617edo - 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"

2026-03-13T13:38:09Z

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
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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 ==

FloraC: Cleanup and update

2025-03-16T14:26:39Z

Cleanup and update

← Older revision		Revision as of 14:26, 16 March 2025
Line 5:		Line 5:
	617edo is [[consistent]] to the [[5-odd-limit]]. The equal temperament can be used in the 2.3.5.7.13.17.19.23.31 [[subgroup]], [[temper out\|tempering out]] [[1701/1700]], [[1216/1215]], [[1729/1728]], [[676/675]], 1127/1125, 260253/260000, [[3969/3968]] and 137241/137200. It [[support]]s [[majvam]].		617edo is [[consistent]] to the [[5-odd-limit]]. The equal temperament can be used in the 2.3.5.7.13.17.19.23.31 [[subgroup]], [[temper out\|tempering out]] [[1701/1700]], [[1216/1215]], [[1729/1728]], [[676/675]], 1127/1125, 260253/260000, [[3969/3968]] and 137241/137200. It [[support]]s [[majvam]].

	Using the 617c val ({{val\|617 978 '''1432''' 1732}}), it tempers out [[15625/15552]], [[2460375/2458624]] and 3276800000/3268642167 in the [[7-limit]], supporting [[kleismic]] and [[marthirds]].		Using the 617c val ({{val\| 617 978 '''1432''' 1732 }}), it tempers out [[15625/15552]], [[2460375/2458624]] and 3276800000/3268642167 in the [[7-limit]], supporting [[kleismic]] and [[marthirds]].

	Using the 617de val ({{val\|617 978 1433 '''1733''' '''2135'''}}), it tempers out [[540/539]], 5632/5631, 43923/43904 and 40960000/40920957 in the [[11-limit]], supporting [[jupiter]].		Using the 617de val ({{val\| 617 978 1433 '''1733''' '''2135''' }}), it tempers out [[540/539]], 5632/5631, 43923/43904 and 40960000/40920957 in the [[11-limit]], supporting [[jupiter]].

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	617edo is the 113th [[prime ~~EDO~~]].		617edo is the 113th [[prime edo]].

	== Regular temperament properties ==		== Regular temperament properties ==
Line 21:		Line 21:
	! 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~~\|978 -617}}		\| {{Monzo\| 978 -617 }}
	\| {{~~mapping~~\|617 978}}		\| {{Mapping\| 617 978 }}
	\| −0.0479		\| −0.0479
	\| 0.0479		\| 0.0479
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\|39 -29 3}}, {{monzo\|40 7 -22}}		\| {{Monzo\| 39 -29 3 }}, {{monzo\| 40 7 -22 }}
	\| {{~~mapping~~\|617 978 1433}}		\| {{Mapping\| 617 978 1433 }}
	\| −0.1354		\| −0.1354
	\| 0.1297		\| 0.1297
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	\| 2.3.5.7		\| 2.3.5.7
	\| 420175/419904, 1959552/1953125, 67108864/66976875		\| 420175/419904, 1959552/1953125, 67108864/66976875
	\| {{~~mapping~~\|617 978 1433 1732}}		\| {{Mapping\| 617 978 1433 1732 }}
	\| −0.0776		\| −0.0776
	\| 0.1504		\| 0.1504
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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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	\| 565.964		\| 565.964
	\| 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]]
	* "purple?" from ''Questions'' (2024) – [https://open.spotify.com/track/0rTRdkO4ttqQaVFO3B42rc Spotify] \| [https://francium223.bandcamp.com/track/purple Bandcamp] \| [https://www.youtube.com/watch?v=lkfvSjQ6GnU YouTube] ~~–~~ majvam in 617edo tuning		* "purple?" from ''Questions'' (2024) – [https://open.spotify.com/track/0rTRdkO4ttqQaVFO3B42rc Spotify] \| [https://francium223.bandcamp.com/track/purple Bandcamp] \| [https://www.youtube.com/watch?v=lkfvSjQ6GnU YouTube] – majvam in 617edo tuning

	[[Category:Listen]]		[[Category:Listen]]

Francium: changed EDO intro to ED intro

2025-02-21T06:03:50Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:03, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|617~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:02, 15 January 2025

2025-01-15T17:02:38Z

← Older revision		Revision as of 17:02, 15 January 2025
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	\| {{monzo\|978 -617}}		\| {{monzo\|978 -617}}
	\| {{mapping\|617 978}}		\| {{mapping\|617 978}}
	\| ~~−0~~.0479		\| −0.0479
	\| 0.0479		\| 0.0479
	\| 2.46		\| 2.46
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	\| {{monzo\|39 -29 3}}, {{monzo\|40 7 -22}}		\| {{monzo\|39 -29 3}}, {{monzo\|40 7 -22}}
	\| {{mapping\|617 978 1433}}		\| {{mapping\|617 978 1433}}
	\| ~~−0~~.1354		\| −0.1354
	\| 0.1297		\| 0.1297
	\| 6.67		\| 6.67
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	\| 420175/419904, 1959552/1953125, 67108864/66976875		\| 420175/419904, 1959552/1953125, 67108864/66976875
	\| {{mapping\|617 978 1433 1732}}		\| {{mapping\|617 978 1433 1732}}
	\| ~~−0~~.0776		\| −0.0776
	\| 0.1504		\| 0.1504
	\| 7.73		\| 7.73
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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]]
	* "purple?" from ''Questions'' (2024) ~~–~~ [https://open.spotify.com/track/0rTRdkO4ttqQaVFO3B42rc Spotify] \| [https://francium223.bandcamp.com/track/purple Bandcamp] \| [https://www.youtube.com/watch?v=lkfvSjQ6GnU YouTube] – majvam in 617edo tuning		* "purple?" from ''Questions'' (2024) – [https://open.spotify.com/track/0rTRdkO4ttqQaVFO3B42rc Spotify] \| [https://francium223.bandcamp.com/track/purple Bandcamp] \| [https://www.youtube.com/watch?v=lkfvSjQ6GnU YouTube] – majvam in 617edo tuning

	[[Category:Listen]]		[[Category:Listen]]

ArrowHead294: Partial undo

2024-11-16T13:09:15Z

Partial undo

← Older revision		Revision as of 13:09, 16 November 2024
Line 16:		Line 16:

	== 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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	\| 0.1504		\| 0.1504
	\| 7.73		\| 7.73
	~~{{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 ==

ArrowHead294 at 02:15, 16 November 2024

2024-11-16T02:15:32Z

← Older revision		Revision as of 02:15, 16 November 2024
Line 16:		Line 16:

	== 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\|978 -617}}		\| {{monzo\|978 -617}}
	\| {{mapping\|617 978}}		\| {{mapping\|617 978}}
	\| -0.0479		\| −0.0479
	\| 0.0479		\| 0.0479
	\| 2.46		\| 2.46
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	\| {{monzo\|39 -29 3}}, {{monzo\|40 7 -22}}		\| {{monzo\|39 -29 3}}, {{monzo\|40 7 -22}}
	\| {{mapping\|617 978 1433}}		\| {{mapping\|617 978 1433}}
	\| -0.1354		\| −0.1354
	\| 0.1297		\| 0.1297
	\| 6.67		\| 6.67
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	\| 420175/419904, 1959552/1953125, 67108864/66976875		\| 420175/419904, 1959552/1953125, 67108864/66976875
	\| {{mapping\|617 978 1433 1732}}		\| {{mapping\|617 978 1433 1732}}
	\| -0.0776		\| −0.0776
	\| 0.1504		\| 0.1504
	\| 7.73		\| 7.73
	\|}		{{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]]
	* "purple?" from ''Questions'' (2024) – [https://open.spotify.com/track/0rTRdkO4ttqQaVFO3B42rc Spotify] \| [https://francium223.bandcamp.com/track/purple Bandcamp] \| [https://www.youtube.com/watch?v=lkfvSjQ6GnU YouTube] – majvam in 617edo tuning		* "purple?" from ''Questions'' (2024) – [https://open.spotify.com/track/0rTRdkO4ttqQaVFO3B42rc Spotify] \| [https://francium223.bandcamp.com/track/purple Bandcamp] \| [https://www.youtube.com/watch?v=lkfvSjQ6GnU YouTube] – majvam in 617edo tuning

			[[Category:Listen]]

Francium: +music

2024-07-28T12:23:28Z

+music

← Older revision		Revision as of 12:23, 28 July 2024
Line 70:		Line 70:
	\|}		\|}
	<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]]
			* "purple?" from ''Questions'' (2024) – [https://open.spotify.com/track/0rTRdkO4ttqQaVFO3B42rc Spotify] \| [https://francium223.bandcamp.com/track/purple Bandcamp] \| [https://www.youtube.com/watch?v=lkfvSjQ6GnU YouTube] – majvam in 617edo tuning

Francium: Created page with "{{Infobox ET}} {{EDO intro|617}} == Theory == 617edo is consistent to the 5-odd-limit. The equal temperament can be used in the 2.3.5.7.13.17.19.23.31 subgroup, [..."

2024-06-13T16:41:00Z

Created page with "{{Infobox ET}} {{EDO intro|617}} == Theory == 617edo is consistent to the 5-odd-limit. The equal temperament can be used in the 2.3.5.7.13.17.19.23.31 subgroup, [..."

New page

{{Infobox ET}}
{{EDO intro|617}}

== Theory ==
617edo is [[consistent]] to the [[5-odd-limit]]. The equal temperament can be used in the 2.3.5.7.13.17.19.23.31 [[subgroup]], [[temper out|tempering out]] [[1701/1700]], [[1216/1215]], [[1729/1728]], [[676/675]], 1127/1125, 260253/260000, [[3969/3968]] and 137241/137200. It [[support]]s [[majvam]].

Using the 617c val ({{val|617 978 '''1432''' 1732}}), it tempers out [[15625/15552]], [[2460375/2458624]] and 3276800000/3268642167 in the [[7-limit]], supporting [[kleismic]] and [[marthirds]].

Using the 617de val ({{val|617 978 1433 '''1733''' '''2135'''}}), it tempers out [[540/539]], 5632/5631, 43923/43904 and 40960000/40920957 in the [[11-limit]], supporting [[jupiter]].

=== Prime harmonics ===
{{Harmonics in equal|617}}

=== Subsets and supersets ===
617edo is the 113th [[prime EDO]].

== 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|978 -617}}
| {{mapping|617 978}}
| -0.0479
| 0.0479
| 2.46
|-
| 2.3.5
| {{monzo|39 -29 3}}, {{monzo|40 7 -22}}
| {{mapping|617 978 1433}}
| -0.1354
| 0.1297
| 6.67
|-
| 2.3.5.7
| 420175/419904, 1959552/1953125, 67108864/66976875
| {{mapping|617 978 1433 1732}}
| -0.0776
| 0.1504
| 7.73
|}

=== 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
| 236\617
| 458.995
| 125/96
| [[Majvam]]
|-
| 1
| 291\617
| 565.964
| 81920/59049
| [[Tricot]]
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct