34edo - Revision history

CompactStar: /* Regular temperament properties */

2026-11-05T11:27:13Z

Regular temperament properties

← Older revision		Revision as of 11:27, 5 November 2026
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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]], 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]], [[diaschismic]], [[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 (which is the same as [[17edo]]'s 7/4). By way of the patent val 34 supports [[keemun]] temperament. The two different 7-limit vals allow for different extensions of diaschismic: the patent val supports [[septimal diaschismic]], while 34d supports [[pajara]], being an excellent alternative to [[22edo]] for 7-limit pajara temperament. In the [[11-limit]], the 34d val supports undecimal 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 ===

FloraC: /* Music */ sorting

2026-11-02T11:23:32Z

Music: sorting

← Older revision		Revision as of 11:23, 2 November 2026
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	=== 21st century ===		=== 21st century ===
			; [[Amano Hideya]]
			* [https://www.youtube.com/watch?v=wT6v8dlUFWo ''Like refracted light''] (2023)

	; [[bili_33093783396]]		; [[bili_33093783396]]
	* [https://www.bilibili.com/video/BV1CggPztEEi/ ''A Show of Tetracot Modulation''] (2025)		* [https://www.bilibili.com/video/BV1CggPztEEi/ ''A Show of Tetracot Modulation''] (2025)
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	* [https://youtu.be/SoMEMYpRV4w?si=0COl0PwuPo-eQG8K ''No Threes For You''] (2019)		* [https://youtu.be/SoMEMYpRV4w?si=0COl0PwuPo-eQG8K ''No Threes For You''] (2019)
	* [https://youtu.be/_dOIyByMTfU?si=DsWUSQnERSKi0zbu "Elements - Water"] from ''Elements'' (2019–2020)		* [https://youtu.be/_dOIyByMTfU?si=DsWUSQnERSKi0zbu "Elements - Water"] from ''Elements'' (2019–2020)

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

	; [[Francium]]		; [[Francium]]
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	; [[Adam Freese]]		; [[Adam Freese]]
	* [https://www.youtube.com/watch?v=lfdHBBPHvLc ''Austice''] (2023)		* [https://www.youtube.com/watch?v=lfdHBBPHvLc ''Austice''] (2023)

	~~; [[Amano Hideya]]~~
	* [https://www.youtube.com/watch?v=wT6v8dlUFWo ''Like refracted light''] (2023)

	; [[Peter Kosmorsky]]		; [[Peter Kosmorsky]]
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	** "Escapade" – [https://open.spotify.com/track/5An9IJRQSG43gKtLnAUpOY Spotify] \| [https://xotla.bandcamp.com/track/escapade Bandcamp] \| [https://www.youtube.com/watch?v=3dRQy9hvWaU YouTube] – electronic rock		** "Escapade" – [https://open.spotify.com/track/5An9IJRQSG43gKtLnAUpOY Spotify] \| [https://xotla.bandcamp.com/track/escapade Bandcamp] \| [https://www.youtube.com/watch?v=3dRQy9hvWaU YouTube] – electronic rock
	* [https://www.youtube.com/watch?v=56HuAL1jC8E ''Between Space''] (2022) – ambient sci-fi		* [https://www.youtube.com/watch?v=56HuAL1jC8E ''Between Space''] (2022) – ambient sci-fi

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

	== See also ==		== See also ==

FloraC: Document people, not accounts

2026-11-02T10:43:13Z

Document people, not accounts

← Older revision		Revision as of 10:43, 2 November 2026
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	* [https://www.youtube.com/watch?v=lfdHBBPHvLc ''Austice''] (2023)		* [https://www.youtube.com/watch?v=lfdHBBPHvLc ''Austice''] (2023)

	; [[Hideya]]		; [[Amano Hideya]]
	* [https://www.youtube.com/watch?v=wT6v8dlUFWo ''Like refracted light''] (2023)		* [https://www.youtube.com/watch?v=wT6v8dlUFWo ''Like refracted light''] (2023)

Naren: Use non-archive link

2026-09-24T20:03:39Z

Use non-archive link

← Older revision		Revision as of 20:03, 24 September 2026
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	== External links ==		== External links ==
	* [https~~://web.archive.org/web/20180902123545/http~~://microstick.net/~~products/~~34-equal-guitar-by-larry-a-hanson/ 34 Equal Guitar] by [[Larry Hanson]]		* [https://microstick.net/a-34-equal-guitar-by-larry-a-hanson/ 34 Equal Guitar] by [[Larry Hanson]]
	* [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)

Naren: Fix dead link

2026-09-24T19:44:36Z

Fix dead link

← Older revision		Revision as of 19:44, 24 September 2026
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	== External links ==		== External links ==
	* [http://microstick.net/products/34-equal-guitar-by-larry-a-hanson/ 34 Equal Guitar] by [[Larry Hanson]] ~~{{dead link}}~~		* [https://web.archive.org/web/20180902123545/http://microstick.net/products/34-equal-guitar-by-larry-a-hanson/ 34 Equal Guitar] by [[Larry Hanson]]
	* [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)

Lucius Chiaraviglio: /* 21st century */ Add Ocean Stegosaurus Tardigrade's ''4 string instrument test (34ed2)'' (2026)

2026-08-17T17:16:19Z

21st century: Add Ocean Stegosaurus Tardigrade's ''4 string instrument test (34ed2)'' (2026)

← Older revision		Revision as of 17:16, 17 August 2026
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	; [[Claudi Meneghin]]		; [[Claudi Meneghin]]
	* [https://www.youtube.com/watch?v=O_7w4KoaOY4 ''Semitone-Canon on The Mother's Malison Theme, for Cor Anglais & Violin''] (2022)		* [https://www.youtube.com/watch?v=O_7w4KoaOY4 ''Semitone-Canon on The Mother's Malison Theme, for Cor Anglais & Violin''] (2022)

			; [[Ocean Stegosaurus Tardigrade]]
			* [https://www.youtube.com/watch?v=-D1ZjT3H5xM ''4 string instrument test (34ed2)''] (2026)

	; [[Ray Perlner]]		; [[Ray Perlner]]

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}}