653edo - Revision history

FloraC: Expand for 23-limit

2026-06-18T05:46:00Z

Expand for 23-limit

← Older revision		Revision as of 05:46, 18 June 2026
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	== Theory ==		== Theory ==
	653edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] {{monzo\| 39 -29 3 }} ([[alphatricot comma]]) and {{monzo\| -20 -24 25 }} ([[counterhanson comma]]) in the [[5-limit]]; [[2401/2400]], [[65625/65536]], and {{monzo\| 7 -27 13 2 }} in the [[7-limit]]; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the [[11-limit]]; [[2080/2079]], [[4459/4455]], [[6656/6655]], [[10985/10976]], and 170625/170368 in the [[13-limit]]; [[1225/1224]], [[2058/2057]], [[2431/2430]], [[2500/2499]], [[4914/4913]], and 11271/11264 in the [[17-limit]]; [[1445/1444]], [[1521/1520]], [[1540/1539]], [[1729/1728]], [[3136/3135]], [[4200/4199]], and 4394/4389 in the [[19-limit]].		653edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], and the [[23-odd-limit]] if not for the [[23/13]] and its [[octave complement]] barely missing the mark. Although the [[25/1\|25]] is flat enough to create more inconsistencies, the [[29/1\|29]] and [[31/1\|31]] blend well with the lower primes, together making it a fairly strong [[31-limit]] system.

			As an equal temperament, it [[tempering out\|tempers out]] {{monzo\| 39 -29 3 }} ([[alphatricot comma]]) and {{monzo\| -20 -24 25 }} ([[counterhanson comma]]) in the [[5-limit]]; [[2401/2400]], [[65625/65536]], and {{monzo\| 7 -27 13 2 }} in the [[7-limit]]; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the [[11-limit]]; [[2080/2079]], [[4459/4455]], [[6656/6655]], [[10985/10976]], and 170625/170368 in the [[13-limit]]; [[1225/1224]], [[2058/2057]], [[2431/2430]], [[2500/2499]], [[4914/4913]], and 11271/11264 in the [[17-limit]]; [[1445/1444]], [[1521/1520]], [[1540/1539]], [[1729/1728]], [[3136/3135]], [[4200/4199]], and 4394/4389 in the [[19-limit]]; [[875/874]], [[1105/1104]] among others in the [[23-limit]].

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	653edo is the 119th [[prime edo]].		653edo is the 119th [[prime edo]]. As such, it does not contain any nontrivial subset edo.

	== Regular temperament properties ==		== Regular temperament properties ==
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	\| 0.0867		\| 0.0867
	\| 4.72		\| 4.72
			\|-
			\| 2.3.5.7.11.13.17.19.23
			\| 875/874, 1105/1104, 1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079
			\| {{Mapping\| 653 1035 1516 1833 2259 2416 2669 2774 2954 }}
			\| +0.0489
			\| 0.0884
			\| 4.81
	\|}		\|}

Overthink: /* Prime harmonics */ columns = 10 is awkward

2026-06-05T17:48:45Z

Prime harmonics: columns = 10 is awkward

← Older revision		Revision as of 17:48, 5 June 2026
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|653\|columns=11}}		{{Harmonics in equal\|653\|columns=11}}
	{{Harmonics in equal\|653\|columns=10\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 653edo (continued)}}		{{Harmonics in equal\|653\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 653edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

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"

2026-03-13T13:32:01Z

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
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	\| [[Alphatricot]]		\| [[Alphatricot]]
	\|}		\|}
	<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]]
	* "Seamless Toggle-Style" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/6nGhaXwzE85erYFtxGB9Dt Spotify] \| [https://francium223.bandcamp.com/track/seamless-toggle-style Bandcamp] \| [https://www.youtube.com/watch?v=TQP9W0vIvqw YouTube]		* "Seamless Toggle-Style" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/6nGhaXwzE85erYFtxGB9Dt Spotify] \| [https://francium223.bandcamp.com/track/seamless-toggle-style Bandcamp] \| [https://www.youtube.com/watch?v=TQP9W0vIvqw YouTube]

FloraC: Cleanup and update

2025-03-16T14:04:22Z

Cleanup and update

← Older revision		Revision as of 14:04, 16 March 2025
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	== Theory ==		== Theory ==
	653edo is [[distinctly consistent]] to the [[21-odd-limit]], [[tempering out]] {{monzo\| 39 -29 3 }} ([[~~tricot~~ comma]]) and {{monzo\| -20 -24 25 }} ([[counterhanson comma]]) in the 5-limit; [[2401/2400]], [[65625/65536]], and {{monzo\| 7 -27 13 2 }} in the 7-limit; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the 11-limit; [[2080/2079]], 4459/4455, [[6656/6655]], [[10985/10976]], and 170625/170368 in the 13-limit; [[1225/1224]], [[2058/2057]], [[2431/2430]], [[2500/2499]], [[4914/4913]], and 11271/11264 in the 17-limit; [[1445/1444]], [[1521/1520]], 1540/1539, [[1729/1728]], 3136/3135, 4200/4199, and 4394/4389 in the 19-limit.		653edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] {{monzo\| 39 -29 3 }} ([[alphatricot comma]]) and {{monzo\| -20 -24 25 }} ([[counterhanson comma]]) in the [[5-limit]]; [[2401/2400]], [[65625/65536]], and {{monzo\| 7 -27 13 2 }} in the [[7-limit]]; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the [[11-limit]]; [[2080/2079]], [[4459/4455]], [[6656/6655]], [[10985/10976]], and 170625/170368 in the [[13-limit]]; [[1225/1224]], [[2058/2057]], [[2431/2430]], [[2500/2499]], [[4914/4913]], and 11271/11264 in the [[17-limit]]; [[1445/1444]], [[1521/1520]], [[1540/1539]], [[1729/1728]], [[3136/3135]], [[4200/4199]], and 4394/4389 in the [[19-limit]].

	=== Prime harmonics ===		=== Prime harmonics ===
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	! 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
	\|-		\|-
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	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| 1035 -653 }}		\| {{Monzo\| 1035 -653 }}
	\| {{~~mapping~~\| 653 1035 }}		\| {{Mapping\| 653 1035 }}
	\| −0.0113		\| −0.0113
	\| 0.0113		\| 0.0113
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| 39 -29 3 }}, {{monzo\| -20 -24 25 }}		\| {{Monzo\| 39 -29 3 }}, {{monzo\| -20 -24 25 }}
	\| {{~~mapping~~\| 653 1035 1516 }}		\| {{Mapping\| 653 1035 1516 }}
	\| +0.0503		\| +0.0503
	\| 0.0875		\| 0.0875
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	\| 2.3.5.7		\| 2.3.5.7
	\| 2401/2400, 65625/65536, {{monzo\| 7 -27 13 2 }}		\| 2401/2400, 65625/65536, {{monzo\| 7 -27 13 2 }}
	\| {{~~mapping~~\| 653 1035 1516 1833 }}		\| {{Mapping\| 653 1035 1516 1833 }}
	\| +0.0709		\| +0.0709
	\| 0.0838		\| 0.0838
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 2401/2400, 3025/3024, 65625/65536, 1953125/1948617		\| 2401/2400, 3025/3024, 65625/65536, 1953125/1948617
	\| {{~~mapping~~\| 653 1035 1516 1833 2259 }}		\| {{Mapping\| 653 1035 1516 1833 2259 }}
	\| +0.0576		\| +0.0576
	\| 0.0795		\| 0.0795
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	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 2080/2079, 2401/2400, 3025/3024, 10985/10976, 65625/65536		\| 2080/2079, 2401/2400, 3025/3024, 10985/10976, 65625/65536
	\| {{~~mapping~~\| 653 1035 1516 1833 2259 2416 }}		\| {{Mapping\| 653 1035 1516 1833 2259 2416 }}
	\| +0.0801		\| +0.0801
	\| 0.0882		\| 0.0882
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	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 1225/1224, 2058/2057, 2080/2079, 2401/2400, 4914/4913, 10985/10976		\| 1225/1224, 2058/2057, 2080/2079, 2401/2400, 4914/4913, 10985/10976
	\| {{~~mapping~~\| 653 1035 1516 1833 2259 2416 2669 }}		\| {{Mapping\| 653 1035 1516 1833 2259 2416 2669 }}
	\| +0.0759		\| +0.0759
	\| 0.0823		\| 0.0823
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	\| 2.3.5.7.11.13.17.19		\| 2.3.5.7.11.13.17.19
	\| 1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079, 2401/2400		\| 1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079, 2401/2400
	\| {{~~mapping~~\| 653 1035 1516 1833 2259 2416 2669 2774 }}		\| {{Mapping\| 653 1035 1516 1833 2259 2416 2669 2774 }}
	\| +0.0608		\| +0.0608
	\| 0.0867		\| 0.0867
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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
	\|-		\|-
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	\| 566.00		\| 566.00
	\| 81920/59049		\| 81920/59049
	\| [[~~Tricot~~]]		\| [[Alphatricot]]
	\|}		\|}
	<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]]
	* "Seamless Toggle-Style" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/6nGhaXwzE85erYFtxGB9Dt Spotify] \| [https://francium223.bandcamp.com/track/seamless-toggle-style Bandcamp] \| [https://www.youtube.com/watch?v=TQP9W0vIvqw YouTube]		* "Seamless Toggle-Style" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/6nGhaXwzE85erYFtxGB9Dt Spotify] \| [https://francium223.bandcamp.com/track/seamless-toggle-style Bandcamp] \| [https://www.youtube.com/watch?v=TQP9W0vIvqw YouTube]

ArrowHead294 at 22:39, 20 February 2025

2025-02-20T22:39:20Z

← Older revision		Revision as of 22:39, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|653~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 14:51, 16 January 2025

2025-01-16T14:51:16Z

← Older revision		Revision as of 14:51, 16 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	653edo is [[~~consistency\|~~distinctly consistent]] to the [[21-odd-limit]], [[tempering out]] {{monzo\| 39 -29 3 }} ([[tricot comma]]) and {{monzo\| -20 -24 25 }} ([[counterhanson comma]]) in the 5-limit; [[2401/2400]], [[65625/65536]], and {{monzo\| 7 -27 13 2 }} in the 7-limit; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the 11-limit; [[2080/2079]], 4459/4455, [[6656/6655]], [[10985/10976]], and 170625/170368 in the 13-limit; [[1225/1224]], [[2058/2057]], [[2431/2430]], [[2500/2499]], [[4914/4913]], and 11271/11264 in the 17-limit; [[1445/1444]], [[1521/1520]], 1540/1539, [[1729/1728]], 3136/3135, 4200/4199, and 4394/4389 in the 19-limit.		653edo is [[distinctly consistent]] to the [[21-odd-limit]], [[tempering out]] {{monzo\| 39 -29 3 }} ([[tricot comma]]) and {{monzo\| -20 -24 25 }} ([[counterhanson comma]]) in the 5-limit; [[2401/2400]], [[65625/65536]], and {{monzo\| 7 -27 13 2 }} in the 7-limit; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the 11-limit; [[2080/2079]], 4459/4455, [[6656/6655]], [[10985/10976]], and 170625/170368 in the 13-limit; [[1225/1224]], [[2058/2057]], [[2431/2430]], [[2500/2499]], [[4914/4913]], and 11271/11264 in the 17-limit; [[1445/1444]], [[1521/1520]], 1540/1539, [[1729/1728]], 3136/3135, 4200/4199, and 4394/4389 in the 19-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
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	\| {{monzo\| 1035 -653 }}		\| {{monzo\| 1035 -653 }}
	\| {{mapping\| 653 1035 }}		\| {{mapping\| 653 1035 }}
	\| ~~−0~~.0113		\| −0.0113
	\| 0.0113		\| 0.0113
	\| 0.61		\| 0.61
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	\| [[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]]
	* "Seamless Toggle-Style" from ''Take Advantage'' (2024) ~~–~~ [https://open.spotify.com/track/6nGhaXwzE85erYFtxGB9Dt Spotify] \| [https://francium223.bandcamp.com/track/seamless-toggle-style Bandcamp] \| [https://www.youtube.com/watch?v=TQP9W0vIvqw YouTube]		* "Seamless Toggle-Style" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/6nGhaXwzE85erYFtxGB9Dt Spotify] \| [https://francium223.bandcamp.com/track/seamless-toggle-style Bandcamp] \| [https://www.youtube.com/watch?v=TQP9W0vIvqw YouTube]

Lériendil at 01:00, 14 December 2024

2024-12-14T01:00:38Z

← Older revision		Revision as of 01:00, 14 December 2024
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|653\|columns=11}}		{{Harmonics in equal\|653\|columns=11}}
			{{Harmonics in equal\|653\|columns=10\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 653edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

ArrowHead294: Partial undo

2024-11-16T12:35:06Z

Partial undo

← Older revision		Revision as of 12:35, 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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	\| 0.0867		\| 0.0867
	\| 4.72		\| 4.72
	~~{{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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	\| 81920/59049		\| 81920/59049
	\| [[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]]
	* "Seamless Toggle-Style" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/6nGhaXwzE85erYFtxGB9Dt Spotify] \| [https://francium223.bandcamp.com/track/seamless-toggle-style Bandcamp] \| [https://www.youtube.com/watch?v=TQP9W0vIvqw YouTube]		* "Seamless Toggle-Style" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/6nGhaXwzE85erYFtxGB9Dt Spotify] \| [https://francium223.bandcamp.com/track/seamless-toggle-style Bandcamp] \| [https://www.youtube.com/watch?v=TQP9W0vIvqw YouTube]

ArrowHead294 at 04:22, 16 November 2024

2024-11-16T04:22:10Z

← Older revision		Revision as of 04:22, 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\| 1035 -653 }}		\| {{monzo\| 1035 -653 }}
	\| {{mapping\| 653 1035 }}		\| {{mapping\| 653 1035 }}
	\| -0.0113		\| −0.0113
	\| 0.0113		\| 0.0113
	\| 0.61		\| 0.61
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	\| 0.0867		\| 0.0867
	\| 4.72		\| 4.72
	\|}		{{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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	\| 81920/59049		\| 81920/59049
	\| [[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]]
	* "Seamless Toggle-Style" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/6nGhaXwzE85erYFtxGB9Dt Spotify] \| [https://francium223.bandcamp.com/track/seamless-toggle-style Bandcamp] \| [https://www.youtube.com/watch?v=TQP9W0vIvqw YouTube]		* "Seamless Toggle-Style" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/6nGhaXwzE85erYFtxGB9Dt Spotify] \| [https://francium223.bandcamp.com/track/seamless-toggle-style Bandcamp] \| [https://www.youtube.com/watch?v=TQP9W0vIvqw YouTube]

Francium: +music

2024-09-16T12:44:19Z

+music

← Older revision		Revision as of 12:44, 16 September 2024
Line 106:		Line 106:
	\|}		\|}
	<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]]
			* "Seamless Toggle-Style" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/6nGhaXwzE85erYFtxGB9Dt Spotify] \| [https://francium223.bandcamp.com/track/seamless-toggle-style Bandcamp] \| [https://www.youtube.com/watch?v=TQP9W0vIvqw YouTube]