541edo - Revision history

ArrowHead294 at 17:38, 20 February 2025

2025-02-20T17:38:29Z

← Older revision		Revision as of 17:38, 20 February 2025
Line 13:		Line 13:
	== 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]]
Line 25:		Line 26:
	\| {{monzo\| 1715 -541 }}		\| {{monzo\| 1715 -541 }}
	\| {{mapping\| 541 1715 }}		\| {{mapping\| 541 1715 }}
	\| -0.0247		\| −0.0247
	\| 0.0247		\| 0.0247
	\| 1.11		\| 1.11
Line 39:		Line 40:
	\| 40500000/40353607, 43046721/43025920, 95703125/95551488		\| 40500000/40353607, 43046721/43025920, 95703125/95551488
	\| {{mapping\| 541 1715 1256 1519 }}		\| {{mapping\| 541 1715 1256 1519 }}
	\| -0.0171		\| −0.0171
	\| 0.1184		\| 0.1184
	\| 5.34		\| 5.34
Line 46:		Line 47:
	\| 4096/4095, 10985/10976, 2734375/2729376, 11390625/11361532		\| 4096/4095, 10985/10976, 2734375/2729376, 11390625/11361532
	\| {{mapping\| 541 1715 1256 1519 2002 }}		\| {{mapping\| 541 1715 1256 1519 2002 }}
	\| -0.0211		\| −0.0211
	\| 0.1062		\| 0.1062
	\| 4.79		\| 4.79
	\|}		\|}

Francium: changed EDO intro to ED intro

2025-02-20T17:19:24Z

changed EDO intro to ED intro

← Older revision		Revision as of 17:19, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|541~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Review

2024-01-01T10:06:33Z

Review

← Older revision		Revision as of 10:06, 1 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	541et is only consistent to the [[5-odd-limit]] and the [[harmonic]] 3 is about halfway between its steps. It has a reasonable approximation to the 2.9.5.7~~.11~~.13 [[subgroup]].		541et is only [[consistent]] to the [[5-odd-limit]] and the [[harmonic]] [[3/1\|3]] is about halfway between its steps. It has a reasonable approximation to the 2.9.5.7.13 [[subgroup]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	541edo is the 100th [[prime ~~EDO~~]]. [[1082edo]], which doubles it, gives a good correction to the harmonic 3.		541edo is the 100th [[prime edo]]. [[1082edo]], which doubles it, gives a good correction to the harmonic 3.

	== 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\|1715 -541}}		\| {{monzo\| 1715 -541 }}
	\|{{mapping\|541 1715}}		\| {{mapping\| 541 1715 }}
	\| -0.0247		\| -0.0247
	\| 0.0247		\| 0.0247
	\| 1.11		\| 1.11
	\|-		\|-
	\|2.9.5		\| 2.9.5
	\|{{monzo\|-20 -12 25}}, {{monzo\|63 -25 7}}		\| {{monzo\| -20 -12 25 }}, {{monzo\| 63 -25 7 }}
	\|{{mapping\|541 1715 1256}}		\| {{mapping\| 541 1715 1256 }}
	\| +0.0355		\| +0.0355
	\| 0.0874		\| 0.0874
	\| 3.94		\| 3.94
	\|-		\|-
	\|2.9.5.7		\| 2.9.5.7
	\|~~95703125~~/~~95551488~~, 43046721/43025920, ~~1280000000~~/~~1275989841~~		\| 40500000/40353607, 43046721/43025920, 95703125/95551488
	\|{{mapping\|541 1715 1256 1519}}		\| {{mapping\| 541 1715 1256 1519 }}
	\| -0.0171		\| -0.0171
	\| 0.1184		\| 0.1184
	\| 5.34		\| 5.34
	\|-		\|-
	\|2.9.5.7~~.11~~		\| 2.9.5.7.13
	~~\|6250/6237, 496125/495616, 46656/46585, 275653125/275365888~~		\| 4096/4095, 10985/10976, 2734375/2729376, 11390625/11361532
	~~\|{{mapping\|541 1715 1256 1519 1872}}~~		\| {{mapping\| 541 1715 1256 1519 2002 }}
	~~\| -0.0710~~		\| -0.0211
	~~\| 0.1512~~		\| 0.1062
	~~\| 6.82~~		\| 4.79
	\|-
	~~\|2.9.5.7.11~~.13
	\|~~1575/1573,~~ 4096/4095, ~~6250~~/~~6237~~, ~~67392~~/~~67375~~, ~~3247695~~/~~3246152~~
	\|{{mapping\|541 1715 1256 1519 ~~1872~~ 2002}}
	\| -0.~~0654~~
	\| 0.~~1386~~
	\| 6.25
	\|}		\|}

Francium: /* Theory */ typo

2023-12-20T15:05:42Z

Theory: typo

← Older revision		Revision as of 15:05, 20 December 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	541et is only consistent to the [[5-odd-limit]] and the [[harmonic]] 3 is about halfway between ~~ist~~ steps. It has a reasonable approximation to the 2.9.5.7.11.13 [[subgroup]].		541et is only consistent to the [[5-odd-limit]] and the [[harmonic]] 3 is about halfway between its steps. It has a reasonable approximation to the 2.9.5.7.11.13 [[subgroup]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	541edo is the 100th [[prime EDO]]. [[1082edo]], which doubles it, gives a good correction to the harmonic 3.		541edo is the 100th [[prime EDO]]. [[1082edo]], which doubles it, gives a good correction to the harmonic 3.

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

Francium at 14:57, 20 December 2023

2023-12-20T14:57:44Z

← Older revision		Revision as of 14:57, 20 December 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	541et is only consistent to the [[5-odd-limit]] and the [[harmonic 3]] is about halfway between ist steps. It has a reasonable approximation to the 2.9.5.7.11.13 [[subgroup]].		541et is only consistent to the [[5-odd-limit]] and the [[harmonic]] 3 is about halfway between ist steps. It has a reasonable approximation to the 2.9.5.7.11.13 [[subgroup]].

	=== Odd harmonics ===		=== Odd harmonics ===

Francium at 14:55, 20 December 2023

2023-12-20T14:55:45Z

← Older revision		Revision as of 14:55, 20 December 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro}}		{{EDO intro\|541}}

	== Theory ==		== Theory ==

Francium: Created page with "{{Infobox ET}} {{EDO intro}} == Theory == 541et is only consistent to the 5-odd-limit and the harmonic 3 is about halfway between ist steps. It has a reasonable appro..."

2023-12-20T14:55:25Z

Created page with "{{Infobox ET}} {{EDO intro}} == Theory == 541et is only consistent to the 5-odd-limit and the harmonic 3 is about halfway between ist steps. It has a reasonable appro..."

New page

{{Infobox ET}}
{{EDO intro}}

== Theory ==
541et is only consistent to the [[5-odd-limit]] and the [[harmonic 3]] is about halfway between ist steps. It has a reasonable approximation to the 2.9.5.7.11.13 [[subgroup]].

=== Odd harmonics ===
{{Harmonics in equal|541}}

=== Subsets and supersets ===
541edo is the 100th [[prime EDO]]. [[1082edo]], which doubles it, gives a good correction to the harmonic 3.

== 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|1715 -541}}
|{{mapping|541 1715}}
| -0.0247
| 0.0247
| 1.11
|-
|2.9.5
|{{monzo|-20 -12 25}}, {{monzo|63 -25 7}}
|{{mapping|541 1715 1256}}
| +0.0355
| 0.0874
| 3.94
|-
|2.9.5.7
|95703125/95551488, 43046721/43025920, 1280000000/1275989841
|{{mapping|541 1715 1256 1519}}
| -0.0171
| 0.1184
| 5.34
|-
|2.9.5.7.11
|6250/6237, 496125/495616, 46656/46585, 275653125/275365888
|{{mapping|541 1715 1256 1519 1872}}
| -0.0710
| 0.1512
| 6.82
|-
|2.9.5.7.11.13
|1575/1573, 4096/4095, 6250/6237, 67392/67375, 3247695/3246152
|{{mapping|541 1715 1256 1519 1872 2002}}
| -0.0654
| 0.1386
| 6.25
|}