1289edo - 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"

2026-03-13T13:32:11Z

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 101:		Line 101:
	\| [[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: /* Music */ +music

2025-04-17T11:36:20Z

Music: +music

← Older revision		Revision as of 11:36, 17 April 2025
Line 106:		Line 106:
	; [[Francium]]		; [[Francium]]
	* "Baking With Honey" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/4MS4KuEo2jocbD1F968mBE Spotify] \| [https://francium223.bandcamp.com/track/baking-with-honey Bandcamp] \| [https://www.youtube.com/watch?v=mh0-dZt9NI8 YouTube] – in Honeybrookic, 1289edo tuning		* "Baking With Honey" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/4MS4KuEo2jocbD1F968mBE Spotify] \| [https://francium223.bandcamp.com/track/baking-with-honey Bandcamp] \| [https://www.youtube.com/watch?v=mh0-dZt9NI8 YouTube] – in Honeybrookic, 1289edo tuning
			* "Those Peas, With That Hat?" from ''Questions, Vol. 2'' (2025) – [https://open.spotify.com/track/3huEuNHvcAeKM6smXRSALR Spotify] \| [https://francium223.bandcamp.com/track/those-peas-with-that-hat Bandcamp] \| [https://www.youtube.com/watch?v=6us1wSQjn7w YouTube]

Francium: changed EDO intro to ED intro

2025-02-21T06:16:08Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:16, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1289~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:48, 15 January 2025

2025-01-15T18:48:30Z

← Older revision		Revision as of 18:48, 15 January 2025
Line 33:		Line 33:
	\| {{monzo\|-16 35 -17}}, {{monzo\|91 -12 -31}}		\| {{monzo\|-16 35 -17}}, {{monzo\|91 -12 -31}}
	\| {{mapping\|1289 2043 2993}}		\| {{mapping\|1289 2043 2993}}
	\| ~~−0~~.0014		\| −0.0014
	\| 0.0097		\| 0.0097
	\| 1.04		\| 1.04
Line 40:		Line 40:
	\| 2460375/2458624, 78125000/78121827, 12884901888/12867859375		\| 2460375/2458624, 78125000/78121827, 12884901888/12867859375
	\| {{mapping\|1289 2043 2993 3619}}		\| {{mapping\|1289 2043 2993 3619}}
	\| ~~−0~~.0275		\| −0.0275
	\| 0.0461		\| 0.0461
	\| 4.95		\| 4.95
Line 47:		Line 47:
	\| 3025/3024, 180224/180075, 2460375/2458624, 50014503/50000000		\| 3025/3024, 180224/180075, 2460375/2458624, 50014503/50000000
	\| {{mapping\|1289 2043 2993 3619 4459}}		\| {{mapping\|1289 2043 2993 3619 4459}}
	\| ~~−0~~.0109		\| −0.0109
	\| 0.0530		\| 0.0530
	\| 5.69		\| 5.69
Line 54:		Line 54:
	\| 3025/3024, 1716/1715, 4096/4095, 91125/91091, 5282739/5281250		\| 3025/3024, 1716/1715, 4096/4095, 91125/91091, 5282739/5281250
	\| {{mapping\|1289 2043 2993 3619 4459 4770}}		\| {{mapping\|1289 2043 2993 3619 4459 4770}}
	\| ~~−0~~.0146		\| −0.0146
	\| 0.0491		\| 0.0491
	\| 5.27		\| 5.27
Line 61:		Line 61:
	\| 3025/3024, 1716/1715, 4096/4095, 2500/2499, 37180/37179, 3536379/3536000		\| 3025/3024, 1716/1715, 4096/4095, 2500/2499, 37180/37179, 3536379/3536000
	\| {{mapping\|1289 2043 2993 3619 4459 4770 5269}}		\| {{mapping\|1289 2043 2993 3619 4459 4770 5269}}
	\| ~~−0~~.0210		\| −0.0210
	\| 0.0481		\| 0.0481
	\| 5.17		\| 5.17
Line 68:		Line 68:
	\| 3025/3024, 1716/1715, 2376/2375, 4096/4095, 2500/2499, 270864/270725, 75735/75712		\| 3025/3024, 1716/1715, 2376/2375, 4096/4095, 2500/2499, 270864/270725, 75735/75712
	\| {{mapping\|1289 2043 2993 3619 4459 4770 5269 5476}}		\| {{mapping\|1289 2043 2993 3619 4459 4770 5269 5476}}
	\| ~~−0~~.0299		\| −0.0299
	\| 0.0508		\| 0.0508
	\| 5.46		\| 5.46
Line 101:		Line 101:
	\| [[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]]
	* "Baking With Honey" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/4MS4KuEo2jocbD1F968mBE Spotify] \| [https://francium223.bandcamp.com/track/baking-with-honey Bandcamp] \| [https://www.youtube.com/watch?v=mh0-dZt9NI8 YouTube] – in Honeybrookic, 1289edo tuning		* "Baking With Honey" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/4MS4KuEo2jocbD1F968mBE Spotify] \| [https://francium223.bandcamp.com/track/baking-with-honey Bandcamp] \| [https://www.youtube.com/watch?v=mh0-dZt9NI8 YouTube] – in Honeybrookic, 1289edo tuning

Francium: +music

2025-01-12T12:41:43Z

+music

← Older revision		Revision as of 12:41, 12 January 2025
Line 102:		Line 102:
	\|}		\|}
	<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]]
			* "Baking With Honey" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/4MS4KuEo2jocbD1F968mBE Spotify] \| [https://francium223.bandcamp.com/track/baking-with-honey Bandcamp] \| [https://www.youtube.com/watch?v=mh0-dZt9NI8 YouTube] – in Honeybrookic, 1289edo tuning

ArrowHead294: Partial undo

2024-11-16T12:53:49Z

Partial undo

← Older revision		Revision as of 12:53, 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
Line 65:		Line 74:

	=== 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 84:		Line 100:
	\| 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 03:20, 16 November 2024

2024-11-16T03:20:46Z

← Older revision		Revision as of 03:20, 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
Line 32:		Line 24:
	\| {{monzo\|-16 35 -17}}, {{monzo\|91 -12 -31}}		\| {{monzo\|-16 35 -17}}, {{monzo\|91 -12 -31}}
	\| {{mapping\|1289 2043 2993}}		\| {{mapping\|1289 2043 2993}}
	\| -0.0014		\| −0.0014
	\| 0.0097		\| 0.0097
	\| 1.04		\| 1.04
Line 39:		Line 31:
	\| 2460375/2458624, 78125000/78121827, 12884901888/12867859375		\| 2460375/2458624, 78125000/78121827, 12884901888/12867859375
	\| {{mapping\|1289 2043 2993 3619}}		\| {{mapping\|1289 2043 2993 3619}}
	\| -0.0275		\| −0.0275
	\| 0.0461		\| 0.0461
	\| 4.95		\| 4.95
Line 46:		Line 38:
	\| 3025/3024, 180224/180075, 2460375/2458624, 50014503/50000000		\| 3025/3024, 180224/180075, 2460375/2458624, 50014503/50000000
	\| {{mapping\|1289 2043 2993 3619 4459}}		\| {{mapping\|1289 2043 2993 3619 4459}}
	\| -0.0109		\| −0.0109
	\| 0.0530		\| 0.0530
	\| 5.69		\| 5.69
Line 53:		Line 45:
	\| 3025/3024, 1716/1715, 4096/4095, 91125/91091, 5282739/5281250		\| 3025/3024, 1716/1715, 4096/4095, 91125/91091, 5282739/5281250
	\| {{mapping\|1289 2043 2993 3619 4459 4770}}		\| {{mapping\|1289 2043 2993 3619 4459 4770}}
	\| -0.0146		\| −0.0146
	\| 0.0491		\| 0.0491
	\| 5.27		\| 5.27
Line 60:		Line 52:
	\| 3025/3024, 1716/1715, 4096/4095, 2500/2499, 37180/37179, 3536379/3536000		\| 3025/3024, 1716/1715, 4096/4095, 2500/2499, 37180/37179, 3536379/3536000
	\| {{mapping\|1289 2043 2993 3619 4459 4770 5269}}		\| {{mapping\|1289 2043 2993 3619 4459 4770 5269}}
	\| -0.0210		\| −0.0210
	\| 0.0481		\| 0.0481
	\| 5.17		\| 5.17
Line 67:		Line 59:
	\| 3025/3024, 1716/1715, 2376/2375, 4096/4095, 2500/2499, 270864/270725, 75735/75712		\| 3025/3024, 1716/1715, 2376/2375, 4096/4095, 2500/2499, 270864/270725, 75735/75712
	\| {{mapping\|1289 2043 2993 3619 4459 4770 5269 5476}}		\| {{mapping\|1289 2043 2993 3619 4459 4770 5269 5476}}
	\| -0.0299		\| −0.0299
	\| 0.0508		\| 0.0508
	\| 5.46		\| 5.46
Line 73:		Line 65:

	=== 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
Line 98:		Line 84:
	\| 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~~

FloraC: /* Theory */ nullity-1 temps are best given by commas

2024-11-08T12:52:52Z

Theory: nullity-1 temps are best given by commas

← Older revision		Revision as of 12:52, 8 November 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1289edo is [[consistent]] to the [[9-odd-limit]]. Using the [[patent val]], it [[tempering out\|tempers out]] [[3025/3024]], 180224/180075, [[2460375/2458624]] and 50014503/50000000 in the [[11-limit]]; ~~3025/3024,~~ [[1716/1715]], [[4096/4095]], 91125/91091 and 5282739/5281250 in the [[13-limit]]. It [[~~support]]s [[honeybrookic~~]], [[~~totziensismic]] and [[minortone~~]].		1289edo is [[consistent]] to the [[9-odd-limit]]. As an equal temperament, it tempers out {{monzo\| -16 35 -17 }} ([[minortone comma]]) in the 5-limit. Using the [[patent val]], it [[tempering out\|tempers out]] [[3025/3024]], 180224/180075, [[2460375/2458624]] and 50014503/50000000 in the [[11-limit]]; [[1716/1715]], [[4096/4095]], 91125/91091 and 5282739/5281250 in the [[13-limit]]. In the 2.3.13.23.29.31 subgroup it tempers out [[19344/19343]], in the 2.3.5.7.11.23.31 subgroup [[19251/19250]].

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

	=== Subsets and supersets ===		=== Subsets and supersets ===
	1289edo is the 209th [[prime ~~EDO~~]].		1289edo is the 209th [[prime edo]].

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

Francium: Created page with "{{Infobox ET}} {{EDO intro|1289}} == Theory == 1289edo is consistent to the 9-odd-limit. Using the patent val, it tempers out 3025/3024, 180..."

2024-10-28T10:57:47Z

Created page with "{{Infobox ET}} {{EDO intro|1289}} == Theory == 1289edo is consistent to the 9-odd-limit. Using the patent val, it tempers out 3025/3024, 180..."

New page

{{Infobox ET}}
{{EDO intro|1289}}

== Theory ==
1289edo is [[consistent]] to the [[9-odd-limit]]. Using the [[patent val]], it [[tempering out|tempers out]] [[3025/3024]], 180224/180075, [[2460375/2458624]] and 50014503/50000000 in the [[11-limit]]; 3025/3024, [[1716/1715]], [[4096/4095]], 91125/91091 and 5282739/5281250 in the [[13-limit]]. It [[support]]s [[honeybrookic]], [[totziensismic]] and [[minortone]].

=== Prime harmonics ===
{{Harmonics in equal|1289}}

=== Subsets and supersets ===
1289edo is the 209th [[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|-2043 1289}}
| {{mapping|1289 2043}}
| +0.0049
| 0.0049
| 0.53
|-
| 2.3.5
| {{monzo|-16 35 -17}}, {{monzo|91 -12 -31}}
| {{mapping|1289 2043 2993}}
| -0.0014
| 0.0097
| 1.04
|-
| 2.3.5.7
| 2460375/2458624, 78125000/78121827, 12884901888/12867859375
| {{mapping|1289 2043 2993 3619}}
| -0.0275
| 0.0461
| 4.95
|-
| 2.3.5.7.11
| 3025/3024, 180224/180075, 2460375/2458624, 50014503/50000000
| {{mapping|1289 2043 2993 3619 4459}}
| -0.0109
| 0.0530
| 5.69
|-
| 2.3.5.7.11.13
| 3025/3024, 1716/1715, 4096/4095, 91125/91091, 5282739/5281250
| {{mapping|1289 2043 2993 3619 4459 4770}}
| -0.0146
| 0.0491
| 5.27
|-
| 2.3.5.7.11.13.17
| 3025/3024, 1716/1715, 4096/4095, 2500/2499, 37180/37179, 3536379/3536000
| {{mapping|1289 2043 2993 3619 4459 4770 5269}}
| -0.0210
| 0.0481
| 5.17
|-
| 2.3.5.7.11.13.17.19
| 3025/3024, 1716/1715, 2376/2375, 4096/4095, 2500/2499, 270864/270725, 75735/75712
| {{mapping|1289 2043 2993 3619 4459 4770 5269 5476}}
| -0.0299
| 0.0508
| 5.46
|}

=== 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
| 142\1289
| 132.196
| {{monzo|-38 5 13}}
| [[Astro]]
|-
| 1
| 196\1289
| 182.467
| 10/9
| [[Minortone]]
|-
| 1
| 238\1289
| 221.567
| 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