19edo - Revision history

Inthar: /* 171edo */

2026-04-09T00:24:11Z

171edo

← Older revision		Revision as of 00:24, 9 April 2026
Line 45:		Line 45:
	== Multiples ==		== Multiples ==
	=== 171edo ===		=== 171edo ===
	Combining 19edo's accurate 28/27 and 6/5 ~~and~~ [[9edo]]'s accurate 7/6 results in 171edo which is a very accurate model of 7-limit JI, even more accurate than [[99edo]]. 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]]. 171edo supports [[Schismic]] and [[Ennealimmal]].
	{{Harmonics in ED\|171}}		{{Harmonics in ED\|171}}

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

Inthar: /* Scales */

2026-04-09T00:20:13Z

Scales

← Older revision		Revision as of 00:20, 9 April 2026
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	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 MOS (3-1-3-1-3-1-3-1-3) is also commonly used in 19edo.		The semiquartal (5L4s) MOS (3-1-3-1-3-1-3-1-3) is also commonly used in 19edo. Also note the Kleismic MOSes:
			* 4L7s, interpreted as Kleismic[11]: 1 1 3 1 1 3 1 1 3 1 4
			* 4L11s, Kleismic[15]: 1 1 1 2 1 1 1 2 1 1 1 2 1 1 2

	== Multiples ==		== Multiples ==

Inthar: /* Scales */

2026-04-09T00:17:32Z

Scales

← Older revision		Revision as of 00:17, 9 April 2026
Line 38:		Line 38:

	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 MOS (3-1-3-1-3-1-3-1-3) is also commonly used in 19edo.

	== Multiples ==		== Multiples ==

Inthar: /* 171edo */

2026-04-09T00:13:57Z

171edo

← Older revision		Revision as of 00:13, 9 April 2026
Line 41:		Line 41:
	== Multiples ==		== Multiples ==
	=== 171edo ===		=== 171edo ===
	Combining 19edo's accurate 28/27 and 6/5 and [[9edo]]'s accurate 7/6 results in 171edo which is a very accurate model of 7-limit JI, even more accurate than [[99edo]] ~~(and provides prime 17 as a bonus)~~. 171edo supports [[Schismic]] and [[Ennealimmal]].		Combining 19edo's accurate 28/27 and 6/5 and [[9edo]]'s accurate 7/6 results in 171edo which is a very accurate model of 7-limit JI, even more accurate than [[99edo]]. 171edo supports [[Schismic]] and [[Ennealimmal]].
	{{Harmonics in ED\|171}}		{{Harmonics in ED\|171}}

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

Inthar: /* 171edo */

2026-04-09T00:12:49Z

171edo

← Older revision		Revision as of 00:12, 9 April 2026
Line 41:		Line 41:
	== Multiples ==		== Multiples ==
	=== 171edo ===		=== 171edo ===
	Combining 19edo's accurate 28/27 and 6/5 and 9edo's accurate 7/6 results in 171edo which is a very accurate model of 7-limit JI, even more accurate than [[99edo]] (and provides prime 17 as a bonus). 171edo supports [[Schismic]] and [[Ennealimmal]].		Combining 19edo's accurate 28/27 and 6/5 and [[9edo]]'s accurate 7/6 results in 171edo which is a very accurate model of 7-limit JI, even more accurate than [[99edo]] (and provides prime 17 as a bonus). 171edo supports [[Schismic]] and [[Ennealimmal]].
	{{Harmonics in ED\|171}}		{{Harmonics in ED\|171}}

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

Inthar: /* 171edo */

2026-04-09T00:12:24Z

171edo

← Older revision		Revision as of 00:12, 9 April 2026
Line 41:		Line 41:
	== Multiples ==		== Multiples ==
	=== 171edo ===		=== 171edo ===
	~~By combining~~ 19edo's accurate 28/27 and 6/5 and 9edo's accurate 7/6, 171edo ~~provides~~ a very accurate model of 7-limit JI, even more accurate than [[99edo]] (and provides prime 17 as a bonus). 171edo supports [[Schismic]] and [[Ennealimmal]].		Combining 19edo's accurate 28/27 and 6/5 and 9edo's accurate 7/6 results in 171edo which is a very accurate model of 7-limit JI, even more accurate than [[99edo]] (and provides prime 17 as a bonus). 171edo supports [[Schismic]] and [[Ennealimmal]].
	{{Harmonics in ED\|171}}		{{Harmonics in ED\|171}}

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

Inthar: /* 171edo */

2026-04-09T00:11:29Z

171edo

← Older revision		Revision as of 00:11, 9 April 2026
Line 41:		Line 41:
	== Multiples ==		== Multiples ==
	=== 171edo ===		=== 171edo ===
	By combining 19edo's accurate 28/27 and 6/5 and 9edo's accurate 7/6, 171edo provides a very accurate model of 7-limit JI, even more accurate than [[99edo]] (and provides prime 17 as a bonus). 171edo supports [[Schismic]] and [[Ennealimmal]]		By combining 19edo's accurate 28/27 and 6/5 and 9edo's accurate 7/6, 171edo provides a very accurate model of 7-limit JI, even more accurate than [[99edo]] (and provides prime 17 as a bonus). 171edo supports [[Schismic]] and [[Ennealimmal]].

	{{Harmonics in ED\|171}}		{{Harmonics in ED\|171}}

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

Inthar: /* Scales */

2026-04-09T00:11:21Z

Scales

← Older revision		Revision as of 00:11, 9 April 2026
Line 38:		Line 38:

	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).

			== Multiples ==
			=== 171edo ===
			By combining 19edo's accurate 28/27 and 6/5 and 9edo's accurate 7/6, 171edo provides a very accurate model of 7-limit JI, even more accurate than [[99edo]] (and provides prime 17 as a bonus). 171edo supports [[Schismic]] and [[Ennealimmal]]

			{{Harmonics in ED\|171}}

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

Inthar at 08:38, 25 February 2026

2026-02-25T08:38:12Z

← Older revision		Revision as of 08:38, 25 February 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 ~~cycle~~]] 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 */

2026-02-23T04:53:12Z

Scales

← Older revision		Revision as of 04:53, 23 February 2026
Line 38:		Line 38:

	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).

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