29edo - Revision history

Squib: /* Stacking fifths */

2026-06-18T02:52:42Z

Stacking fifths

← Older revision		Revision as of 02:52, 18 June 2026
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	Edson is a 2.3.7/5.11/5.13/5 subgroup temperament, and 29edo represents the 2.3.11/5.13/5 subgroup to very high accuracy, and the 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the [[7:11:13\|1-11/7-13/7 (7:11:13)]] chord, the [[The Archipelago\|barbados]] triad [[10:13:15\|1-13/10-3/2 (10:13:15)]], the minor barbados triad [[26:30:39\|1-15/13-3/2 (26:30:39)]], the [[22:28:33\|1-14/11-3/2 (22:28:33)]] triad, the [[22:26:33\|1-13/11-3/2 (22:26:33)]] triad, and the [[petrmic triad]], a 13-limit [[Dyadic chord\|essentially tempered dyadic chord]].		Edson is a 2.3.7/5.11/5.13/5 subgroup temperament, and 29edo represents the 2.3.11/5.13/5 subgroup to very high accuracy, and the 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the [[7:11:13\|1-11/7-13/7 (7:11:13)]] chord, the [[The Archipelago\|barbados]] triad [[10:13:15\|1-13/10-3/2 (10:13:15)]], the minor barbados triad [[26:30:39\|1-15/13-3/2 (26:30:39)]], the [[22:28:33\|1-14/11-3/2 (22:28:33)]] triad, the [[22:26:33\|1-13/11-3/2 (22:26:33)]] triad, and the [[petrmic triad]], a 13-limit [[Dyadic chord\|essentially tempered dyadic chord]].

	29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 ~~and~~ 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. A larger subgroup containing both of these subgroups is the [[kN subgroups\|329 subgroup]] 2.3.125.175.275.325; on this subgroup 29 tunes the same as 87, and the commas of 29 on this subgroup are the same as the 13-limit commas of 87. Still another subgroup of interest is the [[kN subgroups\|229 subgroup]] 2.3.25.35.55.65.85; on this subgroup 29 tunes the same as 58 and has the same 17-limit commas.		29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195, 364/363, and 847/845 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. A larger subgroup containing both of these subgroups is the [[kN subgroups\|329 subgroup]] 2.3.125.175.275.325; on this subgroup 29 tunes the same as 87, and the commas of 29 on this subgroup are the same as the 13-limit commas of 87. Still another subgroup of interest is the [[kN subgroups\|229 subgroup]] 2.3.25.35.55.65.85; on this subgroup 29 tunes the same as 58 and has the same 17-limit commas.

	Due to 29edo's tone-efficient mapping of 2.3.7/5.11/5.13/5, it makes sense to collapse this subgroup to 29edo. One may then expand the subgroup to the full 13-limit, adding an independent generator to reach primes 5, 7, 11, and 13 in one generator. This is [[mystery]] temperament, which has very low [[badness]] despite so many periods per octave. The 58-note MOS gives scope for harmony, with 29 15-odd-limit otonal chords and 29 utonal chords.		Due to 29edo's tone-efficient mapping of 2.3.7/5.11/5.13/5, it makes sense to collapse this subgroup to 29edo. One may then expand the subgroup to the full 13-limit, adding an independent generator to reach primes 5, 7, 11, and 13 in one generator. This is [[mystery]] temperament, which has very low [[badness]] despite so many periods per octave. The 58-note MOS gives scope for harmony, with 29 15-odd-limit otonal chords and 29 utonal chords.

Lucius Chiaraviglio: /* Intervals */ Add 64/63 and 63/32

2026-06-07T04:36:28Z

Intervals: Add 64/63 and 63/32

← Older revision		Revision as of 04:36, 7 June 2026
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	\| 1		\| 1
	\| 41.379		\| 41.379
	\| [[33/32]], [[40/39]], [[45/44]], [[81/80]]		\| [[33/32]], [[40/39]], [[45/44]],<br>[[81/80]], [[64/63]]
	\| negative diminished 2nd,<br>double diminished 3rd		\| negative diminished 2nd,<br>double diminished 3rd
	\| ^1, vm2		\| ^1, vm2
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	\| 28		\| 28
	\| 1158.621		\| 1158.621
	\| [[64/33]], [[39/20]], [[88/45]] [[160/81]]		\| [[64/33]], [[39/20]], [[88/45]],<br>[[160/81]], [[63/32]]
	\| diminished 9th,<br>double augmented 6th		\| diminished 9th,<br>double augmented 6th
	\| ^M7, v8		\| ^M7, v8

Lucius Chiaraviglio: /* 21st century */ Add Bryan Deister's ''an idea in 29edo'' (2026)

2026-06-07T04:01:57Z

21st century: Add Bryan Deister's ''an idea in 29edo'' (2026)

← Older revision		Revision as of 04:01, 7 June 2026
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	* [https://www.youtube.com/watch?v=ktk0VWbUbDg ''microtonal improvisation in 29edo''] (2023)		* [https://www.youtube.com/watch?v=ktk0VWbUbDg ''microtonal improvisation in 29edo''] (2023)
	* [https://www.youtube.com/shorts/SH5IQOi33Oo ''29edo groove''] (2025)		* [https://www.youtube.com/shorts/SH5IQOi33Oo ''29edo groove''] (2025)
			* [https://www.youtube.com/shorts/PuaNvxX11II ''an idea in 29edo''] (2026)

	; [[duckapus]]		; [[duckapus]]

Lucius Chiaraviglio: /* Modern renderings */ Toby Fox/Deltarune: Make Modern Rendering format consistent with other entries

2026-06-03T04:59:10Z

Modern renderings: Toby Fox/Deltarune: Make Modern Rendering format consistent with other entries

← Older revision		Revision as of 04:59, 3 June 2026
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	* [https://www.youtube.com/shorts/lOaG5mgYMuM ''Concertina Ballerina''] (1983) – microtonal cover in 29edo by [[Bryan Deister]] (2026)		* [https://www.youtube.com/shorts/lOaG5mgYMuM ''Concertina Ballerina''] (1983) – microtonal cover in 29edo by [[Bryan Deister]] (2026)

	; {{W\|Toby Fox}} ~~(via {{W\|Deltarune}})~~		; {{W\|Toby Fox}}
	* [https://www.youtube.com/shorts/NYN8EBllJkE ''~~Deltarune Chapter 2 -~~ A Cyber's World''] (2021) – microtonal cover in 29edo by [[Bryan Deister]] (2023)		* [https://www.youtube.com/shorts/NYN8EBllJkE ''A Cyber's World''] via ''{{W\|Deltarune}} Chapter 2'' (2021) – microtonal cover in 29edo by [[Bryan Deister]] (2023)
	* [https://www.youtube.com/watch?v=JOqnRPIOb5o ''Deltarune Chapter 2 ~~- Dialtone~~''] (2021) – microtonal cover in 29edo by [[Bryan Deister]] (2024)		* [https://www.youtube.com/watch?v=JOqnRPIOb5o ''Dialtone''] via ''{{W\|Deltarune}} Chapter 2'' (2021) – microtonal cover in 29edo by [[Bryan Deister]] (2024)

	; {{W\|Bart Howard}}		; {{W\|Bart Howard}}

FloraC: /* Notation */ SZG notation

2026-05-12T14:27:34Z

Notation: SZG notation

← Older revision		Revision as of 14:27, 12 May 2026
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	29edo can be notated three different ways. Using only sharps and flats, the chromatic scale from C is:		29edo can be notated three different ways. Using only sharps and flats, the chromatic scale from C is:

	{{dash\|C, B♯, D♭, C♯, B𝄪/E𝄫, D, C𝄪/F𝄫, E♭, D♯, F♭, E, D𝄪/G𝄫, F, E♯, G♭, F♯, E𝄪/A𝄫, G, F𝄪, A♭, G♯, B𝄫, A, G𝄪/C𝄫, B♭, A♯, C♭, B, A𝄪/D𝄫, C\|s=hair~~\|d=long~~}}		{{dash\|C, B♯, D♭, C♯, B𝄪/E𝄫, D, C𝄪/F𝄫, E♭, D♯, F♭, E, D𝄪/G𝄫, F, E♯, G♭, F♯, E𝄪/A𝄫, G, F𝄪, A♭, G♯, B𝄫, A, G𝄪/C𝄫, B♭, A♯, C♭, B, A𝄪/D𝄫, C\|s=hair}}

	Here, six pairs of enharmonic equivalents exist:		Here, six pairs of enharmonic equivalents exist:
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	* C𝄪 = F𝄫		* C𝄪 = F𝄫

	=== ~~Ups and downs~~ notation ===		=== Stein–Zimmermann–Gould notation ===
	Since a sharp raises by three steps, 29edo is a good candidate for [[~~ups and downs~~ notation]], ~~similar to [[22edo]]. Spoken as up, downsharp, sharp, etc. Note that downsharp (v#) can be respelled as dup (^^).~~		Since a sharp raises by three steps, 29edo is a good candidate for [[Stein–Zimmermann–Gould notation]], using sharps and flats with arrows similar to [[22edo]]:
	~~{{Ups and downs sharpness}}~~		{{Sharpness-sharp3-szg}}

	~~Here,~~ sharps and flats with arrows ~~from~~ [[~~Helmholtz–Ellis notation~~]] ~~are used~~:
	{{Sharpness-sharp3}}

	Note that C♯ is enharmonic to D{{flatup}}, and D♭ is enharmonic to C{{sharpdown}}.		Note that C♯ is enharmonic to D{{flatup}}, and D♭ is enharmonic to C{{sharpdown}}.

	If arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best spelled with double arrows.		If arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best spelled with double arrows.

			=== Kite's ups and downs notation ===
			29edo can also be notated with [[Kite's ups and downs notation\|Kite's ups and downs]], spoken as up, downsharp, sharp, etc. Note that downsharp (v#) can be respelled as dup (^^).
			{{Ups and downs sharpness}}

	=== Sagittal notation ===		=== Sagittal notation ===
	This notation uses the same sagittal sequence as ~~EDOs~~ [[15edo#Sagittal notation\|15]] and [[22edo#Sagittal notation\|22]].		This notation uses the same sagittal sequence as edos [[15edo #Sagittal notation\|15]] and [[22edo #Sagittal notation\|22]].

	==== Evo flavor ====		==== Evo flavor ====

Lucius Chiaraviglio: /* Music */ Convert 10 microtonal covers by Bryan Deister and 1 microtonal cover (2 videos) by Stephen Weigel and Clarissa to Modern Renderings format (and move accordingly); move Randy Wells entry to the proper place

2026-05-11T17:06:26Z

Music: Convert 10 microtonal covers by Bryan Deister and 1 microtonal cover (2 videos) by Stephen Weigel and Clarissa to Modern Renderings format (and move accordingly); move Randy Wells entry to the proper place

@@ Line 1,009: / Line 1,009: @@
 * [https://www.youtube.com/watch?v=me7dHmo3cVs ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)
 * [https://www.youtube.com/watch?v=-E-2mszlgWM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)
 === 21st century ===
 ; [[Charles Loli A.]] ([http://musicool.us/musicool/armonia.htm site]{{dead link}})
 * [http://www.microtonalismo.com/el-teclado-29-edo ''Mp3 29EDO - Escala tonal de 17 notas''] {{dead link}}
 ; [[User:CellularAutomaton|CellularAutomaton]]
@@ Line 1,022: / Line 1,048: @@
 ; [[Bryan Deister]]
 * [https://www.youtube.com/watch?v=HGQ2b6v0TWE ''Glass Animals - Life Itself''] (2023)
 * [https://www.youtube.com/watch?v=ktk0VWbUbDg ''microtonal improvisation in 29edo''] (2023)
 * [https://www.youtube.com/shorts/SH5IQOi33Oo ''29edo groove''] (2025)
 ; [[duckapus]]
@@ Line 1,084: / Line 1,098: @@
 * [http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3 ''Route 14 in Bridgetown'']
-; [[Stephen Weigel]] and [[Clarissa]]
+; [[Randy Wells]] (Australopithecine XEN)
-* ''Fly Me to the Moon (29-TET) microtonal cover'' (2026) (Stephen Weigel on Lumatone/soft synthesizer; Clarissa on trumpet)
+* [https://www.youtube.com/watch?v=yvCVAxyU5ZU ''Toy Shoppe''] (2024)
-** [https://www.youtube.com/watch?v=FFrHIMrAS-E (original performance video)]
+* [https://www.youtube.com/watch?v=3pAU6_QunmU ''The Sea of Swirly Twirly Gumdrops''] (2024)
 ; [[Xotla]]

FloraC: /* Music */ cleanup. Mark todo. +1 music

2026-05-07T09:57:50Z

Music: cleanup. Mark todo. +1 music

← Older revision		Revision as of 09:57, 7 May 2026
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	* [https://www.youtube.com/shorts/lOaG5mgYMuM ''Concertina Ballerina - Alternative Radio (microtonal cover in 29edo)''] (2026)		* [https://www.youtube.com/shorts/lOaG5mgYMuM ''Concertina Ballerina - Alternative Radio (microtonal cover in 29edo)''] (2026)
	* [https://www.youtube.com/shorts/WEu7NzK7u0I ''Cat - C418 (microtonal cover in 29edo)''] (2026)		* [https://www.youtube.com/shorts/WEu7NzK7u0I ''Cat - C418 (microtonal cover in 29edo)''] (2026)

			{{Todo\|inline=1\|research\|comment = Identify the original composers.}}

	; [[duckapus]]		; [[duckapus]]
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	; [[E8 Heterotic]]		; [[E8 Heterotic]]
	* [https://~~youtu~~.be/~~_1snAPXErOQ~~?si=~~p2Pucp9aQDW6DMZE~~ ''Glaukos Circuit''] (2019) – chiptune		* [https://www.youtube.com/watch?v=_1snAPXErOQ ''Glaukos Circuit''] (2019) – chiptune

	; [[Pedro Laranjeira Finisterra]]		; [[Pedro Laranjeira Finisterra]]
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	* [https://www.youtube.com/watch?v=di4qn2VFYbs ''Plane Sonatina No. 1''] (2025)		* [https://www.youtube.com/watch?v=di4qn2VFYbs ''Plane Sonatina No. 1''] (2025)
	* [https://www.youtube.com/watch?v=ifvvww20XAU ''Strank Running''] (2025)		* [https://www.youtube.com/watch?v=ifvvww20XAU ''Strank Running''] (2025)

			; [[groundfault]]
			* "The Lake Reflects a Black Sky" from ''A New Dusk'' (2024) – [https://groundfco.bandcamp.com/track/the-lake-reflects-a-black-sky-29-31-20edo Bandcamp] \| [https://www.youtube.com/watch?v=1bnEO8vGvbo YouTube (0:00–2:38)] – in part, the rest being in 31edo and 20edo

	; [[Igliashon Jones]]		; [[Igliashon Jones]]
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	; [[NullPointerException Music]]		; [[NullPointerException Music]]
	* [https://www.youtube.com/watch?v=RtbY64I-vYg ''Edolian ~~- Chamber~~''] (2020)		* [https://www.youtube.com/watch?v=RtbY64I-vYg "Chamber"], from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020)

	; [[Mats Öljare]]		; [[Mats Öljare]]

Lucius Chiaraviglio: /* 21st century */ ''Fly Me to the Moon (29-TET) microtonal cover'' (2026) (Stephen Weigel on Lumatone/soft synthesizer; Clarissa on trumpet): add transcribed version

2026-04-26T01:11:55Z

21st century: ''Fly Me to the Moon (29-TET) microtonal cover'' (2026) (Stephen Weigel on Lumatone/soft synthesizer; Clarissa on trumpet): add transcribed version

← Older revision		Revision as of 01:11, 26 April 2026
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	; [[Stephen Weigel]] and [[Clarissa]]		; [[Stephen Weigel]] and [[Clarissa]]
	* ~~[https://www.youtube.com/watch?v=FFrHIMrAS-E~~ ''Fly Me to the Moon (29-TET) microtonal cover''] (2026) (Stephen Weigel on Lumatone/soft synthesizer; Clarissa on trumpet)		* ''Fly Me to the Moon (29-TET) microtonal cover'' (2026) (Stephen Weigel on Lumatone/soft synthesizer; Clarissa on trumpet)
			** [https://www.youtube.com/watch?v=FFrHIMrAS-E (original performance video)]
			** [https://www.youtube.com/watch?v=ZWDCWPOhPAA (transcription)]

	; [[Xotla]]		; [[Xotla]]

Lucius Chiaraviglio: /* 21st century */ Add ''Fly Me to the Moon (29-TET) microtonal cover''] (2026) (Stephen Weigel on Lumatone/soft synthesizer; Clarissa on trumpet)

2026-04-23T01:19:23Z

21st century: Add ''Fly Me to the Moon (29-TET) microtonal cover''] (2026) (Stephen Weigel on Lumatone/soft synthesizer; Clarissa on trumpet)

← Older revision		Revision as of 01:19, 23 April 2026
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	; [[Chris Vaisvil]]		; [[Chris Vaisvil]]
	* [http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3 ''Route 14 in Bridgetown'']		* [http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3 ''Route 14 in Bridgetown'']

			; [[Stephen Weigel]] and [[Clarissa]]
			* [https://www.youtube.com/watch?v=FFrHIMrAS-E ''Fly Me to the Moon (29-TET) microtonal cover''] (2026) (Stephen Weigel on Lumatone/soft synthesizer; Clarissa on trumpet)

	; [[Xotla]]		; [[Xotla]]

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

2026-04-13T09:36:59Z

Text replacement - "garibaldi temperament" to "garibaldi temperament"

← Older revision		Revision as of 09:36, 13 April 2026
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	=== Stacking fifths ===		=== Stacking fifths ===
	Another possible use for 29edo is as an equally tempered para-pythagorean scale. Using its fifth as a generator leads to a variant of [[garibaldi ~~temperament~~]] which is not very accurate but which has relatively low 13-limit complexity. However, it gives the POL2 generator for [[Subgroup temperaments #Edson (2.3.7/5.11/5.13/5 subgroup)\|edson temperament]] with essentially perfect accuracy, only 0.034 cents sharp of it.		Another possible use for 29edo is as an equally tempered para-pythagorean scale. Using its fifth as a generator leads to a variant of [[garibaldi]] temperament which is not very accurate but which has relatively low 13-limit complexity. However, it gives the POL2 generator for [[Subgroup temperaments #Edson (2.3.7/5.11/5.13/5 subgroup)\|edson temperament]] with essentially perfect accuracy, only 0.034 cents sharp of it.

	Edson is a 2.3.7/5.11/5.13/5 subgroup temperament, and 29edo represents the 2.3.11/5.13/5 subgroup to very high accuracy, and the 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the [[7:11:13\|1-11/7-13/7 (7:11:13)]] chord, the [[The Archipelago\|barbados]] triad [[10:13:15\|1-13/10-3/2 (10:13:15)]], the minor barbados triad [[26:30:39\|1-15/13-3/2 (26:30:39)]], the [[22:28:33\|1-14/11-3/2 (22:28:33)]] triad, the [[22:26:33\|1-13/11-3/2 (22:26:33)]] triad, and the [[petrmic triad]], a 13-limit [[Dyadic chord\|essentially tempered dyadic chord]].		Edson is a 2.3.7/5.11/5.13/5 subgroup temperament, and 29edo represents the 2.3.11/5.13/5 subgroup to very high accuracy, and the 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the [[7:11:13\|1-11/7-13/7 (7:11:13)]] chord, the [[The Archipelago\|barbados]] triad [[10:13:15\|1-13/10-3/2 (10:13:15)]], the minor barbados triad [[26:30:39\|1-15/13-3/2 (26:30:39)]], the [[22:28:33\|1-14/11-3/2 (22:28:33)]] triad, the [[22:26:33\|1-13/11-3/2 (22:26:33)]] triad, and the [[petrmic triad]], a 13-limit [[Dyadic chord\|essentially tempered dyadic chord]].