4349edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:32:17Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:32, 13 March 2026
Line 82:		Line 82:
	\| [[Fortune]]		\| [[Fortune]]
	\|}		\|}
	<nowiki/>* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Naughty Girl Era" from ''Naughty Girl Era'' (2024) – [https://open.spotify.com/track/0ulmRt6G21G2X5RyxHLYHT Spotify] \| [https://francium223.bandcamp.com/track/naughty-girl-era Bandcamp] \| [https://www.youtube.com/watch?v=gJ9ZAKfgigA YouTube] – girardic in 4349edo		* "Naughty Girl Era" from ''Naughty Girl Era'' (2024) – [https://open.spotify.com/track/0ulmRt6G21G2X5RyxHLYHT Spotify] \| [https://francium223.bandcamp.com/track/naughty-girl-era Bandcamp] \| [https://www.youtube.com/watch?v=gJ9ZAKfgigA YouTube] – girardic in 4349edo

Francium: changed EDO intro to ED intro

2025-02-21T06:15:33Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:15, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|4349~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Review

2025-01-12T10:10:08Z

Review

← Older revision		Revision as of 10:10, 12 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	4349edo is [[consistent]] to the [[29-odd-limit]], [[~~temper~~ out\|~~tempering~~ out]] [[12376/12375]], 10241/10240, 13377/13376, 89376/89375~~, 25025/25024,~~ [[~~123201~~/~~123200~~]], 76545/76544, 47125/47124 and 25840/25839. ~~It [[support]]s [[counterquectismic]]~~, [[~~chalmersic]], [[tritomere]] and [[girardic]]. [[Essentially tempered~~ chords]] ~~available~~ in ~~4349et include~~ [[~~vicetertismic chords~~]].		4349edo is a fairly strong [[29-limit]] system, [[consistent]] to the [[29-odd-limit]]. We may note it is a [[counterquectismic]], [[fortune]], and [[euzenius]] system. Some of the simpler commas in [[tempering out\|tempers out]] in the higher limits include [[151263/151250]] and [[1771561/1771470]] in the 11-limit; [[123201/123200]] in the 13-limit; [[12376/12375]] in the 17-limit; 10241/10240, 13377/13376, 89376/89375 in the 19-limit; [[12168/12167]], 25025/25024, 76545/76544 in the 23-limit; 47125/47124 and 25840/25839. Since it tempers out 12168/12167, it allows [[vicetertismic chords]] in the [[23-odd-limit]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	4349edo is the 594th [[prime ~~EDO~~]].		4349edo is the 594th [[prime edo]].

	== Regular temperament properties ==		== Regular temperament properties ==
Line 17:		Line 17:
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[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
	\|-		\|-
Line 24:		Line 24:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\|-6893 4349}}		\| {{monzo\| -6893 4349 }}
	\| {{mapping\|4349 6893}}		\| {{mapping\| 4349 6893 }}
	\| +0.0002		\| +0.0002
	\| 0.0002		\| 0.0002
Line 31:		Line 31:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{monzo\|-107 47 14}}, {{monzo\|-35 -79 69}}		\| {{monzo\| -107 47 14 }}, {{monzo\| -35 -79 69 }}
	\| {{mapping\|4349 6893 10098}}		\| {{mapping\| 4349 6893 10098 }}
	\| +0.0027		\| +0.0027
	\| 0.0036		\| 0.0036
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	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
	\| 78125000/78121827, {{monzo\|-1 -18 -3 13}}, {{monzo\|-52 17 12 -1}}		\| 78125000/78121827, {{monzo\| -1 -18 -3 13 }}, {{monzo\| -52 17 12 -1 }}
	\| {{mapping\|4349 6893 10098 12209}}		\| {{mapping\| 4349 6893 10098 12209 }}
	\| +0.0066		\| +0.0066
	\| 0.0074		\| 0.0074
Line 46:		Line 46:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 151263/151250, 21437500/21434787, 246071287/246037500, 369140625/369098752		\| 151263/151250, 21437500/21434787, 246071287/246037500, 369140625/369098752
	\| {{mapping\|4349 6893 10098 12209 15045}}		\| {{mapping\| 4349 6893 10098 12209 15045 }}
	\| +0.0064		\| +0.0064
	\| 0.0067		\| 0.0067
Line 52:		Line 52:
	\|-		\|-
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 123201/123200, 196625/196608~~, 151263/151250~~, 492128/492075, 5175625/5174928		\| 123201/123200, 151263/151250, 196625/196608, 492128/492075, 5175625/5174928
	\| {{mapping\|4349 6893 10098 12209 15045 16093}}		\| {{mapping\| 4349 6893 10098 12209 15045 16093 }}
	\| +0.0079		\| +0.0079
	\| 0.0070		\| 0.0070
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	\|-		\|-
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 12376/12375, 123201/123200~~, 37180/37179~~, 194481/194480, 221221/221184, 1328125/1328096		\| 12376/12375, 37180/37179, 123201/123200, 194481/194480, 221221/221184, 1328125/1328096
	\| {{mapping\|4349 6893 10098 12209 15045 16093 17776}}		\| {{mapping\| 4349 6893 10098 12209 15045 16093 17776 }}
	\| +0.0104		\| +0.0104
	\| 0.0089		\| 0.0089
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	\|+ style="font-size: 105%;" \| 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
	\|-		\|-
Line 82:		Line 82:
	\| [[Fortune]]		\| [[Fortune]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Naughty Girl Era" from ''Naughty Girl Era'' (2024) – [https://open.spotify.com/track/0ulmRt6G21G2X5RyxHLYHT Spotify] \| [https://francium223.bandcamp.com/track/naughty-girl-era Bandcamp] \| [https://www.youtube.com/watch?v=gJ9ZAKfgigA YouTube] – girardic in 4349edo		* "Naughty Girl Era" from ''Naughty Girl Era'' (2024) – [https://open.spotify.com/track/0ulmRt6G21G2X5RyxHLYHT Spotify] \| [https://francium223.bandcamp.com/track/naughty-girl-era Bandcamp] \| [https://www.youtube.com/watch?v=gJ9ZAKfgigA YouTube] – girardic in 4349edo

Francium: +music

2024-11-29T12:15:11Z

+music

← Older revision		Revision as of 12:15, 29 November 2024
Line 83:		Line 83:
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

			== Music ==
			; [[Francium]]
			* "Naughty Girl Era" from ''Naughty Girl Era'' (2024) – [https://open.spotify.com/track/0ulmRt6G21G2X5RyxHLYHT Spotify] \| [https://francium223.bandcamp.com/track/naughty-girl-era Bandcamp] \| [https://www.youtube.com/watch?v=gJ9ZAKfgigA YouTube] – girardic in 4349edo

ArrowHead294: Partial undo

2024-11-16T13:10:54Z

Partial undo

← Older revision		Revision as of 13:10, 16 November 2024
Line 12:		Line 12:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
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	\| 0.0089		\| 0.0089
	\| 3.23		\| 3.23
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
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	\| 8388608/7381125		\| 8388608/7381125
	\| [[Fortune]]		\| [[Fortune]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

ArrowHead294 at 02:04, 16 November 2024

2024-11-16T02:04:22Z

← Older revision		Revision as of 02:04, 16 November 2024
Line 11:		Line 11:
	4349edo is the 594th [[prime EDO]].		4349edo is the 594th [[prime EDO]].

	~~{\| class~~=~~"wikitable center-4 center-5 center-6"~~		== Regular temperament properties ==
	~~! rowspan~~=~~"2" \|[[Subgroup]]~~		{{comma basis begin}}
	~~! 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		\| 2.3
	\| {{monzo\|-6893 4349}}		\| {{monzo\|-6893 4349}}
	\| {{mapping\|4349 6893}}		\| {{mapping\|4349 6893}}
	\| 0.0002		\| +0.0002
	\| 0.0002		\| 0.0002
	\| 0.07		\| 0.07
Line 31:		Line 24:
	\| {{monzo\|-107 47 14}}, {{monzo\|-35 -79 69}}		\| {{monzo\|-107 47 14}}, {{monzo\|-35 -79 69}}
	\| {{mapping\|4349 6893 10098}}		\| {{mapping\|4349 6893 10098}}
	\| 0.0027		\| +0.0027
	\| 0.0036		\| 0.0036
	\| 1.30		\| 1.30
Line 38:		Line 31:
	\| 78125000/78121827, {{monzo\|-1 -18 -3 13}}, {{monzo\|-52 17 12 -1}}		\| 78125000/78121827, {{monzo\|-1 -18 -3 13}}, {{monzo\|-52 17 12 -1}}
	\| {{mapping\|4349 6893 10098 12209}}		\| {{mapping\|4349 6893 10098 12209}}
	\| 0.0066		\| +0.0066
	\| 0.0074		\| 0.0074
	\| 2.68		\| 2.68
Line 45:		Line 38:
	\| 151263/151250, 21437500/21434787, 246071287/246037500, 369140625/369098752		\| 151263/151250, 21437500/21434787, 246071287/246037500, 369140625/369098752
	\| {{mapping\|4349 6893 10098 12209 15045}}		\| {{mapping\|4349 6893 10098 12209 15045}}
	\| 0.0064		\| +0.0064
	\| 0.0067		\| 0.0067
	\| 2.43		\| 2.43
Line 52:		Line 45:
	\| 123201/123200, 196625/196608, 151263/151250, 492128/492075, 5175625/5174928		\| 123201/123200, 196625/196608, 151263/151250, 492128/492075, 5175625/5174928
	\| {{mapping\|4349 6893 10098 12209 15045 16093}}		\| {{mapping\|4349 6893 10098 12209 15045 16093}}
	\| 0.0079		\| +0.0079
	\| 0.0070		\| 0.0070
	\| 2.54		\| 2.54
Line 59:		Line 52:
	\| 12376/12375, 123201/123200, 37180/37179, 194481/194480, 221221/221184, 1328125/1328096		\| 12376/12375, 123201/123200, 37180/37179, 194481/194480, 221221/221184, 1328125/1328096
	\| {{mapping\|4349 6893 10098 12209 15045 16093 17776}}		\| {{mapping\|4349 6893 10098 12209 15045 16093 17776}}
	\| 0.0104		\| +0.0104
	\| 0.0089		\| 0.0089
	\| 3.23		\| 3.23
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\|1		\| 1
	\|803\4349		\| 803\4349
	\|221.5682		\| 221.5682
	\|8388608/7381125		\| 8388608/7381125
	\|[[Fortune]]		\| [[Fortune]]
	\|}		{{rank-2 end}}
			{{orf}}
	~~<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|4349}} == Theory == 4349edo is consistent to the 29-odd-limit, tempering out 12376/12375, 10241/10240, 13377/13376, 8937..."

2024-10-15T17:12:03Z

Created page with "{{Infobox ET}} {{EDO intro|4349}} == Theory == 4349edo is consistent to the 29-odd-limit, tempering out 12376/12375, 10241/10240, 13377/13376, 8937..."

New page

{{Infobox ET}}
{{EDO intro|4349}}

== Theory ==
4349edo is [[consistent]] to the [[29-odd-limit]], [[temper out|tempering out]] [[12376/12375]], 10241/10240, 13377/13376, 89376/89375, 25025/25024, [[123201/123200]], 76545/76544, 47125/47124 and 25840/25839. It [[support]]s [[counterquectismic]], [[chalmersic]], [[tritomere]] and [[girardic]]. [[Essentially tempered chords]] available in 4349et include [[vicetertismic chords]].

=== Prime harmonics ===
{{Harmonics in equal|4349}}

=== Subsets and supersets ===
4349edo is the 594th [[prime EDO]].

{| 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|-6893 4349}}
| {{mapping|4349 6893}}
| 0.0002
| 0.0002
| 0.07
|-
| 2.3.5
| {{monzo|-107 47 14}}, {{monzo|-35 -79 69}}
| {{mapping|4349 6893 10098}}
| 0.0027
| 0.0036
| 1.30
|-
| 2.3.5.7
| 78125000/78121827, {{monzo|-1 -18 -3 13}}, {{monzo|-52 17 12 -1}}
| {{mapping|4349 6893 10098 12209}}
| 0.0066
| 0.0074
| 2.68
|-
| 2.3.5.7.11
| 151263/151250, 21437500/21434787, 246071287/246037500, 369140625/369098752
| {{mapping|4349 6893 10098 12209 15045}}
| 0.0064
| 0.0067
| 2.43
|-
| 2.3.5.7.11.13
| 123201/123200, 196625/196608, 151263/151250, 492128/492075, 5175625/5174928
| {{mapping|4349 6893 10098 12209 15045 16093}}
| 0.0079
| 0.0070
| 2.54
|-
| 2.3.5.7.11.13.17
| 12376/12375, 123201/123200, 37180/37179, 194481/194480, 221221/221184, 1328125/1328096
| {{mapping|4349 6893 10098 12209 15045 16093 17776}}
| 0.0104
| 0.0089
| 3.23
|}

=== 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
|803\4349
|221.5682
|8388608/7381125
|[[Fortune]]
|}

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