19edo - Revision history

Inthar at 00:08, 8 June 2026

2026-06-08T00:08:34Z

← Older revision		Revision as of 00:08, 8 June 2026
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	'''19edo''' is an equal division of 2/1 into 19 steps of 1200c/19 ~= 63.2c each.		'''19edo''' is an equal division of 2/1 into 19 steps of 1200c/19 ~= 63.2c each.

	19edo is interesting as a ~~flatter~~ [[Meantone]] system; it is in fact very close to 1/3-comma Meantone (i.e. Meantone with exact 6/5). It has [[interordinal]]s and supports [[Semaphore]], which means that it treats half of its perfect fourth as a septimal (8/7) major second, leading to a 9-note MOS [[semiquartal]] (5L4s) that can be created from stacking its 8/7. 19edo is also a tuning of the following temperaments which provide non-12edo [[comma pump\|comma loop]] progressions in the 5-limit:		19edo is interesting as a softer [[Meantone]] system; it is in fact very close to 1/3-comma Meantone (i.e. Meantone with exact 6/5). It has [[interordinal]]s and supports [[Semaphore]], which means that it treats half of its perfect fourth as a septimal (8/7) major second, leading to a 9-note MOS [[semiquartal]] (5L4s) that can be created from stacking its 8/7. 19edo is also a tuning of the following temperaments which provide non-12edo [[comma pump\|comma loop]] progressions in the 5-limit:
	* [[Kleismic]] temperament (six 6/5's = 3/1) but with lower accuracy due to its 6/5 being barely sharpened at all		* [[Kleismic]] temperament (six 6/5's = 3/1) but with lower accuracy due to its 6/5 being barely sharpened at all
	* [[Magic]] temperament (five 5/4's = 3/1) with the generator 5/4 on the flat end for Magic		* [[Magic]] temperament (five 5/4's = 3/1) with the generator 5/4 on the flat end for Magic

Inthar at 10:42, 7 June 2026

2026-06-07T10:42:53Z

← Older revision		Revision as of 10:42, 7 June 2026
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	'''19edo''' is an equal division of 2/1 into 19 steps of 1200c/19 ~= 63.2c each.		'''19edo''' is an equal division of 2/1 into 19 steps of 1200c/19 ~= 63.2c each.

	19edo is interesting as a flatter [[Meantone]] system; it is in fact very close to 1/3-comma Meantone (i.e. Meantone with exact 6/5). It has [[interordinal]]s and supports [[Semaphore]], which means that it treats half of its perfect fourth as a septimal (8/7) major second, leading to a 9-note MOS [[semiquartal]] (5L4s) that can be created from stacking its 8/7. 19edo is also a tuning of the following temperaments which provide non-12edo [[comma pump\|comma loop]] progressions:		19edo is interesting as a flatter [[Meantone]] system; it is in fact very close to 1/3-comma Meantone (i.e. Meantone with exact 6/5). It has [[interordinal]]s and supports [[Semaphore]], which means that it treats half of its perfect fourth as a septimal (8/7) major second, leading to a 9-note MOS [[semiquartal]] (5L4s) that can be created from stacking its 8/7. 19edo is also a tuning of the following temperaments which provide non-12edo [[comma pump\|comma loop]] progressions in the 5-limit:
	* [[Kleismic]] temperament (six 6/5's = 3/1) but with lower accuracy due to its 6/5 being barely sharpened at all		* [[Kleismic]] temperament (six 6/5's = 3/1) but with lower accuracy due to its 6/5 being barely sharpened at all
	* [[Magic]] temperament (five 5/4's = 3/1) with the generator 5/4 on the flat end for Magic		* [[Magic]] temperament (five 5/4's = 3/1) with the generator 5/4 on the flat end for Magic

Inthar: /* 665edo */

2026-06-07T10:41:16Z

665edo

← Older revision		Revision as of 10:41, 7 June 2026
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	{{Harmonics in ED\|665}}		{{Harmonics in ED\|665}}

			== Music ==
			* [https://www.youtube.com/watch?v=Xpujgr-0QTc Tapeworm Saga - Prelude for playing no. 1, for retuned MIDI keyboard in 19edo]
	{{Navbox EDO}}		{{Navbox EDO}}
	{{Cat\|Edos}}		{{Cat\|Edos}}

Inthar at 10:38, 7 June 2026

2026-06-07T10:38:59Z

← Older revision		Revision as of 10:38, 7 June 2026
Line 1:		Line 1:
	'''19edo''' is an equal division of 2/1 into 19 steps of 1200c/19 ~= 63.2c each.		'''19edo''' is an equal division of 2/1 into 19 steps of 1200c/19 ~= 63.2c each.

	19edo is interesting as a flatter [[Meantone]] system; it is in fact very close to 1/3-comma Meantone (i.e. Meantone with exact 6/5). It has [[interordinal]]s and supports [[Semaphore]], which means that it treats half of its perfect fourth as a septimal (8/7) major second, leading to a 9-note MOS semiquartal (5L4s) that can be created from stacking its 8/7. 19edo is also a tuning of the following temperaments which provide non-12edo [[comma pump\|comma loop]] progressions:		19edo is interesting as a flatter [[Meantone]] system; it is in fact very close to 1/3-comma Meantone (i.e. Meantone with exact 6/5). It has [[interordinal]]s and supports [[Semaphore]], which means that it treats half of its perfect fourth as a septimal (8/7) major second, leading to a 9-note MOS [[semiquartal]] (5L4s) that can be created from stacking its 8/7. 19edo is also a tuning of the following temperaments which provide non-12edo [[comma pump\|comma loop]] progressions:
	* [[Kleismic]] temperament (six 6/5's = 3/1) but with lower accuracy due to its 6/5 being barely sharpened at all		* [[Kleismic]] temperament (six 6/5's = 3/1) but with lower accuracy due to its 6/5 being barely sharpened at all
	* [[Magic]] temperament (five 5/4's = 3/1) with the generator 5/4 on the flat end for Magic		* [[Magic]] temperament (five 5/4's = 3/1) with the generator 5/4 on the flat end for Magic

Inthar: /* Scales */

2026-06-07T02:31:59Z

Scales

← Older revision		Revision as of 02:31, 7 June 2026
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	* antisubneutralic (2-2-2-2-2-2-2-2-3)		* antisubneutralic (2-2-2-2-2-2-2-2-3)

	Due to being a ~~meantone~~ tuning with an interval in between 5/4 and 4/3, 19edo has a 7-limit [[omnidiatonic]] scale (3-4-1-3-4-3-1).		Due to being a Meantone tuning with an interval in between 5/4 and 4/3, 19edo has a 7-limit [[omnidiatonic]] scale (3-4-1-3-4-3-1).

	The semiquartal (5L4s) MOS (3-1-3-1-3-1-3-1-3) is also commonly used in 19edo. Also note the Kleismic MOSes:		The semiquartal (5L4s) MOS (3-1-3-1-3-1-3-1-3) is also commonly used in 19edo. Also note the Kleismic MOSes:

Overthink: /* 665edo */ wait that kinda breaks it

2026-05-11T23:04:48Z

665edo: wait that kinda breaks it

← Older revision		Revision as of 23:04, 11 May 2026
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	=== 665edo ===		=== 665edo ===
	665edo = 19 * 35 is mostly known for its absurdly accurate Pythagorean tuning, supporting the "Satanic" temperament equating a stack of 666 perfect fifths (octave reduced) to a single perfect fifth, with an accuracy within 1/1000 of a cent. It additionally shares 19edo's tunings of 6/5 and 28/27, supporting Enneadecal temperament, and is a strong no-11 23-limit tuning.		665edo = 19 * 35 is mostly known for its absurdly accurate Pythagorean tuning, supporting the "Satanic" temperament equating a stack of 666 perfect fifths (octave reduced) to a single perfect fifth, with an accuracy within 1/1000 of a cent. It additionally shares 19edo's tunings of 6/5 and 28/27, supporting Enneadecal temperament, and is a strong no-11 23-limit tuning.

	{{Harmonics in ED\|665}}		{{Harmonics in ED\|665}}

	{{Navbox EDO}}		{{Navbox EDO}}
	{{Cat\|Edos}}		{{Cat\|Edos}}

Overthink: /* 665edo */ more info

2026-05-11T23:04:26Z

665edo: more info

← Older revision		Revision as of 23:04, 11 May 2026
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	=== 665edo ===		=== 665edo ===
	665edo = 19 * 35 is mostly known for its absurdly accurate Pythagorean tuning, supporting the "Satanic" temperament equating a stack of 666 perfect fifths (octave reduced) to a single perfect fifth, with an accuracy within 1/1000 of a cent. It additionally shares 19edo's ~~tuning~~ of 6/5.		665edo = 19 * 35 is mostly known for its absurdly accurate Pythagorean tuning, supporting the "Satanic" temperament equating a stack of 666 perfect fifths (octave reduced) to a single perfect fifth, with an accuracy within 1/1000 of a cent. It additionally shares 19edo's tunings of 6/5 and 28/27, supporting Enneadecal temperament, and is a strong no-11 23-limit tuning.

	{{Harmonics in ED\|665}}		{{Harmonics in ED\|665}}

	{{Navbox EDO}}		{{Navbox EDO}}
	{{Cat\|Edos}}		{{Cat\|Edos}}

Inthar: /* 665edo */

2026-05-09T16:10:04Z

665edo

← Older revision		Revision as of 16:10, 9 May 2026
Line 54:		Line 54:

	=== 665edo ===		=== 665edo ===
	665edo is mostly known for its absurdly accurate Pythagorean tuning, supporting the "Satanic" temperament equating a stack of 666 perfect fifths (octave reduced) to a single perfect fifth, with an accuracy within 1/1000 of a cent. It additionally shares 19edo's tuning of 6/5.		665edo = 19 * 35 is mostly known for its absurdly accurate Pythagorean tuning, supporting the "Satanic" temperament equating a stack of 666 perfect fifths (octave reduced) to a single perfect fifth, with an accuracy within 1/1000 of a cent. It additionally shares 19edo's tuning of 6/5.
	{{Harmonics in ED\|665}}		{{Harmonics in ED\|665}}

	{{Navbox EDO}}		{{Navbox EDO}}
	{{Cat\|Edos}}		{{Cat\|Edos}}

Hotcrystal0 at 14:00, 9 May 2026

2026-05-09T14:00:25Z

← Older revision		Revision as of 14:00, 9 May 2026
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	=== 57edo ===		=== 57edo ===
	57edo is a good no-threes no-fives 19-limit ~~system,~~ or ~~alternatively the~~ 2.5/3.7.11.13.19 subgroup.		57edo is a good no-threes no-fives 19-limit or 2.5/3.7.11.13.19 subgroup system.
	{{Harmonics in ED\|57}}		{{Harmonics in ED\|57}}

Hotcrystal0 at 13:32, 9 May 2026

2026-05-09T13:32:57Z

← Older revision		Revision as of 13:32, 9 May 2026
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	== Multiples ==		== Multiples ==

			=== 57edo ===
			57edo is a good no-threes no-fives 19-limit system, or alternatively the 2.5/3.7.11.13.19 subgroup.
			{{Harmonics in ED\|57}}

	=== 171edo ===		=== 171edo ===
	Combining 19edo's accurate 28/27 and 6/5 with [[9edo]]'s accurate 7/6 results in 171edo which is a very accurate model of 7-limit JI, even more accurate than [[99edo]]. Since its 14/13 is inherited from 19edo, its 13th harmonic is acceptable too. 171edo supports [[Schismic]] and [[Ennealimmal]].		Combining 19edo's accurate 28/27 and 6/5 with [[9edo]]'s accurate 7/6 results in 171edo which is a very accurate model of 7-limit JI, even more accurate than [[99edo]]. Since its 14/13 is inherited from 19edo, its 13th harmonic is acceptable too. 171edo supports [[Schismic]] and [[Ennealimmal]].