613edo - Revision history

ArrowHead294 at 13:19, 21 February 2025

2025-02-21T13:19:11Z

← Older revision		Revision as of 13:19, 21 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" \|[[Comma list~~\|Comma List~~]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \|Optimal<br>8ve ~~Stretch~~ (¢)		! rowspan="2" \| [[Mapping]]
	! colspan="2" \|Tuning ~~Error~~		! rowspan="2" \| Optimal<br />8ve stretch (¢)
	\|-		! colspan="2" \| Tuning error
	![[TE error\|Absolute]] (¢)		\|-
	![[TE simple badness\|Relative]] (%)		! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.9		\| 2.9
	\| {{monzo\|-1943 613}}		\| {{monzo\|-1943 613}}
	\| {{mapping\|613 1943}}		\| {{mapping\|613 1943}}
	\| 0.0506		\| +0.0506
	\| 0.0506		\| 0.0506
	\| 2.58		\| 2.58
Line 32:		Line 33:
	\| 32805/32768, {{monzo\|-97 -69 136}}		\| 32805/32768, {{monzo\|-97 -69 136}}
	\| {{mapping\|613 1943 1423}}		\| {{mapping\|613 1943 1423}}
	\| 0.1299		\| +0.1299
	\| 0.1194		\| 0.1194
	\| 6.10		\| 6.10
Line 39:		Line 40:
	\| 32805/32768, 40500000/40353607, {{monzo\|-23 -7 11 7}}		\| 32805/32768, 40500000/40353607, {{monzo\|-23 -7 11 7}}
	\| {{mapping\|613 1943 1423 1721}}		\| {{mapping\|613 1943 1423 1721}}
	\| 0.0814		\| +0.0814
	\| 0.1331		\| 0.1331
	\| 6.80		\| 6.80

Francium: changed EDO intro to ED intro

2025-02-21T05:37:45Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:37, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|613~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: +music

2024-07-19T12:20:53Z

+music

← Older revision		Revision as of 12:20, 19 July 2024
Line 43:		Line 43:
	\| 6.80		\| 6.80
	\|}		\|}

			== Music ==
			; [[Francium]]
			* "Donut" from ''You Are A...'' (2024) – [https://open.spotify.com/track/4vYmtSdt7sU38eYIeUYFf1 Spotify] \| [https://francium223.bandcamp.com/track/donut Bandcamp] \| [https://www.youtube.com/watch?v=QhAI2F4taxU YouTube] – porcupinefish[15] in 613edo tuning

Francium: Created page with "{{Infobox ET}} {{EDO intro|613}} == Theory == 613edo is only consistent to the 3-odd-limit and the harmonic 3 is about halfway its steps. It can be used i..."

2024-06-06T17:18:31Z

Created page with "{{Infobox ET}} {{EDO intro|613}} == Theory == 613edo is only consistent to the 3-odd-limit and the harmonic 3 is about halfway its steps. It can be used i..."

New page

{{Infobox ET}}
{{EDO intro|613}}

== Theory ==
613edo is only [[consistent]] to the [[3-odd-limit]] and the [[harmonic]] [[3/1|3]] is about halfway its steps. It can be used in the 2.9.5.7.13.19.23.29.31.37 [[subgroup]], [[tempering out]] [[1521/1520]], [[875/874]], [[1863/1862]], 38475/38416, 2205/2204, 1520/1519, 186875/186624, 1665/1664 and 194560/194481.

=== Odd harmonics ===
{{Harmonics in equal|613}}

=== Subsets and supersets ===
613edo is the 112th [[prime EDO]]. [[1226edo]], 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|-1943 613}}
| {{mapping|613 1943}}
| 0.0506
| 0.0506
| 2.58
|-
| 2.9.5
| 32805/32768, {{monzo|-97 -69 136}}
| {{mapping|613 1943 1423}}
| 0.1299
| 0.1194
| 6.10
|-
| 2.9.5.7
| 32805/32768, 40500000/40353607, {{monzo|-23 -7 11 7}}
| {{mapping|613 1943 1423 1721}}
| 0.0814
| 0.1331
| 6.80
|}