691edo - Revision history

ArrowHead294 at 13:07, 21 February 2025

2025-02-21T13:07:29Z

← Older revision		Revision as of 13:07, 21 February 2025
Line 15:		Line 15:
	== 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]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\|-1095 691}}		\| {{monzo\|-1095 691}}
	\| {{mapping\|691 1095}}		\| {{mapping\|691 1095}}
	\| 0.1145		\| +0.1145
	\| 0.1146		\| 0.1146
	\| 6.60		\| 6.60
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	\| {{monzo\|-51 19 9}}, {{monzo\|-20 -24 25}}		\| {{monzo\|-51 19 9}}, {{monzo\|-20 -24 25}}
	\| {{mapping\|691 1095 1604}}		\| {{mapping\|691 1095 1604}}
	\| 0.1891		\| +0.1891
	\| 0.1410		\| 0.1410
	\| 8.12		\| 8.12

Francium: changed EDO intro to ED intro

2025-02-21T05:44:02Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:44, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|691~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: +music

2024-11-16T17:55:53Z

+music

← Older revision		Revision as of 17:55, 16 November 2024
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	\| 8.12		\| 8.12
	\|}		\|}

			== Music ==
			; [[Francium]]
			* "Caneelines and Porks" from ''Scoop'' (2024) – [https://open.spotify.com/track/2MKhJxCb5HldODGFx5IOpQ Spotify] \| [https://francium223.bandcamp.com/track/caneelines-and-porks Bandcamp] \| [https://www.youtube.com/watch?v=NJMCFiQmW2U YouTube]

FloraC: /* Theory */ certainly not prime 7

2024-09-28T09:27:40Z

Theory: certainly not prime 7

← Older revision		Revision as of 09:27, 28 September 2024
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	691edo is the 125th [[prime ~~EDO~~]]. [[2764edo]], which quadruples it, gives a good correction to ~~the harmonic 7~~.		691edo is the 125th [[prime edo]]. [[2764edo]], which quadruples it, gives a good correction to a number of lower harmonics.

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

Francium: Created page with "{{Infobox ET}} {{EDO intro|691}} == Theory == 691edo is consistent to the 5-odd-limit, having a flat tendency in the first few harmonics except the harmonic 7/1..."

2024-09-27T15:52:24Z

Created page with "{{Infobox ET}} {{EDO intro|691}} == Theory == 691edo is consistent to the 5-odd-limit, having a flat tendency in the first few harmonics except the harmonic 7/1..."

New page

{{Infobox ET}}
{{EDO intro|691}}

== Theory ==
691edo is [[consistent]] to the [[5-odd-limit]], having a flat tendency in the first few [[harmonic]]s except the harmonic [[7/1|7]]. Its harmonic [[13/1|13]] is highly accurate with a relative error of only 0.4 percent. It can be used in the 2.3.5.11.17.19 [[subgroup]], [[temper out|tempering out]] [[1089/1088]], 455625/454784, 334611/334400, 374000/373977 and 45125/45056.

Using the 691d val ({{val|691 1095 1604 '''1939''' 2390}}) can also be considered. It tempers out [[3025/3024]], 42875/42768, 759375/758912 and 6417873/6400000 in the [[11-limit]].

=== Odd harmonics ===
{{Harmonics in equal|691}}

=== Subsets and supersets ===
691edo is the 125th [[prime EDO]]. [[2764edo]], which quadruples it, gives a good correction to the harmonic 7.

== 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]] (%)
|-
| 2.3
| {{monzo|-1095 691}}
| {{mapping|691 1095}}
| 0.1145
| 0.1146
| 6.60
|-
| 2.3.5
| {{monzo|-51 19 9}}, {{monzo|-20 -24 25}}
| {{mapping|691 1095 1604}}
| 0.1891
| 0.1410
| 8.12
|}