43edt - Revision history

ArrowHead294 at 19:09, 25 June 2025

2025-06-25T19:09:42Z

← Older revision		Revision as of 19:09, 25 June 2025
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	== See also ==		== See also ==
			* [[16edf]] – relative edf
	* [[27edo]] – relative edo		* [[27edo]] – relative edo
	* [[70ed6]] – relative ed6		* [[70ed6]] – relative ed6
			* [[90ed10]] – relative ed10
	* [[97ed12]] – relative ed12		* [[97ed12]] – relative ed12

	[[Category:27edo]]		[[Category:27edo]]

ArrowHead294: /* Theory */

2025-06-19T15:26:56Z

Theory

← Older revision		Revision as of 15:26, 19 June 2025
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	== Theory ==		== Theory ==
	43edt is related to [[27edo]], but with the 3/1 rather than the 2/1 being just. ~~It has octaves compressed by about 5.7492{{c}} and~~ is consistent to the [[9-odd-limit\|10-integer-limit]]. ~~The octave compression is~~ a small but significant deviation. This is particularly relevant because the harmonics 27edo approximates well—3, 5, 7, and 13—are all tuned sharp, so 43edt improves those approximations.		43edt is related to [[27edo]], but with the 3/1 rather than the 2/1 being just. Like 27edo, it is consistent to the [[9-odd-limit\|10-integer-limit]]. It has octaves compressed by about 5.7492{{c}}, a small but significant deviation. This is particularly relevant because the harmonics 27edo approximates well—3, 5, 7, and 13—are all tuned sharp, so 43edt improves those approximations.

	However, in addition to its rich octave-based harmony, the 43edt is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, [[Bohlen–Pierce]] harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that [[13edt]] is not. The {{mos scalesig\|4L 5s<3/1>\|link=1}} [[mos]] has {{nowrap\|L {{=}} 7\|s {{=}} 3}}.		However, in addition to its rich octave-based harmony, the 43edt is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, [[Bohlen–Pierce]] harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that [[13edt]] is not. The {{mos scalesig\|4L 5s<3/1>\|link=1}} [[mos]] has {{nowrap\|L {{=}} 7\|s {{=}} 3}}.

ArrowHead294 at 13:21, 10 June 2025

2025-06-10T13:21:05Z

← Older revision		Revision as of 13:21, 10 June 2025
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	* [[70ed6]] – relative ed6		* [[70ed6]] – relative ed6
	* [[97ed12]] – relative ed12		* [[97ed12]] – relative ed12

			[[Category:27edo]]

ArrowHead294: Replace {{scale link}} with {{mos scalesig}}

2025-03-08T00:30:19Z

Replace {{scale link}} with {{mos scalesig}}

← Older revision		Revision as of 00:30, 8 March 2025
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	43edt is related to [[27edo]], but with the 3/1 rather than the 2/1 being just. It has octaves compressed by about 5.7492{{c}} and is consistent to the [[9-odd-limit\|10-integer-limit]]. The octave compression is a small but significant deviation. This is particularly relevant because the harmonics 27edo approximates well—3, 5, 7, and 13—are all tuned sharp, so 43edt improves those approximations.		43edt is related to [[27edo]], but with the 3/1 rather than the 2/1 being just. It has octaves compressed by about 5.7492{{c}} and is consistent to the [[9-odd-limit\|10-integer-limit]]. The octave compression is a small but significant deviation. This is particularly relevant because the harmonics 27edo approximates well—3, 5, 7, and 13—are all tuned sharp, so 43edt improves those approximations.

	However, in addition to its rich octave-based harmony, the 43edt is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, [[Bohlen–Pierce]] harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that [[13edt]] is not. The {{sl\|4L 5s}} [[mos]] has {{nowrap\|L {{=}} 7~~}}, {{nowrap~~\|s {{=}} 3}}.		However, in addition to its rich octave-based harmony, the 43edt is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, [[Bohlen–Pierce]] harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that [[13edt]] is not. The {{mos scalesig\|4L 5s<3/1>\|link=1}} [[mos]] has {{nowrap\|L {{=}} 7\|s {{=}} 3}}.

	=== Harmonics ===		=== Harmonics ===
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	43edt tempers out the no-twos comma of {{monzo\| 0 63 -43 }}, leading to the regular temperament [[support]]ed by [[27edo\|27-]], [[190edo\|190-]], and [[217edo]].		43edt tempers out the no-twos comma of {{monzo\| 0 63 -43 }}, leading to the regular temperament [[support]]ed by [[27edo\|27-]], [[190edo\|190-]], and [[217edo]].

	=== 27 & 190 temperament ===		=== 27 & 190 temperament ===
	==== 5-limit ====		==== 5-limit ====
	Subgroup: 2.3.5		Subgroup: 2.3.5
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	Badness: 0.1659		Badness: 0.1659

	=== 217 & 407 temperament ===		=== 217 & 407 temperament ===
	==== 7-limit ====		==== 7-limit ====
	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

FloraC: +see also

2025-03-04T08:17:16Z

+see also

← Older revision		Revision as of 08:17, 4 March 2025
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	\|}		\|}

	== ~~As a~~ regular ~~temperament~~ ==		== Related regular temperaments ==
	43edt tempers out the no-twos comma of {{monzo\| 0 63 -43 }}, leading to the regular temperament [[support]]ed by [[27edo\|27-]], [[190edo\|190-]], and [[217edo]].		43edt tempers out the no-twos comma of {{monzo\| 0 63 -43 }}, leading to the regular temperament [[support]]ed by [[27edo\|27-]], [[190edo\|190-]], and [[217edo]].

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	Badness: 0.0503		Badness: 0.0503

			== See also ==
			* [[27edo]] – relative edo
			* [[70ed6]] – relative ed6
			* [[97ed12]] – relative ed12

FloraC: /* Theory */ +subsets and supersets

2025-03-04T08:01:28Z

Theory: +subsets and supersets

← Older revision		Revision as of 08:01, 4 March 2025
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	{{Harmonics in equal\|43\|3\|1}}		{{Harmonics in equal\|43\|3\|1}}
	{{Harmonics in equal\|43\|3\|1\|start=12\|columns=12\|collapsed=true\|title=Approximation of harmonics in 43edt (continued)}}		{{Harmonics in equal\|43\|3\|1\|start=12\|columns=12\|collapsed=true\|title=Approximation of harmonics in 43edt (continued)}}

			=== Subsets and supersets ===
			43edt is the 14th [[prime equal division\|prime edt]], following [[41edt]] and coming before [[47edt]].

	== Intervals ==		== Intervals ==

FloraC: Cleanup

2025-03-04T07:59:47Z

Cleanup

Show changes

ArrowHead294 at 14:57, 25 February 2025

2025-02-25T14:57:49Z

Show changes

ArrowHead294 at 14:56, 25 February 2025

2025-02-25T14:56:56Z

Show changes

BudjarnLambeth: /* Properties */ Split wide harmonics table into 2 short tables

2024-10-06T07:06:29Z

Properties: Split wide harmonics table into 2 short tables

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 ==Properties==
 This tuning is related to 27EDO having ~5.7 cent octave compression, a small but significant deviation. This is particularly relevant because 27EDO tunes the 3rd, 5th, 7th and 13th harmonics sharp, thus 43EDT improves those approximations.
 However, in addition to its rich octave-based harmony, the 43EDT is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, Bohlen-Pierce harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that [[13edt|13EDT]] is not. The 4L+5s MOS has L=7 s=3.
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