1559edo - 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"

2026-03-13T13:33:20Z

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 13:33, 13 March 2026
Line 81:		Line 81:
	\| [[Raider]]		\| [[Raider]]
	\|}		\|}
	<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: changed EDO intro to ED intro

2025-02-21T06:06:18Z

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~~\|1559~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:04, 15 January 2025

2025-01-15T18:04:27Z

← Older revision		Revision as of 18:04, 15 January 2025
Line 26:		Line 26:
	\| {{monzo\| 2471 -1559 }}		\| {{monzo\| 2471 -1559 }}
	\| {{mapping\| 1559 2471 }}		\| {{mapping\| 1559 2471 }}
	\| -0.0106		\| −0.0106
	\| 0.0106		\| 0.0106
	\| 1.38		\| 1.38
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	\| {{monzo\| 38 -2 -15 }}, {{monzo\| 71 -99 37 }}		\| {{monzo\| 38 -2 -15 }}, {{monzo\| 71 -99 37 }}
	\| {{mapping\| 1559 2471 3620 }}		\| {{mapping\| 1559 2471 3620 }}
	\| ~~−0~~.0196		\| −0.0196
	\| 0.0155		\| 0.0155
	\| 2.01		\| 2.01
Line 40:		Line 40:
	\| 43046721/43025920, 78125000/78121827, 12884901888/12867859375		\| 43046721/43025920, 78125000/78121827, 12884901888/12867859375
	\| {{mapping\| 1559 2471 3620 4377 }}		\| {{mapping\| 1559 2471 3620 4377 }}
	\| ~~−0~~.0376		\| −0.0376
	\| 0.0339		\| 0.0339
	\| 4.40		\| 4.40
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	\| 3025/3024, 180224/180075, 50014503/50000000, 56953125/56942116		\| 3025/3024, 180224/180075, 50014503/50000000, 56953125/56942116
	\| {{mapping\| 1559 2471 3620 4377 5393 }}		\| {{mapping\| 1559 2471 3620 4377 5393 }}
	\| ~~−0~~.0188		\| −0.0188
	\| 0.0483		\| 0.0483
	\| 6.27		\| 6.27
Line 54:		Line 54:
	\| 1716/1715, 3025/3024, 4096/4095, 492128/492075, 5282739/5281250		\| 1716/1715, 3025/3024, 4096/4095, 492128/492075, 5282739/5281250
	\| {{mapping\| 1559 2471 3620 4377 5393 5769 }}		\| {{mapping\| 1559 2471 3620 4377 5393 5769 }}
	\| ~~−0~~.0162		\| −0.0162
	\| 0.0445		\| 0.0445
	\| 5.78		\| 5.78
Line 81:		Line 81:
	\| [[Raider]]		\| [[Raider]]
	\|}		\|}
	<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]]
	* "confluenceprettype" from ''albumwithoutspaces'' (2024) ~~–~~ [https://open.spotify.com/track/0jCzkUrwVEHevs7xAWgsvh Spotify] \| [https://francium223.bandcamp.com/track/confluenceprettype Bandcamp] \| [https://www.youtube.com/watch?v=4rxv7ec4BEM YouTube] ~~–~~ luna[25] in 1559edo tuning		* "confluenceprettype" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/0jCzkUrwVEHevs7xAWgsvh Spotify] \| [https://francium223.bandcamp.com/track/confluenceprettype Bandcamp] \| [https://www.youtube.com/watch?v=4rxv7ec4BEM YouTube] – luna[25] in 1559edo tuning

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

ArrowHead294: Partial undo

2024-11-16T13:08:17Z

Partial undo

← Older revision		Revision as of 13:08, 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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	\| 0.0445		\| 0.0445
	\| 5.78		\| 5.78
	~~{{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 64:		Line 80:
	\| 8000/6561		\| 8000/6561
	\| [[Raider]]		\| [[Raider]]
	~~{{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 02:29, 16 November 2024

2024-11-16T02:29:29Z

← Older revision		Revision as of 02:29, 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
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	\| {{monzo\| 38 -2 -15 }}, {{monzo\| 71 -99 37 }}		\| {{monzo\| 38 -2 -15 }}, {{monzo\| 71 -99 37 }}
	\| {{mapping\| 1559 2471 3620 }}		\| {{mapping\| 1559 2471 3620 }}
	\| -0.0196		\| −0.0196
	\| 0.0155		\| 0.0155
	\| 2.01		\| 2.01
Line 39:		Line 31:
	\| 43046721/43025920, 78125000/78121827, 12884901888/12867859375		\| 43046721/43025920, 78125000/78121827, 12884901888/12867859375
	\| {{mapping\| 1559 2471 3620 4377 }}		\| {{mapping\| 1559 2471 3620 4377 }}
	\| -0.0376		\| −0.0376
	\| 0.0339		\| 0.0339
	\| 4.40		\| 4.40
Line 46:		Line 38:
	\| 3025/3024, 180224/180075, 50014503/50000000, 56953125/56942116		\| 3025/3024, 180224/180075, 50014503/50000000, 56953125/56942116
	\| {{mapping\| 1559 2471 3620 4377 5393 }}		\| {{mapping\| 1559 2471 3620 4377 5393 }}
	\| -0.0188		\| −0.0188
	\| 0.0483		\| 0.0483
	\| 6.27		\| 6.27
Line 53:		Line 45:
	\| 1716/1715, 3025/3024, 4096/4095, 492128/492075, 5282739/5281250		\| 1716/1715, 3025/3024, 4096/4095, 492128/492075, 5282739/5281250
	\| {{mapping\| 1559 2471 3620 4377 5393 5769 }}		\| {{mapping\| 1559 2471 3620 4377 5393 5769 }}
	\| -0.0162		\| −0.0162
	\| 0.0445		\| 0.0445
	\| 5.78		\| 5.78
	\|}		{{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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	\| 8000/6561		\| 8000/6561
	\| [[Raider]]		\| [[Raider]]
	\|}		{{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]]
	* "confluenceprettype" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/0jCzkUrwVEHevs7xAWgsvh Spotify] \| [https://francium223.bandcamp.com/track/confluenceprettype Bandcamp] \| [https://www.youtube.com/watch?v=4rxv7ec4BEM YouTube] – luna[25] in 1559edo tuning		* "confluenceprettype" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/0jCzkUrwVEHevs7xAWgsvh Spotify] \| [https://francium223.bandcamp.com/track/confluenceprettype Bandcamp] \| [https://www.youtube.com/watch?v=4rxv7ec4BEM YouTube] – luna[25] in 1559edo tuning

			[[Category:Listen]]

Francium at 12:09, 12 June 2024

2024-06-12T12:09:00Z

← Older revision		Revision as of 12:09, 12 June 2024
Line 80:		Line 80:
	\|}		\|}
	<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 ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "confluenceprettype" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/0jCzkUrwVEHevs7xAWgsvh Spotify] \| [https://francium223.bandcamp.com/track/confluenceprettype Bandcamp] \| [https://www.youtube.com/watch?v=4rxv7ec4BEM YouTube] – luna[25] in 1559edo tuning		* "confluenceprettype" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/0jCzkUrwVEHevs7xAWgsvh Spotify] \| [https://francium223.bandcamp.com/track/confluenceprettype Bandcamp] \| [https://www.youtube.com/watch?v=4rxv7ec4BEM YouTube] – luna[25] in 1559edo tuning

Francium: +music

2024-06-12T12:08:37Z

+music

← Older revision		Revision as of 12:08, 12 June 2024
Line 80:		Line 80:
	\|}		\|}
	<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]]
			* "confluenceprettype" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/0jCzkUrwVEHevs7xAWgsvh Spotify] \| [https://francium223.bandcamp.com/track/confluenceprettype Bandcamp] \| [https://www.youtube.com/watch?v=4rxv7ec4BEM YouTube] – luna[25] in 1559edo tuning

FloraC: Review

2024-05-19T07:44:13Z

Review

← Older revision		Revision as of 07:44, 19 May 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1559edo is [[consistent]] to the [[9-odd-limit]]. Using the patent val, it tempers out [[43046721/43025920]], [[78125000/78121827]] and {{monzo\|32 1 -6 -7}} in the 7-limit, [[3025/3024]], 180224/180075, 50014503/50000000 and 56953125/56942116 in the 11-limit~~. It [[support]]s [[luna]]~~.		1559edo is [[consistent]] to the [[9-odd-limit]]. Using the [[patent val]], it [[tempering out\|tempers out]] {{monzo\| 38 -2 -15 }} (luna comma) and {{monzo\| 71 -99 37 }} (raider comma) in the 5-limit; [[43046721/43025920]], [[78125000/78121827]] and {{monzo\| 32 1 -6 -7 }} in the 7-limit, [[3025/3024]], 180224/180075, 50014503/50000000 and 56953125/56942116 in the 11-limit.

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

	=== Subsets and supersets ===		=== Subsets and supersets ===
	1559edo is the 246th [[prime ~~EDO~~]].		1559edo is the 246th [[prime edo]].

	== 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" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|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
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\|2471 -1559}}		\| {{monzo\| 2471 -1559 }}
	\| {{mapping\|1559 2471}}		\| {{mapping\| 1559 2471 }}
	\| -0.0106		\| -0.0106
	\| 0.0106		\| 0.0106
Line 30:		Line 30:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{monzo\|38 -2 -15}}, {{monzo\|71 -99 37}}		\| {{monzo\| 38 -2 -15 }}, {{monzo\| 71 -99 37 }}
	\| {{mapping\|1559 2471 3620}}		\| {{mapping\| 1559 2471 3620 }}
	\| -0.0196		\| -0.0196
	\| 0.0155		\| 0.0155
Line 38:		Line 38:
	\| 2.3.5.7		\| 2.3.5.7
	\| 43046721/43025920, 78125000/78121827, 12884901888/12867859375		\| 43046721/43025920, 78125000/78121827, 12884901888/12867859375
	\| {{mapping\|1559 2471 3620 4377}}		\| {{mapping\| 1559 2471 3620 4377 }}
	\| -0.0376		\| -0.0376
	\| 0.0339		\| 0.0339
Line 45:		Line 45:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 3025/3024, 180224/180075, 50014503/50000000, 56953125/56942116		\| 3025/3024, 180224/180075, 50014503/50000000, 56953125/56942116
	\| {{mapping\|1559 2471 3620 4377 5393}}		\| {{mapping\| 1559 2471 3620 4377 5393 }}
	\| -0.0188		\| -0.0188
	\| 0.0483		\| 0.0483
Line 51:		Line 51:
	\|-		\|-
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 3025/3024~~, 1716/1715~~, 4096/4095, 492128/492075, 5282739/5281250		\| 1716/1715, 3025/3024, 4096/4095, 492128/492075, 5282739/5281250
	\| {{mapping\|1559 2471 3620 4377 5393 5769}}		\| {{mapping\| 1559 2471 3620 4377 5393 5769 }}
	\| -0.0162		\| -0.0162
	\| 0.0445		\| 0.0445
Line 79:		Line 79:
	\| [[Raider]]		\| [[Raider]]
	\|}		\|}

	<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

Francium: Created page with "{{Infobox ET}} {{EDO intro|1559}} == Theory == 1559edo is consistent to the 9-odd-limit. Using the patent val, it tempers out 43046721/43025920, 78125000/781218..."

2024-05-18T19:39:02Z

Created page with "{{Infobox ET}} {{EDO intro|1559}} == Theory == 1559edo is consistent to the 9-odd-limit. Using the patent val, it tempers out 43046721/43025920, 78125000/781218..."

New page

{{Infobox ET}}
{{EDO intro|1559}}

== Theory ==
1559edo is [[consistent]] to the [[9-odd-limit]]. Using the patent val, it tempers out [[43046721/43025920]], [[78125000/78121827]] and {{monzo|32 1 -6 -7}} in the 7-limit, [[3025/3024]], 180224/180075, 50014503/50000000 and 56953125/56942116 in the 11-limit. It [[support]]s [[luna]].

=== Prime harmonics ===
{{Harmonics in equal|1559}}

=== Subsets and supersets ===
1559edo is the 246th [[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|2471 -1559}}
| {{mapping|1559 2471}}
| -0.0106
| 0.0106
| 1.38
|-
| 2.3.5
| {{monzo|38 -2 -15}}, {{monzo|71 -99 37}}
| {{mapping|1559 2471 3620}}
| -0.0196
| 0.0155
| 2.01
|-
| 2.3.5.7
| 43046721/43025920, 78125000/78121827, 12884901888/12867859375
| {{mapping|1559 2471 3620 4377}}
| -0.0376
| 0.0339
| 4.40
|-
| 2.3.5.7.11
| 3025/3024, 180224/180075, 50014503/50000000, 56953125/56942116
| {{mapping|1559 2471 3620 4377 5393}}
| -0.0188
| 0.0483
| 6.27
|-
| 2.3.5.7.11.13
| 3025/3024, 1716/1715, 4096/4095, 492128/492075, 5282739/5281250
| {{mapping|1559 2471 3620 4377 5393 5769}}
| -0.0162
| 0.0445
| 5.78
|}

=== 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
| 251\1559
| 193.201
| 262144/234375
| [[Luna]]
|-
| 1
| 446\1559
| 343.297
| 8000/6561
| [[Raider]]
|}

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