59edo - Revision history

Overthink: /* Intervals */ add these ratios

2026-07-12T21:29:18Z

Intervals: add these ratios

← Older revision		Revision as of 21:29, 12 July 2026
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	\| 5		\| 5
	\| 101.7		\| 101.7
	\| [[17/16]], [[18/17]]		\| [[17/16]], [[18/17]], [[35/33]]
	\|		\|
	\|		\|
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	\| 27		\| 27
	\| 549.2		\| 549.2
	\| [[11/8]]		\| [[11/8]], [[48/35]]
	\|		\|
	\|		\|
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	\| 32		\| 32
	\| 650.8		\| 650.8
	\| [[16/11]]		\| [[16/11]], [[35/24]]
	\|		\|
	\|		\|
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	\| 54		\| 54
	\| 1098.3		\| 1098.3
	\| [[17/9]], [[32/17]]		\| [[17/9]], [[32/17]], [[66/35]]
	\|		\|
	\|		\|

Overthink: /* Intervals */ Add these ratios

2026-07-11T17:25:16Z

Intervals: Add these ratios

← Older revision		Revision as of 17:25, 11 July 2026
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	! Steps		! Steps
	! Cents		! Cents
	! Approximate ratios<br>(2.9.5.21.11.17-subgroup)		! Approximate ratios<br>(2.9.5.21.11.39.17-subgroup)
	! Ratios of 3, 7, 13<br>(tending sharp)		! Ratios of 3, 7, 13<br>(tending sharp)
	! Ratios of 3, 7, 13<br>(tending flat)		! Ratios of 3, 7, 13<br>(tending flat)
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	\| 2		\| 2
	\| 40.7		\| 40.7
	\| [[45/44]]		\| [[40/39]], [[45/44]]
	\|		\|
	\|		\|
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	\| 3		\| 3
	\| 61.0		\| 61.0
	\|		\| [[27/26]], [[28/27]]
	\|		\|
	\|		\|
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	\| 6		\| 6
	\| 122.0		\| 122.0
	\| [[15/14]]		\| [[15/14]], [[14/13]]
	\|		\|
	\|		\|
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	\| 7		\| 7
	\| 142.4		\| 142.4
	\|		\| [[13/12]]
	\|		\|
	\|		\|
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	\| 10		\| 10
	\| 203.4		\| 203.4
	\| [[9/8]]		\| [[9/8]], [[44/39]]
	\|		\|
	\|		\|
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	\| 12		\| 12
	\| 244.1		\| 244.1
	\|		\| [[15/13]], [[39/34]]
	\|		\|
	\| [[8/7]]		\| [[8/7]]
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	\| 16		\| 16
	\| 325.4		\| 325.4
	\|		\|
	\|		\|
	\|		\|
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	\| 17		\| 17
	\| 345.8		\| 345.8
	\| [[11/9]]		\| [[11/9]], [[39/32]], [[128/105]]
	\| [[16/13]]		\| [[16/13]]
	\|		\|
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	\| 21		\| 21
	\| 427.1		\| 427.1
	\| [[32/25]]		\| [[32/25]], [[50/39]]
	\|		\|
	\|		\|
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	\| 22		\| 22
	\| 447.5		\| 447.5
	\| [[22/17]], [[128/99]]		\| [[22/17]], [[35/27]], [[128/99]]
	\|		\|
	\|		\|
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	\| 25		\| 25
	\| 508.5		\| 508.5
	\|		\| [[35/26]]
	\|		\|
	\| [[4/3]]		\| [[4/3]]
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	\| 29		\| 29
	\| 589.8		\| 589.8
	\| [[45/32]]		\| [[45/32]], [[128/91]]
	\|		\|
	\|		\|
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	\| 30		\| 30
	\| 610.2		\| 610.2
	\| [[64/45]]		\| [[64/45]], [[91/64]]
	\|		\|
	\|		\|
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	\| 34		\| 34
	\| 691.5		\| 691.5
	\|		\| [[52/35]]
	\|		\|
	\| [[3/2]]		\| [[3/2]]
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	\| 37		\| 37
	\| 752.5		\| 752.5
	\| [[17/11]], [[99/64]]		\| [[17/11]], [[54/35]], [[99/64]]
	\|		\|
	\|		\|
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	\| 38		\| 38
	\| 772.9		\| 772.9
	\| [[25/16]]		\| [[25/16]], [[39/25]]
	\|		\|
	\|		\|
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	\| 42		\| 42
	\| 854.2		\| 854.2
	\| [[18/11]]		\| [[18/11]], [[64/39]], [[105/64]]
	\| [[13/8]]		\| [[13/8]]
	\|		\|
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	\| 47		\| 47
	\| 955.9		\| 955.9
	\|		\| [[26/15]], [[68/39]]
	\|		\|
	\| [[7/4]]		\| [[7/4]]
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	\| 49		\| 49
	\| 996.6		\| 996.6
	\| [[16/9]]		\| [[16/9]], [[39/22]]
	\|		\|
	\|		\|
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	\| 52		\| 52
	\| 1057.6		\| 1057.6
	\|		\| [[24/13]]
	\|		\|
	\|		\|
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	\| 53		\| 53
	\| 1078.0		\| 1078.0
	\| [[28/15]]		\| [[13/7]], [[28/15]]
	\|		\|
	\|		\|
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	\| 56		\| 56
	\| 1139.0		\| 1139.0
	\|		\| [[27/14]], [[52/27]]
	\|		\|
	\|		\|
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	\| 57		\| 57
	\| 1159.3		\| 1159.3
	\| [[88/45]]		\| [[39/20]], [[88/45]]
	\|		\|
	\|		\|

Overthink: /* Intervals */ Decision made: 13 is dual (plain sets 13/12<14/13 if 3 and 7 are sharp)

2026-07-11T17:05:50Z

Intervals: Decision made: 13 is dual (plain sets 13/12<14/13 if 3 and 7 are sharp)

← Older revision		Revision as of 17:05, 11 July 2026
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	! Cents		! Cents
	! Approximate ratios<br>(2.9.5.21.11.17-subgroup)		! Approximate ratios<br>(2.9.5.21.11.17-subgroup)
	!Ratios of 3 ~~and~~ 7<br>(tending sharp)		! Ratios of 3, 7, 13<br>(tending sharp)
	!Ratios of 3 ~~and~~ 7<br>(tending flat)		! Ratios of 3, 7, 13<br>(tending flat)
	\|-		\|-
	\| 0		\| 0
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	\| 345.8		\| 345.8
	\| [[11/9]]		\| [[11/9]]
	\|		\| [[16/13]]
	\|		\|
	\|-		\|-
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	\| [[21/17]]		\| [[21/17]]
	\|		\|
	\|		\| [[16/13]]
	\|-		\|-
	\| 19		\| 19
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	\| [[34/21]]		\| [[34/21]]
	\|		\|
	\|		\| [[13/8]]
	\|-		\|-
	\| 42		\| 42
	\| 854.2		\| 854.2
	\| [[18/11]]		\| [[18/11]]
	\|		\| [[13/8]]
	\|		\|
	\|-		\|-
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	\|		\|
	\|		\|
	\|}{{Todo\|inline=1\|complete table~~\|text=Also figure out what to do about prime 13.~~}}		\|}{{Todo\|inline=1\|complete table}}

	== Notation ==		== Notation ==

Overthink: /* Intervals */ add ratios to first column; start dual columns

2026-07-11T16:51:31Z

Intervals: add ratios to first column; start dual columns

Show changes

Overthink: /* Intervals */ start from a clean slate

2026-07-11T16:01:18Z

Intervals: start from a clean slate

Show changes

Fredg999: /* Intervals */ Specific todo category, details

2026-07-11T15:47:18Z

Intervals: Specific todo category, details

← Older revision		Revision as of 15:47, 11 July 2026
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	== Intervals ==		== Intervals ==
	{{Interval table}}{{Todo\|text=ADD 3~~\|inline=1~~}}		{{Interval table}}{{Todo\|inline=1\|complete table\|text=ADD 3 (add intervals involving prime 3; this would require rebuilding the table manually)}}

	== Notation ==		== Notation ==

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
Line 115:		Line 115:
	* "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
Line 110:		Line 110:
	* [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]]