44th-octave temperaments - Revision history

ArrowHead294 at 03:43, 14 February 2025

2025-02-14T03:43:42Z

← Older revision		Revision as of 03:43, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|44}}		{{Infobox fractional-octave\|44}}
	One step of [[44edo]] is extremely close to the septimal comma, [[64/63]]. The relationship is preserved even up tens of thousands of edos.		One step of [[44edo]] is extremely close to the septimal comma, [[64/63]]. The relationship is preserved even up tens of thousands of edos.

BudjarnLambeth: Navbox

2024-12-05T07:33:11Z

Navbox

← Older revision		Revision as of 07:33, 5 December 2024
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	Badness: 0.0396		Badness: 0.0396

			{{Navbox fractional-octave}}

	[[Category:44edo]]		[[Category:44edo]]
	~~[[Category:Temperament collections]]~~

Recentlymaterialized at 18:25, 16 May 2024

2024-05-16T18:25:01Z

← Older revision		Revision as of 18:25, 16 May 2024
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	{{Fractional-octave navigation\|44}}		{{Fractional-octave navigation\|44}}
	One step of 44edo is extremely close to the septimal comma, [[64/63]]. The relationship is preserved even up tens of thousands of edos.		One step of [[44edo]] is extremely close to the septimal comma, [[64/63]]. The relationship is preserved even up tens of thousands of edos.

	== Septiruthenic ==		== Septiruthenic ==

BudjarnLambeth: Fixed typo

2024-01-26T11:46:23Z

Fixed typo

← Older revision		Revision as of 11:46, 26 January 2024
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	{{Fractional-octave navigation\|44}}		{{Fractional-octave navigation\|44}}
	One step of 44edo is extremely close to the septimal comma, [[64/63]]. The relationship is preserved even up tens thousands of edos.		One step of 44edo is extremely close to the septimal comma, [[64/63]]. The relationship is preserved even up tens of thousands of edos.

	== Septiruthenic ==		== Septiruthenic ==

Eliora at 23:22, 10 July 2023

2023-07-10T23:22:33Z

← Older revision		Revision as of 23:22, 10 July 2023
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			{{Fractional-octave navigation\|44}}
	One step of 44edo is extremely close to the septimal comma, [[64/63]]. The relationship is preserved even up tens thousands of edos.		One step of 44edo is extremely close to the septimal comma, [[64/63]]. The relationship is preserved even up tens thousands of edos.

Eliora: /* Septiruthenian */

2023-06-15T14:32:44Z

Septiruthenian

← Older revision		Revision as of 14:32, 15 June 2023
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	One step of 44edo is extremely close to the septimal comma, [[64/63]]. The relationship is preserved even up tens thousands of edos.		One step of 44edo is extremely close to the septimal comma, [[64/63]]. The relationship is preserved even up tens thousands of edos.

	== ~~Septiruthenian~~ ==		== Septiruthenic ==
	{{Main\|Septiruthenia}}		{{Main\|Septiruthenia}}
	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
Line 14:		Line 14:

	[[Badness]]: 116 × 10<sup>-3</sup>		[[Badness]]: 116 × 10<sup>-3</sup>

			=== Septiruthenian ===
			Subgroup: 2.3.7

			Comma list: {{monzo\| -263 88 44 }}

			[[Mapping]]: [{{val\| 44 0 263 }}, {{val\| 0 1 -2 }}]

			Mapping generators: ~64/63, ~3

	== Ruthenium ==		== Ruthenium ==

Eliora at 14:27, 15 June 2023

2023-06-15T14:27:40Z

@@ Line 1: / Line 1: @@
 One step of 44edo is extremely close to the septimal comma, [[64/63]]. The relationship is preserved even up tens thousands of edos.
-===Ruthenium===
+== Septiruthenian ==
-Ruthenium is named after the 44th element, and can be expressed as the 1848 & 2684 temperament.
+{{Main|Septiruthenia}}
 [[Subgroup]]: 2.3.5.7
@@ Line 41: / Line 55: @@
 Badness: 0.0396

Eliora: setting up new pages for my improvement of fractional-octave temperaments I'm about to do

2023-06-15T13:51:26Z

setting up new pages for my improvement of fractional-octave temperaments I'm about to do

New page

One step of 44edo is extremely close to the septimal comma, [[64/63]]. The relationship is preserved even up tens thousands of edos.

===Ruthenium===
Ruthenium is named after the 44th element, and can be expressed as the 1848 & 2684 temperament.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: {{monzo| -8 23 -5 -6 }}, {{monzo| 51 -13 -1 -10 }}

[[Mapping]]: [{{val| 44 0 -386 263 }}, {{val| 0 1 7 -2 }}]

Mapping generators: ~64/63, ~3

[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.9420

{{Optimal ET sequence|legend=1| 176, 660, 836, 1848, 2684, 4532, 19976, 24508, 29040, 33572 }}

[[Badness]]: 0.111
====11-limit====
Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 1771561/1771470, 67110351/67108864

Mapping: [{{val| 44 0 -386 263 -57 }}, {{val| 0 1 7 -2 3 }}]

Optimal tuning (CTE): ~3/2 = 701.9429

Optiml GPV sequence: {{Optimal ET sequence| 176, 660, 836, 1848, 2684, 4532, 15444, 19976e }}

Badness: 0.0209
====13-limit====
Subgroup: 2.3.5.7.11.13

Comma list: 9801/9800, 196625/196608, 823680/823543, 1771561/1771470

Mapping: [{{val| 44 0 -386 263 -57 1976 }}, {{val| 0 1 7 -2 3 -26 }}]

Optimal tuning (CTE): ~3/2 = 701.939

Optiml GPV sequence: {{Optimal ET sequence| 836, 1848, 2684, 7216, 9900, 12584 }}

Badness: 0.0396