann–Gould notation ===
34edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
{{Sharpness-sharp4-szg}}
 
=== Kite's ups and downs notation ===
34edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
{{Ups and downs sharpness}}
{{Ups and downs sharpness}}
[[Alternative symbols for ups and downs notation]] uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp4}}


=== Sagittal notation ===
=== Sagittal notation ===
This notation uses the same sagittal sequence as [[41edo#Sagittal notation|41-EDO]], and is a superset of the notation for [[17edo#Sagittal notation|17-EDO]].
This notation uses the same sagittal sequence as [[41edo #Sagittal notation|41edo]], and is a superset of the notation for [[17edo #Sagittal notation|17edo]].


==== Evo flavor ====
==== Evo flavor ====
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=== Counterpoint ===
=== Counterpoint ===
34edo has such an excellent [[sqrt(25/24)]] that the next edo to have a better one is [[441edo|441]]. Every sequence of intervals available in [[17edo]] are reachable by [[strict contrary motion]] in 34edo.
34edo has such an excellent [[sqrt(25/24)]] that the next edo to have a better one is [[441edo|441]]. Every sequence of intervals available in [[17edo]] is reachable by {{W|Contrary motion|strict contrary motion}} in 34edo.


== Regular temperament properties ==
== Regular temperament properties ==
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|}
|}


In the 5-limit, 34edo [[support]]s [[hanson]], [[srutal]], [[tetracot]], [[würschmidt]], and [[vishnu]] temperaments. It does less well in the [[7-limit]], with two mappings possible for [[7/4]]: a flat one from the [[patent val]], and a sharp one from the 34d val. By way of the patent val 34 supports [[keemun]] temperament, and 34d is an excellent alternative to [[22edo]] for 7-limit [[pajara]] temperament. In the [[11-limit]], 34de supports 11-limit [[pajaric]], and in fact is quite close to the [[POTE tuning]]; it adds [[4375/4374]] to the commas of 11-limit pajaric. On the other hand, the 34d val supports pajara, vishnu and würschmidt, adding 4375/4374 to the commas of pajara. Among subgroup temperaments, the patent val supports [[semaphore]] on the 2.3.7 subgroup.  
In the 5-limit, 34edo [[support]]s [[hanson]], [[srutal]], [[tetracot]], [[würschmidt]], and [[vishnu]] temperaments. It does less well in the [[7-limit]], with two mappings possible for [[7/4]]: a flat one from the [[patent val]], and a sharp one from the 34d val. By way of the patent val 34 supports [[keemun]] temperament, and 34d is an excellent alternative to [[22edo]] for 7-limit [[pajara]] temperament. In the [[11-limit]], the 34d val supports pajara, vishnu and würschmidt, adding 4375/4374 to the commas of pajara. Among subgroup temperaments, the patent val supports [[semaphore]] on the 2.3.7 subgroup.  


=== Uniform maps ===
=== Uniform maps ===
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| Superleap
| Superleap
|}
|}
<references group="note" />


== Octave stretch or compression ==
== Octave stretch or compression ==
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* Antikythera[16]: 1 4 1 1 4 1 4 1 1 4 1 1 4 1 4 1
* Antikythera[16]: 1 4 1 1 4 1 4 1 1 4 1 1 4 1 4 1
* [[Diaschismic]][8]: 3 8 3 3 3 8 3 3
* [[Diaschismic]][8]: 3 8 3 3 3 8 3 3
* Diaschismic[10]: 3 3 5 3 3 3 3 5 3 3
* Diaschismic[12]: 3 3 2 3 3 3 3 3 2 3 3 3
* Diaschismic[12]: 3 3 2 3 3 3 3 3 2 3 3 3
* Diaschismic[22]: 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2
* Diaschismic[22]: 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2
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* [[Blackdye]] (5:3:1)
* [[Blackdye]] (5:3:1)
* [[Diachrome]] (5:2:1)
* [[Diachrome]] (5:2:1)
* [[Cthon5m]] (4:2:1) === Combination product sets ===
* [[Cthon5m]] (4:2:1)  
 
=== Combination product sets ===
* [[1-3-5-9 hexany]]: 6 5 9 5 6 3
* [[1-3-5-9 hexany]]: 6 5 9 5 6 3
* Rotated [[1-3-5-11 hexany]]: 5 4 7 4 5 9
* Rotated [[1-3-5-11 hexany]]: 5 4 7 4 5 9
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=== 21st century ===
=== 21st century ===
; [[bili_33093783396]]
* [https://www.bilibili.com/video/BV1CggPztEEi/ ''A Show of Tetracot Modulation''] (2025)
; [[Flora Canou]]
; [[Flora Canou]]
* [https://soundcloud.com/floracanou/october-dieting-plan?in=floracanou/sets/totmc-suite "October Dieting Plan"] from [https://soundcloud.com/floracanou/sets/totmc-suite ''TOTMC Suite''] (2023–2025) – in [[modus]], 34edo tuning
* [https://soundcloud.com/floracanou/october-dieting-plan?in=floracanou/sets/totmc-suite "October Dieting Plan"] from [https://soundcloud.com/floracanou/sets/totmc-suite ''TOTMC Suite''] (2023–2025) – in [[modus]], 34edo tuning
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* [https://www.youtube.com/shorts/uVZ6tJ1y6ak ''34edo improv''] (2025)
* [https://www.youtube.com/shorts/uVZ6tJ1y6ak ''34edo improv''] (2025)
* [https://www.youtube.com/shorts/Azk7a2bAwOo ''In My Room - Julia Wolf (microtonal cover in 34edo)''] (2026)
* [https://www.youtube.com/shorts/Azk7a2bAwOo ''In My Room - Julia Wolf (microtonal cover in 34edo)''] (2026)
* [https://www.youtube.com/shorts/PDANHoJhs3I ''34edo groove''] (2026)
* [https://www.youtube.com/watch?v=CY4IlT1UEFs ''groove 34edo''] (2026)


; [[E8 Heterotic]]
; [[E8 Heterotic]]
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; [[Tapeworm Saga]]
; [[Tapeworm Saga]]
* [https://www.youtube.com/watch?v=BhgxwP9_cSw ''A 3/4 piece in 34edo on 12/31/23''] (2023)
* [https://www.youtube.com/watch?v=BhgxwP9_cSw ''A 3/4 piece in 34edo on 12/31/23''] (2023)
; [[Shanyuan Baihe-Yuri]] (杉原百合-Yuri)
* [https://www.bilibili.com/video/BV1CK411b72L/ ''Lost Memories -1#''] (2023)
* [https://www.bilibili.com/video/BV1Dw411h7Af/ ''Hold a Memorial Ceremony for Myself''] (2023)


; [[Sintel]]
; [[Sintel]]
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* [https://microstick.net Websites of Neil Haverstick]
* [https://microstick.net Websites of Neil Haverstick]
* [https://myspace.com/microstick] – somehow broken (if you scroll to right, you'll find the songs, playing them, you can't hear anything)
* [https://myspace.com/microstick] – somehow broken (if you scroll to right, you'll find the songs, playing them, you can't hear anything)
== Notes ==
<references group="note" />


[[Category:Diaschismic]]
[[Category:Diaschismic]]
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