589edo - Revision history

ArrowHead294 at 12:22, 21 February 2025

2025-02-21T12:22:40Z

← Older revision		Revision as of 12:22, 21 February 2025
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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]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve ~~Stretch~~ (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning ~~Error~~		! colspan="2" \| Tuning error
	\|-		\|-
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
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	\| {{monzo\| -37 19 -10 }}, {{monzo\| 72 0 -31 }}		\| {{monzo\| -37 19 -10 }}, {{monzo\| 72 0 -31 }}
	\| {{mapping\| 589 1867 1368 }}		\| {{mapping\| 589 1867 1368 }}
	\| -0.0940		\| −0.0940
	\| 0.1734		\| 0.1734
	\| 8.51		\| 8.51

Francium: changed EDO intro to ED intro

2025-02-21T06:18:09Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:18, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|589~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T13:30:09Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 13:30, 2 November 2023
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	589 factors into ~~19 × 31 with subset edos~~ {{~~EDOs~~\| 19, and ~~31 }}~~. [[1178edo]], which doubles it, gives good corrections to harmonics 3, 5, 7, 11, 13, and 17.		Since 589 factors into {{factorization\|589}}, 589edo contains [[19edo]] and [[31edo]] as subsets. [[1178edo]], which doubles it, gives good corrections to harmonics 3, 5, 7, 11, 13, and 17.

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

Eliora: /* Subsets and supersets */

2023-10-26T17:08:40Z

Subsets and supersets

← Older revision		Revision as of 17:08, 26 October 2023
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	589 factors into 19 × 31 with subset edos {{EDOs\| 19, and 31 }}. 1178edo, which doubles it, gives good corrections to harmonics 3, 5, 7, 11, 13, and 17.		589 factors into 19 × 31 with subset edos {{EDOs\| 19, and 31 }}. [[1178edo]], which doubles it, gives good corrections to harmonics 3, 5, 7, 11, 13, and 17.

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

FloraC: Rework

2023-10-25T09:40:41Z

Rework

← Older revision		Revision as of 09:40, 25 October 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|589}}		{{EDO intro\|589}}

	== Theory ==		== Theory ==
	~~589et~~ tempers out 420175/419904 in the 7-limit; ~~55296000~~/~~55240493~~, 117649/117612, ~~107495424~~/~~107421875~~, ~~[[1953125~~/~~1948617]]~~, ~~4302592~~/~~4296875~~, ~~85937500~~/~~85766121, 422576/421875~~, [[~~3025~~/~~3024~~]], ~~766656~~/~~765625~~, ~~456533~~/~~455625~~, ~~3294225~~/~~3294172~~, ~~644204~~/~~643125~~ and 781258401/781250000 in the 11-limit.		589edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]] [[3/1\|3]] is about halfway between its steps. As every other step of [[1178edo]], the approximations to lower harmonics are not impressive, making it only suitable for a 2.9.15.21.19 [[subgroup]] interpretation, in which case it is identical to 1178edo. The full 17-limit [[patent val]], however, is plausible since all the harmonics from 3 to 17 are tuned sharp. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] 420175/419904 in the 7-limit; [[3025/3024]], 117649/117612, 422576/421875, 456533/455625, 644204/643125, 766656/765625, [[1953125/1948617]], 3294225/3294172, 4302592/4296875, 55296000/55240493, 85937500/85766121, 107495424/107421875 and 781258401/781250000 in the 11-limit.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|589}}		{{Harmonics in equal\|589}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	589 factors into 19 × 31 with subset edos {{EDOs\| 19, and 31}}. [[1178edo]], which doubles it, gives a good ~~correction~~ to ~~the 3rd harmonic~~.		589 factors into 19 × 31 with subset edos {{EDOs\| 19, and 31 }}. 1178edo, which doubles it, gives good corrections to harmonics 3, 5, 7, 11, 13, and 17.

	== 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]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \|Tuning Error		! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.9		\| 2.9
	\|{{monzo\|-1867 589}}		\| {{monzo\| -1867 589 }}
	\|{{~~val~~\|589 1867}}		\| {{mapping\| 589 1867 }}
	\| +0.0276		\| +0.0276
	\| 0.0276		\| 0.0276
	\| 1.35		\| 1.35
	\|-		\|-
	\|2.9.5		\| 2.9.5
	\|{{monzo\|-37 19 -10}}, {{monzo\|72 0 -31}}		\| {{monzo\| -37 19 -10 }}, {{monzo\| 72 0 -31 }}
	\|{{~~val~~\|589 1867 1368}}		\| {{mapping\| 589 1867 1368 }}
	\| -0.0940		\| -0.0940
	\| 0.1734		\| 0.1734
	\| 8.51		\| 8.51
	\|}		\|}

	== Scales ==		== Scales ==
	* [[Kryptonite10]]		* [[Kryptonite10]]
	* [[Kryptonite19]]		* [[Kryptonite19]]

Francium: Created page with "{{Infobox ET}} {{EDO intro|589}} == Theory == 589et tempers out 420175/419904 in the 7-limit; 55296000/55240493, 117649/117612, 107495424/107421875, 1953125/1948617, 43025..."

2023-09-30T20:30:50Z

Created page with "{{Infobox ET}} {{EDO intro|589}} == Theory == 589et tempers out 420175/419904 in the 7-limit; 55296000/55240493, 117649/117612, 107495424/107421875, 1953125/1948617, 43025..."

New page

{{Infobox ET}}
{{EDO intro|589}}
== Theory ==
589et tempers out 420175/419904 in the 7-limit; 55296000/55240493, 117649/117612, 107495424/107421875, [[1953125/1948617]], 4302592/4296875, 85937500/85766121, 422576/421875, [[3025/3024]], 766656/765625, 456533/455625, 3294225/3294172, 644204/643125 and 781258401/781250000 in the 11-limit.
=== Odd harmonics ===
{{Harmonics in equal|589}}
=== Subsets and supersets ===
589 factors into 19 × 31 with subset edos {{EDOs| 19, and 31}}. [[1178edo]], which doubles it, gives a good correction to the 3rd harmonic.
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.9
|{{monzo|-1867 589}}
|{{val|589 1867}}
| +0.0276
| 0.0276
| 1.35
|-
|2.9.5
|{{monzo|-37 19 -10}}, {{monzo|72 0 -31}}
|{{val|589 1867 1368}}
| -0.0940
| 0.1734
| 8.51
|}
== Scales ==
* [[Kryptonite10]]
* [[Kryptonite19]]