389edo - Revision history

ArrowHead294 at 22:54, 20 February 2025

2025-02-20T22:54:30Z

← Older revision		Revision as of 22:54, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|389~~}}		{{ED intro}}

	== Theory ==		== Theory ==
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	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
			\|-
	! rowspan="2" \| [[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
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	\| {{monzo\| 20 -17 3 }}, {{monzo\| -39 -12 25 }}		\| {{monzo\| 20 -17 3 }}, {{monzo\| -39 -12 25 }}
	\| {{mapping\| 389 617 903 }}		\| {{mapping\| 389 617 903 }}
	\| -0.19		\| −0.19
	\| 0.500		\| 0.500
	\| 16.2		\| 16.2
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	\| 2109375/2097152, {{monzo\|-7 44 -27 }}		\| 2109375/2097152, {{monzo\|-7 44 -27 }}
	\| {{mapping\| 389 616 903 }} (389b)		\| {{mapping\| 389 616 903 }} (389b)
	\| 0.46		\| +0.46
	\| 0.451		\| 0.451
	\| 14.6		\| 14.6
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	\| 2100875/2097152, {{monzo\| 0 52 -43 }}		\| 2100875/2097152, {{monzo\| 0 52 -43 }}
	\| {{mapping\| 389 903 1092 }}		\| {{mapping\| 389 903 1092 }}
	\| 0.12		\| +0.12
	\| 0.131		\| 0.131
	\| 4.2		\| 4.2
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	\| 6664/6655, 156250/155771, 180625/180224, 184960/184877		\| 6664/6655, 156250/155771, 180625/180224, 184960/184877
	\| {{mapping\| 389 903 1092 1346 1590 }}		\| {{mapping\| 389 903 1092 1346 1590 }}
	\| 0.03		\| +0.03
	\| 0.177		\| 0.177
	\| 5.7		\| 5.7

FloraC: Rework

2023-11-06T16:40:08Z

Rework

← Older revision		Revision as of 16:40, 6 November 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''389edo''' divides the octave into parts of 3.0848c each.~~		{{EDO intro\|389}}

	== Theory ==		== Theory ==
	~~{{Primes~~ in ~~edo~~\|~~389~~\|~~columns=8}}~~		389edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps, which makes it a [[dual-fifth system]]. Otherwise, it has a reasonable approximation to harmonics [[7/1\|7]], [[9/1\|9]], and [[17/1\|17]], with optional additions of either [[5/1\|5]] or [[11/1\|11]] and [[15/1\|15]], making it suitable for a 2.9.5.7.17 or 2.9.15.7.11.17 [[subgroup]] interpretation.

	~~389edo has two mappings for 3, which makes it a [[dual-fifth system]]. The best approach to this tuning is through a 2.5.7.11.17 subgroup.~~		=== Odd harmonics ===
	=== ~~Relation to a calendar reform~~ ===		{{Harmonics in equal\|389}}
	~~389edo represents the '''north solstice''' (summer~~ in the northern hemisphere) '''leap year cycle 69/389''' as devised by Sym454 inventor Irvin Bromberg. The outcome scale uses 327\389, or 62\389 as its generator. The solstice leap day scale with 94 notes uses 269\389 ~~as a generator. Since this is a maximum evenness scale, temperament can be generated by simply merging the numerator and the denominator.~~

	==== Solstice ~~Leap Day~~ (94 & 295) ====		=== Subsets and supersets ===
			389edo is the 77th [[prime edo]].

			=== Miscelleneous properties ===
			389edo represents the ''north solstice'' (summer in the northern hemisphere) ''leap year cycle 69/389'' as devised by Sym454 inventor Irvin Bromberg. The outcome scale uses 327\389, or 62\389 as its generator. The solstice leap day scale with 94 notes uses 269\389 as a generator. Since this is a [[maximal evenness]] scale, temperament can be generated by simply merging the numerator and the denominator.

			==== Solstice leap day (94 & 295) ====
	295 seems to precede 389.		295 seems to precede 389.

Line 20:		Line 25:
	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|Subgroup		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	8ve ~~stretch~~ (¢)		! colspan="2" \| Tuning Error
	! colspan="2" \|Tuning ~~error~~
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|20 -17 3}}, {{monzo\|-39 -12 25}}		\| {{monzo\| 20 -17 3 }}, {{monzo\| -39 -12 25 }}
	\|[{{~~val~~\|389 617 903}}]		\| {{mapping\| 389 617 903 }}
	\| -0.19		\| -0.19
	\|0.500		\| 0.500
	\|16.2		\| 16.2
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|2109375/2097152, {{monzo\|-7, 44, -27}}		\| 2109375/2097152, {{monzo\|-7 44 -27 }}
	\|[{{~~val~~\|389 616 903}}] (389b)		\| {{mapping\| 389 616 903 }} (389b)
	\|0.46		\| 0.46
	\|0.451		\| 0.451
	\|14.6		\| 14.6
	\|-		\|-
	\|2.5.7		\| 2.5.7
	\|2100875/2097152, {{monzo\|0, 52, -43}}		\| 2100875/2097152, {{monzo\| 0 52 -43 }}
	\|[{{~~val~~\|389 903 1092}}]		\| {{mapping\| 389 903 1092 }}
	\|0.12		\| 0.12
	\|0.131		\| 0.131
	\|4.2		\| 4.2
	\|-		\|-
	\|2.5.7.11.17		\| 2.5.7.11.17
	\|6664/6655, 156250/155771, 180625/180224, 184960/184877		\| 6664/6655, 156250/155771, 180625/180224, 184960/184877
	\|[{{~~val~~\|389 903 1092 1346 1590}}]		\| {{mapping\| 389 903 1092 1346 1590 }}
	\|0.03		\| 0.03
	\|0.177		\| 0.177
	\|5.7		\| 5.7
	\|}		\|}

	== Scales ==		== Scales ==
	* Solstice[69]		* Solstice[69]
	* SolsticeDay[94]		* SolsticeDay[94]

	~~== Links ==~~
	~~https://individual.utoronto.ca/kalendis/leap/index.htm#mod~~

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~

Plumtree: Infobox ET added

2022-10-04T21:54:02Z

Infobox ET added

← Older revision		Revision as of 21:54, 4 October 2022
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			{{Infobox ET}}
	'''389edo''' divides the octave into parts of 3.0848c each.		'''389edo''' divides the octave into parts of 3.0848c each.

Fredg999 category edits: Categories

2022-07-03T21:44:29Z

Eliora: /* Theory */

2022-03-14T19:38:28Z

Theory

← Older revision		Revision as of 19:38, 14 March 2022
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	389edo has two mappings for 3, which makes it a [[dual-fifth system]]. The best approach to this tuning is through a 2.5.7.11.17 subgroup.		389edo has two mappings for 3, which makes it a [[dual-fifth system]]. The best approach to this tuning is through a 2.5.7.11.17 subgroup.
	=== Relation to a calendar reform ===		=== Relation to a calendar reform ===
	389edo represents the '''north solstice''' (summer in the northern hemisphere) '''leap year cycle 69/389''' as devised by Sym454 inventor Irvin Bromberg.		389edo represents the '''north solstice''' (summer in the northern hemisphere) '''leap year cycle 69/389''' as devised by Sym454 inventor Irvin Bromberg. The outcome scale uses 327\389, or 62\389 as its generator. The solstice leap day scale with 94 notes uses 269\389 as a generator. Since this is a maximum evenness scale, temperament can be generated by simply merging the numerator and the denominator.

	~~The outcome scale uses 327\~~389~~, or 62\389 as its generator~~.		==== Solstice Leap Day (94 & 295) ====
			295 seems to precede 389.

	~~The solstice leap day scale with 94 notes uses 269\389 as a~~ generator.		Subgroup: 2.5.7.11.17

			POTE generator: 370.1796c

			Comma list: 250000/248897, 2100875/2097152, 4096000/4092529

	== Regular temperament properties ==		== Regular temperament properties ==

Eliora: /* Regular temperament properties */

2022-03-14T16:38:49Z

Regular temperament properties

← Older revision		Revision as of 16:38, 14 March 2022
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	\|0.131		\|0.131
	\|4.2		\|4.2
			\|-
			\|2.5.7.11.17
			\|6664/6655, 156250/155771, 180625/180224, 184960/184877
			\|[{{val\|389 903 1092 1346 1590}}]
			\|0.03
			\|0.177
			\|5.7
	\|}		\|}
	== Scales ==		== Scales ==

Eliora: /* Regular temperament properties */

2022-03-13T19:11:55Z

Regular temperament properties

← Older revision		Revision as of 19:11, 13 March 2022
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	\|2.3.5		\|2.3.5
	\|2109375/2097152, {{monzo\|-7, 44, -27}}		\|2109375/2097152, {{monzo\|-7, 44, -27}}
	\|[{{val\|389 616 903}}]		\|[{{val\|389 616 903}}] (389b)
	\|0.46		\|0.46
	\|0.451		\|0.451

Eliora: /* Theory */

2022-03-13T19:11:13Z

Theory

@@ Line 2: / Line 2: @@
 == Theory ==
-{{Primes in edo|389|columns=13}}
+{{Primes in edo|389|columns=8}}
-The best subgroup for 389edo is 7.17.31.41.
 === Relation to a calendar reform ===
 edo represents the '''north solstice''' (summer in the northern hemisphere) '''leap year cycle 69/389''' as devised by Sym454 inventor Irvin Bromberg.
 The outcome scale uses 327\389, or 62\389 as its generator.
 == Scales ==

Eliora: /* Theory */

2021-11-23T10:55:53Z

Theory

← Older revision		Revision as of 10:55, 23 November 2021
Line 2:		Line 2:

	== Theory ==		== Theory ==
	{{Primes in edo\|389}}		{{Primes in edo\|389\|columns=13}}
			The best subgroup for 389edo is 7.17.31.41.
	=== Relation to a calendar reform ===		=== Relation to a calendar reform ===
	389edo represents the '''north solstice''' (summer in the northern hemisphere) '''leap year cycle 69/389''' as devised by Sym454 inventor Irvin Bromberg.		389edo represents the '''north solstice''' (summer in the northern hemisphere) '''leap year cycle 69/389''' as devised by Sym454 inventor Irvin Bromberg.

Eliora: /* Theory */ repaired template

2021-11-23T10:54:41Z

Theory: repaired template

← Older revision		Revision as of 10:54, 23 November 2021
Line 2:		Line 2:

	== Theory ==		== Theory ==
	{{Primes in edo\|389=}}		{{Primes in edo\|389}}

	=== Relation to a calendar reform ===		=== Relation to a calendar reform ===

← Older revision		Revision as of 21:44, 3 July 2022
Line 1:		Line 1:
	389edo, divides the octave into parts of 3.0848c each.		'''389edo''' divides the octave into parts of 3.0848c each.

	== Theory ==		== Theory ==
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	\|}		\|}
	== Scales ==		== Scales ==

	* Solstice[69]		* Solstice[69]
	* SolsticeDay[94]		* SolsticeDay[94]
Line 64:		Line 63:
	== Links ==		== Links ==
	https://individual.utoronto.ca/kalendis/leap/index.htm#mod		https://individual.utoronto.ca/kalendis/leap/index.htm#mod

			[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->