34edo - Revision history

Lucius Chiaraviglio: /* 21st century */ Add Bryan Deister's ''34edo bossa'' (2026)

2026-07-15T05:53:41Z

21st century: Add Bryan Deister's ''34edo bossa'' (2026)

← Older revision		Revision as of 05:53, 15 July 2026
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	* [https://www.youtube.com/shorts/PDANHoJhs3I ''34edo groove''] (2026)		* [https://www.youtube.com/shorts/PDANHoJhs3I ''34edo groove''] (2026)
	* [https://www.youtube.com/watch?v=CY4IlT1UEFs ''groove 34edo''] (2026)		* [https://www.youtube.com/watch?v=CY4IlT1UEFs ''groove 34edo''] (2026)
			* [https://www.youtube.com/watch?v=JKblQe375pw ''34edo bossa''] (2026)

	; [[E8 Heterotic]]		; [[E8 Heterotic]]

FloraC: Text replacement - "gammic temperament" to "gammic temperament"

2026-06-23T05:16:57Z

Text replacement - "gammic temperament" to "gammic temperament"

← Older revision		Revision as of 05:16, 23 June 2026
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	34edo contains two [[17edo]]'s and the half-octave tritone of 600{{c}}. It excels in approximating harmonics 3, 5, 13, 17, and 23 (2.3.5.13.17.23 [[subgroup]] a.k.a. the no-7's no-11's no-19's 23-limit), with tuning even more accurate than [[31edo]] in the 5-limit, but with a sharp tendency and fifth rather than a flat one, and ''not'' tempering out [[81/80]] unlike 31edo. Its primes 7 and 11 are less accurate, but still usable (with the 34d val for prime 7) with a sharp tendency, in fact mapping all [[15-odd-limit]] intervals consistently except for 7/4 and 8/7 in the 34d val.		34edo contains two [[17edo]]'s and the half-octave tritone of 600{{c}}. It excels in approximating harmonics 3, 5, 13, 17, and 23 (2.3.5.13.17.23 [[subgroup]] a.k.a. the no-7's no-11's no-19's 23-limit), with tuning even more accurate than [[31edo]] in the 5-limit, but with a sharp tendency and fifth rather than a flat one, and ''not'' tempering out [[81/80]] unlike 31edo. Its primes 7 and 11 are less accurate, but still usable (with the 34d val for prime 7) with a sharp tendency, in fact mapping all [[15-odd-limit]] intervals consistently except for 7/4 and 8/7 in the 34d val.

	34edo's significance in regards to JI approximation comes from making many simple and natural equivalences between JI intervals. For example, a key characteristic of 34edo is that it splits the standard whole tone of [[9/8]] into six parts, such that three chromatic semitones of [[25/24]] or two diatonic semitones of [[16/15]] result in 9/8. Additionally, if you stack a five-step [[10/9]] interval four times, you reach the perfect fifth [[3/2]], supporting [[tetracot]]. This also means that the perfect fifth is mapped to 20 steps. Given that and the fact that the major third [[5/4]] is mapped to 11 steps, one can see that 34edo takes advantage of a natural logarithmic approximation of 5/4 as a portion of 3/2, or equivalently [[6/5]] as a portion of 5/4, resulting in [[gammic ~~temperament~~]]. It also has the thirds from 17edo: "neogothic" minor and major thirds of about 282 and 424{{c}}, and a neutral third of 353{{c}}. For [[extraclassical tonality]], a tendo third of 459{{c}} and an arto third of 247{{c}} are also available, approximating 13/10 and 15/13 respectively.		34edo's significance in regards to JI approximation comes from making many simple and natural equivalences between JI intervals. For example, a key characteristic of 34edo is that it splits the standard whole tone of [[9/8]] into six parts, such that three chromatic semitones of [[25/24]] or two diatonic semitones of [[16/15]] result in 9/8. Additionally, if you stack a five-step [[10/9]] interval four times, you reach the perfect fifth [[3/2]], supporting [[tetracot]]. This also means that the perfect fifth is mapped to 20 steps. Given that and the fact that the major third [[5/4]] is mapped to 11 steps, one can see that 34edo takes advantage of a natural logarithmic approximation of 5/4 as a portion of 3/2, or equivalently [[6/5]] as a portion of 5/4, resulting in [[gammic]] temperament. It also has the thirds from 17edo: "neogothic" minor and major thirds of about 282 and 424{{c}}, and a neutral third of 353{{c}}. For [[extraclassical tonality]], a tendo third of 459{{c}} and an arto third of 247{{c}} are also available, approximating 13/10 and 15/13 respectively.

	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).

Contribution: /* Rank-2 temperaments */

2026-06-08T12:24:49Z

Rank-2 temperaments

← Older revision		Revision as of 12:24, 8 June 2026
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	\| 458.824		\| 458.824
	\| [[3L 2s]]<br />[[5L 3s]]<br />[[8L 5s]]<br />[[13L 8s]]		\| [[3L 2s]]<br />[[5L 3s]]<br />[[8L 5s]]<br />[[13L 8s]]
	\| [[Petrtri]]		\| [[Petrtri]], [[Goldis]]
	\|-		\|-
	\| 15\34		\| 15\34

FloraC: /* Notation */ improve description

2026-05-12T14:16:17Z

Notation: improve description

← Older revision		Revision as of 14:16, 12 May 2026
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	== Notation ==		== Notation ==
	=== Stein–Zimmermann–Gould notation ===		=== Stein–Zimmermann–Gould notation ===
	[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:		[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
	{{Sharpness-sharp4-szg}}		{{Sharpness-sharp4-szg}}

FloraC: /* Notation */ SZG notation

2026-05-12T12:52:08Z

Notation: SZG notation

← Older revision		Revision as of 12:52, 12 May 2026
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	== 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 with 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 ====

Lucius Chiaraviglio: /* 21st century */ Add Bryan Deister's ''groove 34edo'' (2026)

2026-05-04T01:53:39Z

21st century: Add Bryan Deister's ''groove 34edo'' (2026)

← Older revision		Revision as of 01:53, 4 May 2026
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	* [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/shorts/PDANHoJhs3I ''34edo groove''] (2026)
			* [https://www.youtube.com/watch?v=CY4IlT1UEFs ''groove 34edo''] (2026)

	; [[E8 Heterotic]]		; [[E8 Heterotic]]

Lucius Chiaraviglio: /* 21st century */ Add Bryan Deister's ''34edo groove'' (2026)

2026-04-27T00:17:20Z

21st century: Add Bryan Deister's ''34edo groove'' (2026)

← Older revision		Revision as of 00:17, 27 April 2026
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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)

	; [[E8 Heterotic]]		; [[E8 Heterotic]]

MisterShafXen at 19:13, 10 April 2026

2026-04-10T19:13:00Z

← Older revision		Revision as of 19:13, 10 April 2026
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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

FloraC: /* Music */ cleanup

2026-03-24T12:26:30Z

Music: cleanup

@@ Line 818: / Line 818: @@
 === 21st century ===
 ; [[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
@@ Line 864: / Line 867: @@
 ; [[Tapeworm Saga]]
 * [https://www.youtube.com/watch?v=BhgxwP9_cSw ''A 3/4 piece in 34edo on 12/31/23''] (2023)
 ; [[Sintel]]
@@ Line 895: / Line 902: @@
 ; [[Zhea Erose]]
 * [https://www.youtube.com/watch?v=xYZwye9PWSo ''Modal Studies in Tetracot''] (2021)
 == See also ==

Haidilao: Adding Shanyuan Baihe's pieces

2026-03-24T07:34:43Z

Adding Shanyuan Baihe's pieces

@@ Line 895: / Line 895: @@
 ; [[Zhea Erose]]
 * [https://www.youtube.com/watch?v=xYZwye9PWSo ''Modal Studies in Tetracot''] (2021)
 == See also ==