59edo - Revision history

Lucius Chiaraviglio: /* Theory */ Add link to 50edo

2026-05-27T20:03:37Z

Theory: Add link to 50edo

← Older revision		Revision as of 20:03, 27 May 2026
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	Using the flat fifth instead of the sharp one allows for the {{nowrap\|12 & 35}} temperament, which is a kind of bizarre cousin to [[garibaldi]] with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth. The flat fifth also acts as a generator for [[flattertone]] temperament in the 59bcd val, a variant of meantone with very flat fifths.		Using the flat fifth instead of the sharp one allows for the {{nowrap\|12 & 35}} temperament, which is a kind of bizarre cousin to [[garibaldi]] with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth. The flat fifth also acts as a generator for [[flattertone]] temperament in the 59bcd val, a variant of meantone with very flat fifths.

	As every other step of [[118edo]], 59edo is an excellent tuning for the 2.9.5.21.11 11-limit [[kN subgroups\|259 subgroup]], on which it takes the same tuning and tempers out the same commas. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50 & 59 temperament with a subminor third generator provides an interesting temperament.		As every other step of [[118edo]], 59edo is an excellent tuning for the 2.9.5.21.11 11-limit [[kN subgroups\|259 subgroup]], on which it takes the same tuning and tempers out the same commas. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the [[50edo\|50]] & 59 temperament with a subminor third generator provides an interesting temperament.

	=== Odd harmonics ===		=== Odd harmonics ===

VectorGraphics at 07:07, 25 May 2026

2026-05-25T07:07:53Z

← Older revision		Revision as of 07:07, 25 May 2026
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	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}{{Todo\|text=ADD 3\|inline=1}}

	== Notation ==		== Notation ==

BudjarnLambeth: /* Music */ add 1

2026-03-12T06:31:52Z

Music: add 1

← Older revision		Revision as of 06:31, 12 March 2026
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	* "too powerful if i had social skills" from ''Melancholie'' (2023) – [https://open.spotify.com/track/1J8zDrAstQNKgLnXPjKwdm Spotify] \| [https://francium223.bandcamp.com/track/too-powerful-if-i-had-social-skills Bandcamp] \| [https://www.youtube.com/watch?v=FyzN0P6icf0 YouTube]		* "too powerful if i had social skills" from ''Melancholie'' (2023) – [https://open.spotify.com/track/1J8zDrAstQNKgLnXPjKwdm Spotify] \| [https://francium223.bandcamp.com/track/too-powerful-if-i-had-social-skills Bandcamp] \| [https://www.youtube.com/watch?v=FyzN0P6icf0 YouTube]
	* "Stay Away From The Fog" from ''Void'' (2025) – [https://open.spotify.com/track/6swFGV70cPYwruPrnu3iHX Spotify] \| [https://francium223.bandcamp.com/track/stay-away-from-the-fog Bandcamp] \| [https://www.youtube.com/watch?v=zVsjM-LRjNo YouTube]		* "Stay Away From The Fog" from ''Void'' (2025) – [https://open.spotify.com/track/6swFGV70cPYwruPrnu3iHX Spotify] \| [https://francium223.bandcamp.com/track/stay-away-from-the-fog Bandcamp] \| [https://www.youtube.com/watch?v=zVsjM-LRjNo YouTube]

			; [[Budjarn Lambeth]]
			* [https://youtu.be/YDbqf3g88BE ''The Odd Effects of Breathing the Fairy Dust''] (2026)

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

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''Le Ciel - Malice Mizer (microtonal cover in 59edo)'' (2026)

2026-02-04T00:48:52Z

Music: Add Bryan Deister's ''Le Ciel - Malice Mizer (microtonal cover in 59edo)'' (2026)

← Older revision		Revision as of 00:48, 4 February 2026
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	* [https://www.youtube.com/watch?v=-UsnINWSvzo ''Microtonal improvisation in 59edo''] (2025)		* [https://www.youtube.com/watch?v=-UsnINWSvzo ''Microtonal improvisation in 59edo''] (2025)
	* [https://www.youtube.com/shorts/unVwXrAWnzI ''icosa - Oliver Buckland (microtonal cover in 59edo)''] (2025)		* [https://www.youtube.com/shorts/unVwXrAWnzI ''icosa - Oliver Buckland (microtonal cover in 59edo)''] (2025)
			* [https://www.youtube.com/shorts/XYr4j6Abwlw ''Le Ciel - Malice Mizer (microtonal cover in 59edo)''] (2026)

	; [[Francium]]		; [[Francium]]

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''icosa - Oliver Buckland (microtonal cover in 59edo)'' (2025)

2025-11-19T22:15:04Z

Music: Add Bryan Deister's ''icosa - Oliver Buckland (microtonal cover in 59edo)'' (2025)

← Older revision		Revision as of 22:15, 19 November 2025
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/watch?v=-UsnINWSvzo ''Microtonal improvisation in 59edo''] (2025)		* [https://www.youtube.com/watch?v=-UsnINWSvzo ''Microtonal improvisation in 59edo''] (2025)
			* [https://www.youtube.com/shorts/unVwXrAWnzI ''icosa - Oliver Buckland (microtonal cover in 59edo)''] (2025)

	; [[Francium]]		; [[Francium]]

BudjarnLambeth: Add scales section

2025-11-17T07:33:16Z

Add scales section

← Older revision		Revision as of 07:33, 17 November 2025
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	== Scales ==		== Scales ==
			; [[Porcupine]] scales
			* Porcupine[7]: 8 8 8 11 8 8 8
			* Porcupine[15]: 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3
			* Porcupine[22]: 3 2 3 3 2 3 3 2 3 3 3 2 3 3 2 3 3 2 3 3 2 3
	* [[User:BudjarnLambeth/Antechinus\|Antechinus]] (''nonoctave period'')		* [[User:BudjarnLambeth/Antechinus\|Antechinus]] (''nonoctave period'')

BudjarnLambeth: add scales section

2025-11-17T07:30:00Z

add scales section

← Older revision		Revision as of 07:30, 17 November 2025
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	If one prefers ''[[Octave shrinking\|compressed octaves]]'', then [[ed6\|153ed6]] is a viable option. It improves upon 59edo’s 3/1, 7/1 and 13/1 at the cost of a slightly worse 2/1 and 5/1, but substantially worse 11/1.		If one prefers ''[[Octave shrinking\|compressed octaves]]'', then [[ed6\|153ed6]] is a viable option. It improves upon 59edo’s 3/1, 7/1 and 13/1 at the cost of a slightly worse 2/1 and 5/1, but substantially worse 11/1.

			== Scales ==
			* [[User:BudjarnLambeth/Antechinus\|Antechinus]] (''nonoctave period'')

	== Instruments ==		== Instruments ==

BudjarnLambeth: /* Octave stretch or compression */

2025-09-23T03:26:21Z

Octave stretch or compression

@@ Line 92: / Line 92: @@
 [[ed12|211ed12]] is also a solid stretched-octave option, which improves 59edo's 3/1, doing a little, but not much, damage to most other primes.
-If one prefers ''[[Octave shrinking|compressed octaves]]'', then [[zpi|296zpi]] is a viable option. It improves upon 59edo’s 3/1, 7/1 and 13/1 at the cost of a slightly worse 2/1 and 5/1, but substantially worse 11/1.
+If one prefers ''[[Octave shrinking|compressed octaves]]'', then [[ed6|153ed6]] is a viable option. It improves upon 59edo’s 3/1, 7/1 and 13/1 at the cost of a slightly worse 2/1 and 5/1, but substantially worse 11/1.
 == Instruments ==

BudjarnLambeth: /* Octave stretch or compression */

2025-09-02T07:01:17Z

Octave stretch or compression

← Older revision		Revision as of 07:01, 2 September 2025
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	; [[zpi\|295zpi]]		; [[zpi\|295zpi]]
	* Step size: 20.342{{c}}, octave size: 1200.18{{c}}		* Step size: 20.342{{c}}, octave size: 1200.18{{c}}
	Stretching the octave of 59edo by around a fifth of a cent results in slightly improved primes 11 and 13, but slightly worse primes 2, 3, 5 and 7. This approximates all harmonics up to 16 within 9.97{{c}}. The tuning 294zpi does this. 294zpi shares error equally between the two mappings of harmonic 3, so it is the best [[dual fifth]] option for 59edo.		Stretching the octave of 59edo by around a fifth of a cent results in slightly improved primes 11 and 13, but slightly worse primes 2, 3, 5 and 7. This approximates all harmonics up to 16 within 9.97{{c}}. The tuning 294zpi does this. 294zpi shares error equally between the two mappings of harmonic 3, so it is the best [[dual-fifth]] option for 59edo.
	{{Harmonics in cet\|20.342\|intervals=integer\|columns=11\|collapsed=true\|title=Approximation of harmonics in 295zpi}}		{{Harmonics in cet\|20.342\|intervals=integer\|columns=11\|collapsed=true\|title=Approximation of harmonics in 295zpi}}
	{{Harmonics in cet\|20.342\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 295zpi (continued)}}		{{Harmonics in cet\|20.342\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 295zpi (continued)}}
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	{{Harmonics in cet\|20.301\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 59et, 7-limit WE tuning (continued)}}		{{Harmonics in cet\|20.301\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 59et, 7-limit WE tuning (continued)}}

	; [[166ed7]]		; [[ed7\|166ed7]]
	* Octave size: 1197.35{{c}}		* Octave size: 1197.35{{c}}
	Compressing the octave of 59edo by around 2.5{{c}} results in improved primes 3, 7 and 13, but worse primes 2, 5 and 11. This approximates all harmonics up to 16 within 9.71{{c}}. The tuning 166ed7 does this.		Compressing the octave of 59edo by around 2.5{{c}} results in improved primes 3, 7 and 13, but worse primes 2, 5 and 11. This approximates all harmonics up to 16 within 9.71{{c}}. The tuning 166ed7 does this.
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	{{Harmonics in equal\|166\|7\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 166ed7 (continued)}}		{{Harmonics in equal\|166\|7\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 166ed7 (continued)}}

	; [[212ed12]]		; [[ed12\|212ed12]]
	* Octave size: 1197.24{{c}}		* Octave size: 1197.24{{c}}
	Compressing the octave of 59edo by around 3{{c}} results in improved primes 3, 7 and 13, but worse primes 2, 5 and 11. This approximates all harmonics up to 16 within 9.26{{c}}. The tuning 212ed12 does this.		Compressing the octave of 59edo by around 3{{c}} results in improved primes 3, 7 and 13, but worse primes 2, 5 and 11. This approximates all harmonics up to 16 within 9.26{{c}}. The tuning 212ed12 does this.

BudjarnLambeth: /* Instruments */ stretch compression

2025-09-02T07:00:34Z

Instruments: stretch compression

@@ Line 86: / Line 86: @@
 Because it contains no Sagittal symbols, this Evo-SZ Sagittal notation is also a Stein–Zimmerman notation.
 == Instruments ==
 ; Lumatone
 See [[Lumatone mapping for 59edo]].
 == Music ==