743edo - Revision history

Francium: +music

2025-03-03T12:24:35Z

+music

← Older revision		Revision as of 12:24, 3 March 2025
Line 65:		Line 65:
	\| 5.86		\| 5.86
	\|}		\|}

			== Music ==
			; [[Francium]]
			* "focus" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/4dAsGgZMItvNjGeDBGFicY Spotify] \| [https://francium223.bandcamp.com/track/focus Bandcamp] \| [https://www.youtube.com/watch?v=qN2UjaCQZno YouTube]

ArrowHead294 at 13:01, 21 February 2025

2025-02-21T13:01:58Z

← Older revision		Revision as of 13:01, 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\|-2355 743}}		\| {{monzo\|-2355 743}}
	\| {{mapping\|743 2355}}		\| {{mapping\|743 2355}}
	\| 0.0648		\| +0.0648
	\| 0.0648		\| 0.0648
	\| 4.01		\| 4.01
Line 32:		Line 33:
	\| 32805/32768, {{monzo\|-120 -83 165}}		\| 32805/32768, {{monzo\|-120 -83 165}}
	\| {{mapping\|743 2355 1725}}		\| {{mapping\|743 2355 1725}}
	\| 0.0878		\| +0.0878
	\| 0.0621		\| 0.0621
	\| 3.85		\| 3.85
Line 39:		Line 40:
	\| 32805/32768, 30517578125/30474952704, 247669456896/247165842875		\| 32805/32768, 30517578125/30474952704, 247669456896/247165842875
	\| {{mapping\|743 2355 1725 2086}}		\| {{mapping\|743 2355 1725 2086}}
	\| 0.0464		\| +0.0464
	\| 0.0897		\| 0.0897
	\| 5.55		\| 5.55
Line 46:		Line 47:
	\| 32805/32768, 1890625/1889568, 539055/537824, 102487/102400		\| 32805/32768, 1890625/1889568, 539055/537824, 102487/102400
	\| {{mapping\|743 2355 1725 2086 2570}}		\| {{mapping\|743 2355 1725 2086 2570}}
	\| 0.0705		\| +0.0705
	\| 0.0936		\| 0.0936
	\| 5.80		\| 5.80
Line 53:		Line 54:
	\| 67392/67375, 35750/35721, 32805/32768, 91125/91091, 557568/557375		\| 67392/67375, 35750/35721, 32805/32768, 91125/91091, 557568/557375
	\| {{mapping\|743 2355 1725 2086 2570 2749}}		\| {{mapping\|743 2355 1725 2086 2570 2749}}
	\| 0.0898		\| +0.0898
	\| 0.0957		\| 0.0957
	\| 5.93		\| 5.93
Line 60:		Line 61:
	\| 1089/1088, 67392/67375, 35750/35721, 14400/14399, 61965/61952, 75735/75712		\| 1089/1088, 67392/67375, 35750/35721, 14400/14399, 61965/61952, 75735/75712
	\| {{mapping\|743 2355 1725 2086 2570 2749 3037}}		\| {{mapping\|743 2355 1725 2086 2570 2749 3037}}
	\| 0.0761		\| +0.0761
	\| 0.0947		\| 0.0947
	\| 5.86		\| 5.86
	\|}		\|}

Francium: changed EDO intro to ED intro

2025-02-21T05:49:30Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:49, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|743~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: Created page with "{{Infobox ET}} {{EDO intro|743}} == Theory == 743et is only consistent to the 3-odd-limit and its harmonic 3 is about halfway its steps. It can be used in the..."

2024-12-26T19:32:14Z

Created page with "{{Infobox ET}} {{EDO intro|743}} == Theory == 743et is only consistent to the 3-odd-limit and its harmonic 3 is about halfway its steps. It can be used in the..."

New page

{{Infobox ET}}
{{EDO intro|743}}

== Theory ==
743et is only consistent to the [[3-odd-limit]] and its [[harmonic]] [[3/1|3]] is about halfway its steps. It can be used in the 2.9.5.7.11.13.17.19.23.29 [[subgroup]], [[tempering out]] [[2025/2024]], [[1089/1088]], 67392/67375, 35750/35721, [[14400/14399]], 15840/15827, 3520/3519, [[1521/1520]] and 2465/2464.

=== Odd harmonics ===
{{Harmonics in equal|743}}

=== Subsets and supersets ===
743edo is the 132nd [[prime edo]]. [[1486edo]], 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|-2355 743}}
| {{mapping|743 2355}}
| 0.0648
| 0.0648
| 4.01
|-
| 2.9.5
| 32805/32768, {{monzo|-120 -83 165}}
| {{mapping|743 2355 1725}}
| 0.0878
| 0.0621
| 3.85
|-
| 2.9.5.7
| 32805/32768, 30517578125/30474952704, 247669456896/247165842875
| {{mapping|743 2355 1725 2086}}
| 0.0464
| 0.0897
| 5.55
|-
| 2.9.5.7.11
| 32805/32768, 1890625/1889568, 539055/537824, 102487/102400
| {{mapping|743 2355 1725 2086 2570}}
| 0.0705
| 0.0936
| 5.80
|-
| 2.9.5.7.11.13
| 67392/67375, 35750/35721, 32805/32768, 91125/91091, 557568/557375
| {{mapping|743 2355 1725 2086 2570 2749}}
| 0.0898
| 0.0957
| 5.93
|-
| 2.9.5.7.11.13.17
| 1089/1088, 67392/67375, 35750/35721, 14400/14399, 61965/61952, 75735/75712
| {{mapping|743 2355 1725 2086 2570 2749 3037}}
| 0.0761
| 0.0947
| 5.86
|}