769edo - Revision history

Francium: +music

2025-04-12T11:31:05Z

+music

← Older revision		Revision as of 11:31, 12 April 2025
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	\|}		\|}
	<nowiki />* [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

			== Music ==
			; [[Francium]]
			* "Is Madness Sexy?" from ''Questions, Vol. 2'' (2025) − [https://open.spotify.com/track/744opccKPUbk721EsD6Hoa Spotify] \| [https://francium223.bandcamp.com/track/is-madness-sexy Bandcamp] \| [https://www.youtube.com/watch?v=8EZbxtTIukU YouTube] − in Newt, 769edo tuning

Francium: changed EDO intro to ED intro

2025-02-19T18:22:05Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:22, 19 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|769~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:36, 7 February 2025

2025-02-07T18:36:11Z

← Older revision		Revision as of 18:36, 7 February 2025
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	== 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\|1219 -769}}		\| {{monzo\|1219 -769}}
	\| {{mapping\|769 1219}}		\| {{mapping\|769 1219}}
	\| -0.0807		\| −0.0807
	\| 0.0806		\| 0.0806
	\| 5.17		\| 5.17
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	\| {{monzo\|8 14 -13}}, {{monzo\|103 -43 -15}}		\| {{monzo\|8 14 -13}}, {{monzo\|103 -43 -15}}
	\| {{mapping\|769 1219 1786}}		\| {{mapping\|769 1219 1786}}
	\| -0.1517		\| −0.1517
	\| 0.1202		\| 0.1202
	\| 7.70		\| 7.70
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	\| 2401/2400, 359661568/358722675, 1224440064/1220703125		\| 2401/2400, 359661568/358722675, 1224440064/1220703125
	\| {{mapping\|769 1219 1786 2159}}		\| {{mapping\|769 1219 1786 2159}}
	\| -0.1338		\| −0.1338
	\| 0.1086		\| 0.1086
	\| 6.96		\| 6.96
Line 46:		Line 47:
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		\|-
			! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>~~Ratio~~*		! Associated<br />ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\| [[Maviloid]]		\| [[Maviloid]]
	\|}		\|}
			<nowiki />* [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct
	<nowiki>*~~</nowiki>~~ [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct

Francium: Created page with "{{Infobox ET}} {{EDO intro|769}} == Theory == 769edo is consistent to the 9-odd-limit, despite of a large error in its harmonic 5. As an equal temperament..."

2025-01-21T14:35:23Z

Created page with "{{Infobox ET}} {{EDO intro|769}} == Theory == 769edo is consistent to the 9-odd-limit, despite of a large error in its harmonic 5. As an equal temperament..."

New page

{{Infobox ET}}
{{EDO intro|769}}

== Theory ==
769edo is [[consistent]] to the [[9-odd-limit]], despite of a large error in its [[harmonic]] [[5/1|5]]. As an equal temperament, it [[tempering out|tempers out]] [[2401/2400]], 359661568/358722675 and {{monzo|8 14 -13 0}} in the [[7-limit]].

=== Odd harmonics ===
{{Harmonics in equal|769}}

=== Subsets and supersets ===
769edo is the 136th [[prime edo]]. [[1538edo]], which doubles it, gives a good correction to the harmonic 5.

== 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|1219 -769}}
| {{mapping|769 1219}}
| -0.0807
| 0.0806
| 5.17
|-
| 2.3.5
| {{monzo|8 14 -13}}, {{monzo|103 -43 -15}}
| {{mapping|769 1219 1786}}
| -0.1517
| 0.1202
| 7.70
|-
| 2.3.5.7
| 2401/2400, 359661568/358722675, 1224440064/1220703125
| {{mapping|769 1219 1786 2159}}
| -0.1338
| 0.1086
| 6.96
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
| 1
| 202\769
| 315.215
| 6/5
| [[Parakleismic]]
|-
| 1
| 220\769
| 343.303
| 8000/6561
| [[Raider]]
|-
| 1
| 225\769
| 351.105
| 49/40
| [[Newt]]
|-
| 1
| 334\769
| 521.196
| 875/648
| [[Maviloid]]
|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct