829edo - 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"

2026-03-13T13:38:10Z

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 13:38, 13 March 2026
Line 93:		Line 93:
	\| [[Alphatrillium]]		\| [[Alphatrillium]]
	\|}		\|}
	<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]]
	* "confluencelessness" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/7luOwK0nu7Cq9hmJy6W7L9 Spotify] \| [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] \| [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] – Acrokleismic[19] in 829edo tuning		* "confluencelessness" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/7luOwK0nu7Cq9hmJy6W7L9 Spotify] \| [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] \| [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] – Acrokleismic[19] in 829edo tuning

FloraC: Cleanup and update

2025-03-16T14:24:05Z

Cleanup and update

← Older revision		Revision as of 14:24, 16 March 2025
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~~\| 1314 -829 }}		\| {{Monzo\| 1314 -829 }}
	\| {{~~mapping~~\| 829 1314 }}		\| {{Mapping\| 829 1314 }}
	\| –0.0302		\| –0.0302
	\| 0.0302		\| 0.0302
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| 39 -29 3 }}, {{monzo\| 61 4 -29 }}		\| {{Monzo\| 39 -29 3 }}, {{monzo\| 61 4 -29 }}
	\| {{~~mapping~~\| 829 1314 1925 }}		\| {{Mapping\| 829 1314 1925 }}
	\| −0.0454		\| −0.0454
	\| 0.0327		\| 0.0327
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	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, {{monzo\| -25 6 -3 8 }}, {{monzo\| 16 -9 -8 6 }}		\| 4375/4374, {{monzo\| -25 6 -3 8 }}, {{monzo\| 16 -9 -8 6 }}
	\| {{~~mapping~~\| 829 1314 1925 2327 }}		\| {{Mapping\| 829 1314 1925 2327 }}
	\| +0.0043		\| +0.0043
	\| 0.0906		\| 0.0906
Line 46:		Line 46:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 4375/4374, 41503/41472, 200704/200475, 3750705/3748096		\| 4375/4374, 41503/41472, 200704/200475, 3750705/3748096
	\| {{~~mapping~~\| 829 1314 1925 2327 2868 }}		\| {{Mapping\| 829 1314 1925 2327 2868 }}
	\| −0.0076		\| −0.0076
	\| 0.0844		\| 0.0844
Line 53:		Line 53:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 4096/4095, 4375/4374, 4459/4455, 47432/47385, 59535/59488		\| 4096/4095, 4375/4374, 4459/4455, 47432/47385, 59535/59488
	\| {{~~mapping~~\| 829 1314 1925 2327 2868 3068 }}		\| {{Mapping\| 829 1314 1925 2327 2868 3068 }}
	\| −0.0282		\| −0.0282
	\| 0.0898		\| 0.0898
Line 63:		Line 63:
	\|+ 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 91:		Line 91:
	\| 565.983		\| 565.983
	\| 59049/40960		\| 59049/40960
	\| [[~~Tricot~~]]		\| [[Alphatrillium]]
	\|}		\|}
	<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 ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "confluencelessness" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/7luOwK0nu7Cq9hmJy6W7L9 Spotify] \| [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] \| [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] – ~~acrokleismic~~[19] in 829edo tuning		* "confluencelessness" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/7luOwK0nu7Cq9hmJy6W7L9 Spotify] \| [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] \| [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] – Acrokleismic[19] in 829edo tuning

Francium: changed EDO intro to ED intro

2025-02-21T06:06:56Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:06, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|829~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T16:38:03Z

Theory: cleanup

← Older revision		Revision as of 16:38, 17 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	829edo is [[consistent]] to the [[11-odd-limit]]. It [[tempers out]] [[4375/4374]], {{monzo\| -25 6 -3 8 }}, and {{monzo\| 16 -9 -8 6 }} in the 7-limit; [[41503/41472]], [[200704/200475]], and 3750705/3748096 in the 11-limit. It [[support]]s [[squarschmidt]], [[senior]] and [[acrokleismic]].		829edo is [[consistent]] to the [[11-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] [[4375/4374]], {{monzo\| -25 6 -3 8 }}, and {{monzo\| 16 -9 -8 6 }} in the 7-limit; [[41503/41472]], [[200704/200475]], and 3750705/3748096 in the 11-limit. It [[support]]s [[squarschmidt]], [[senior]] and [[acrokleismic]].

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

	=== Subsets and supersets ===		=== Subsets and supersets ===
	829edo is the 145th [[prime edo]].		829edo is the 145th [[prime edo]].

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

ArrowHead294 at 18:14, 15 January 2025

2025-01-15T18:14:40Z

← Older revision		Revision as of 18:14, 15 January 2025
Line 93:		Line 93:
	\| [[Tricot]]		\| [[Tricot]]
	\|}		\|}
	<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]]
	* "confluencelessness" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/7luOwK0nu7Cq9hmJy6W7L9 Spotify] \| [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] \| [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] – acrokleismic[19] in 829edo tuning		* "confluencelessness" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/7luOwK0nu7Cq9hmJy6W7L9 Spotify] \| [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] \| [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] – acrokleismic[19] in 829edo tuning

ArrowHead294 at 18:09, 15 January 2025

2025-01-15T18:09:12Z

← Older revision		Revision as of 18:09, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	829edo is [[consistent]] to the [[11-odd-limit]]. ~~The equal temperament~~ [[~~tempering out\|~~tempers out]] [[4375/4374]], {{monzo\| -25 6 -3 8 }}, and {{monzo\| 16 -9 -8 6 }} in the 7-limit; [[41503/41472]], [[200704/200475]], and 3750705/3748096 in the 11-limit. It [[support]]s [[squarschmidt]], [[senior]] and [[acrokleismic]].		829edo is [[consistent]] to the [[11-odd-limit]]. It [[tempers out]] [[4375/4374]], {{monzo\| -25 6 -3 8 }}, and {{monzo\| 16 -9 -8 6 }} in the 7-limit; [[41503/41472]], [[200704/200475]], and 3750705/3748096 in the 11-limit. It [[support]]s [[squarschmidt]], [[senior]] and [[acrokleismic]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 26:		Line 26:
	\| {{monzo\| 1314 -829 }}		\| {{monzo\| 1314 -829 }}
	\| {{mapping\| 829 1314 }}		\| {{mapping\| 829 1314 }}
	\| ~~−0~~.0302		\| –0.0302
	\| 0.0302		\| 0.0302
	\| 2.09		\| 2.09
Line 33:		Line 33:
	\| {{monzo\| 39 -29 3 }}, {{monzo\| 61 4 -29 }}		\| {{monzo\| 39 -29 3 }}, {{monzo\| 61 4 -29 }}
	\| {{mapping\| 829 1314 1925 }}		\| {{mapping\| 829 1314 1925 }}
	\| ~~−0~~.0454		\| −0.0454
	\| 0.0327		\| 0.0327
	\| 2.26		\| 2.26
Line 47:		Line 47:
	\| 4375/4374, 41503/41472, 200704/200475, 3750705/3748096		\| 4375/4374, 41503/41472, 200704/200475, 3750705/3748096
	\| {{mapping\| 829 1314 1925 2327 2868 }}		\| {{mapping\| 829 1314 1925 2327 2868 }}
	\| ~~−0~~.0076		\| −0.0076
	\| 0.0844		\| 0.0844
	\| 5.83		\| 5.83
Line 54:		Line 54:
	\| 4096/4095, 4375/4374, 4459/4455, 47432/47385, 59535/59488		\| 4096/4095, 4375/4374, 4459/4455, 47432/47385, 59535/59488
	\| {{mapping\| 829 1314 1925 2327 2868 3068 }}		\| {{mapping\| 829 1314 1925 2327 2868 3068 }}
	\| ~~−0~~.0282		\| −0.0282
	\| 0.0898		\| 0.0898
	\| 6.20		\| 6.20
Line 97:		Line 97:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "confluencelessness" from ''albumwithoutspaces'' (2024) ~~–~~ [https://open.spotify.com/track/7luOwK0nu7Cq9hmJy6W7L9 Spotify] \| [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] \| [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] ~~–~~ acrokleismic[19] in 829edo tuning		* "confluencelessness" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/7luOwK0nu7Cq9hmJy6W7L9 Spotify] \| [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] \| [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] – acrokleismic[19] in 829edo tuning

ArrowHead294: Partial undo

2024-11-16T13:04:25Z

Partial undo

← Older revision		Revision as of 13:04, 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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	\| 0.0898		\| 0.0898
	\| 6.20		\| 6.20
	~~{{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
Line 76:		Line 92:
	\| 59049/40960		\| 59049/40960
	\| [[Tricot]]		\| [[Tricot]]
	~~{{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

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "confluencelessness" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/7luOwK0nu7Cq9hmJy6W7L9 Spotify] \| [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] \| [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] – acrokleismic[19] in 829edo tuning		* "confluencelessness" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/7luOwK0nu7Cq9hmJy6W7L9 Spotify] \| [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] \| [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] – acrokleismic[19] in 829edo tuning

ArrowHead294 at 02:40, 16 November 2024

2024-11-16T02:40:35Z

← Older revision		Revision as of 02:40, 16 November 2024
Line 12:		Line 12:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! 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		\| 2.3
	\| {{monzo\| 1314 -829 }}		\| {{monzo\| 1314 -829 }}
	\| {{mapping\| 829 1314 }}		\| {{mapping\| 829 1314 }}
	\| -0.0302		\| −0.0302
	\| 0.0302		\| 0.0302
	\| 2.09		\| 2.09
Line 32:		Line 24:
	\| {{monzo\| 39 -29 3 }}, {{monzo\| 61 4 -29 }}		\| {{monzo\| 39 -29 3 }}, {{monzo\| 61 4 -29 }}
	\| {{mapping\| 829 1314 1925 }}		\| {{mapping\| 829 1314 1925 }}
	\| -0.0454		\| −0.0454
	\| 0.0327		\| 0.0327
	\| 2.26		\| 2.26
Line 46:		Line 38:
	\| 4375/4374, 41503/41472, 200704/200475, 3750705/3748096		\| 4375/4374, 41503/41472, 200704/200475, 3750705/3748096
	\| {{mapping\| 829 1314 1925 2327 2868 }}		\| {{mapping\| 829 1314 1925 2327 2868 }}
	\| -0.0076		\| −0.0076
	\| 0.0844		\| 0.0844
	\| 5.83		\| 5.83
Line 53:		Line 45:
	\| 4096/4095, 4375/4374, 4459/4455, 47432/47385, 59535/59488		\| 4096/4095, 4375/4374, 4459/4455, 47432/47385, 59535/59488
	\| {{mapping\| 829 1314 1925 2327 2868 3068 }}		\| {{mapping\| 829 1314 1925 2327 2868 3068 }}
	\| -0.0282		\| −0.0282
	\| 0.0898		\| 0.0898
	\| 6.20		\| 6.20
	\|}		{{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
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	\| 59049/40960		\| 59049/40960
	\| [[Tricot]]		\| [[Tricot]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "confluencelessness" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/7luOwK0nu7Cq9hmJy6W7L9 Spotify] \| [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] \| [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] – acrokleismic[19] in 829edo tuning		* "confluencelessness" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/7luOwK0nu7Cq9hmJy6W7L9 Spotify] \| [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] \| [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] – acrokleismic[19] in 829edo tuning

Francium: /* Music */ +links

2024-06-07T15:04:46Z

Music: +links

← Older revision		Revision as of 15:04, 7 June 2024
Line 95:		Line 95:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "confluencelessness" from ''albumwithoutspaces'' (2024) – [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] \| [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] – acrokleismic[19] in 829edo tuning		* "confluencelessness" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/7luOwK0nu7Cq9hmJy6W7L9 Spotify] \| [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] \| [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] – acrokleismic[19] in 829edo tuning

Francium: +music

2024-06-07T12:05:12Z

+music

← Older revision		Revision as of 12:05, 7 June 2024
Line 92:		Line 92:
	\|}		\|}
	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is 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

			== Music ==
			; [[Francium]]
			* "confluencelessness" from ''albumwithoutspaces'' (2024) – [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] \| [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] – acrokleismic[19] in 829edo tuning