1889edo - 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 98:		Line 98:
	\| [[Semidimi]]		\| [[Semidimi]]
	\|}		\|}
	<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 ==

FilterNashi at 09:02, 27 August 2025

2025-08-27T09:02:52Z

← Older revision		Revision as of 09:02, 27 August 2025
Line 5:		Line 5:

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1889\|columns=11}}		{{Harmonics in equal\|1889\|columns=9}}
			{{Harmonics in equal\|1889\|columns=9\|start=10\|title=Approximation of prime harmonics in 1889edo (continued)}}

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

Francium: /* Music */ +music

2025-07-05T11:57:50Z

Music: +music

← Older revision		Revision as of 11:57, 5 July 2025
Line 103:		Line 103:
	* "Scoop" from ''Scoop'' (2024) – [https://open.spotify.com/track/7stqQkZKeaaonzwH2rnhzH Spotify] \| [https://francium223.bandcamp.com/track/scoop Bandcamp] \| [https://www.youtube.com/watch?v=387kUkmHIrk YouTube]		* "Scoop" from ''Scoop'' (2024) – [https://open.spotify.com/track/7stqQkZKeaaonzwH2rnhzH Spotify] \| [https://francium223.bandcamp.com/track/scoop Bandcamp] \| [https://www.youtube.com/watch?v=387kUkmHIrk YouTube]
	* "The Technological Harbinger of Death" from ''Void'' (2025) – [https://open.spotify.com/track/3LDPz84VhVrTDgPLHQXWyJ YouTube] \| [https://francium223.bandcamp.com/track/the-technological-harbinger-of-death Bandcamp] \| [https://www.youtube.com/watch?v=CEeXQsHpCc8 YouTube]		* "The Technological Harbinger of Death" from ''Void'' (2025) – [https://open.spotify.com/track/3LDPz84VhVrTDgPLHQXWyJ YouTube] \| [https://francium223.bandcamp.com/track/the-technological-harbinger-of-death Bandcamp] \| [https://www.youtube.com/watch?v=CEeXQsHpCc8 YouTube]
			* "Don't Worry" from ''Don't'' (2025) – [https://open.spotify.com/track/3Kd1Ql1nYOBMhFWi94ljEP Spotify] \| [https://francium223.bandcamp.com/track/dont-worry Bandcamp] \| [https://www.youtube.com/watch?v=8CCFVZkxIgk YouTube]

	[[Category:Monzismic]]		[[Category:Monzismic]]

Francium: /* Music */ +music

2025-05-23T12:55:37Z

Music: +music

← Older revision		Revision as of 12:55, 23 May 2025
Line 102:		Line 102:
	; [[Francium]]		; [[Francium]]
	* "Scoop" from ''Scoop'' (2024) – [https://open.spotify.com/track/7stqQkZKeaaonzwH2rnhzH Spotify] \| [https://francium223.bandcamp.com/track/scoop Bandcamp] \| [https://www.youtube.com/watch?v=387kUkmHIrk YouTube]		* "Scoop" from ''Scoop'' (2024) – [https://open.spotify.com/track/7stqQkZKeaaonzwH2rnhzH Spotify] \| [https://francium223.bandcamp.com/track/scoop Bandcamp] \| [https://www.youtube.com/watch?v=387kUkmHIrk YouTube]
			* "The Technological Harbinger of Death" from ''Void'' (2025) – [https://open.spotify.com/track/3LDPz84VhVrTDgPLHQXWyJ YouTube] \| [https://francium223.bandcamp.com/track/the-technological-harbinger-of-death Bandcamp] \| [https://www.youtube.com/watch?v=CEeXQsHpCc8 YouTube]

	[[Category:Monzismic]]		[[Category:Monzismic]]

FloraC: /* Regular temperament properties */ cleanup

2025-03-02T15:54:47Z

Regular temperament properties: cleanup

← Older revision		Revision as of 15:54, 2 March 2025
Line 19:		Line 19:
	! 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 26:		Line 26:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\|2994 -1889}}		\| {{Monzo\| 2994 -1889 }}
	\| {{~~mapping~~\|1889 2994}}		\| {{Mapping\| 1889 2994 }}
	\| −0.0012		\| −0.0012
	\| 0.0012		\| 0.0012
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\|54 -37 2}}, {{monzo\|-66 -36 53}}		\| {{Monzo\| 54 -37 2 }}, {{monzo\| -66 -36 53 }}
	\| {{~~mapping~~\|1889 2994 4386}}		\| {{Mapping\| 1889 2994 4386 }}
	\| +0.0104		\| +0.0104
	\| 0.0163		\| 0.0163
Line 40:		Line 40:
	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, ~~3955078125/3954653486~~, {{monzo\|-57 16 10 3}}		\| 4375/4374, {{monzo\| -1 4 11 -1 }}, {{monzo\| -57 16 10 3 }}
	\| {{~~mapping~~\|1889 2994 4386 5303}}		\| {{Mapping\| 1889 2994 4386 5303 }}
	\| +0.0131		\| +0.0131
	\| 0.0149		\| 0.0149
Line 47:		Line 47:
	\|-		\|-
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 4375/4374, 151263/151250, 820125/819896, ~~1879453125/1879048192~~		\| 4375/4374, 151263/151250, 820125/819896, {{monzo\| -28 7 7 -1 1 }}
	\| {{~~mapping~~\|1889 2994 4386 5303 6535}}		\| {{Mapping\| 1889 2994 4386 5303 6535 }}
	\| +0.0055		\| +0.0055
	\| 0.0201		\| 0.0201
Line 54:		Line 54:
	\|-		\|-
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 4375/4374, ~~4225~~/~~4224~~, ~~6656~~/~~6655~~, 4100625/4100096~~, 151263/151250~~		\| 4225/4224, 4375/4374, 6656/6655, 151263/151250, 4100625/4100096
	\| {{~~mapping~~\|1889 2994 4386 5303 6535 6990}}		\| {{Mapping\| 1889 2994 4386 5303 6535 6990 }}
	\| +0.0084		\| +0.0084
	\| 0.0194		\| 0.0194
Line 61:		Line 61:
	\|-		\|-
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 4375/4374, 12376/12375~~, 4225/4224, 14400/14399~~, 14875/14872, 194481/194480		\| 4225/4224, 4375/4374, 6656/6655, 12376/12375, 14875/14872, 194481/194480
	\| {{~~mapping~~\|1889 2994 4386 5303 6535 6990 7721}}		\| {{Mapping\| 1889 2994 4386 5303 6535 6990 7721 }}
	\| +0.0120		\| +0.0120
	\| 0.0200		\| 0.0200
Line 68:		Line 68:
	\|-		\|-
	\| 2.3.5.7.11.13.17.19		\| 2.3.5.7.11.13.17.19
	\| 4375/4374~~, 12376/12375~~, 5985/5984, ~~4225~~/~~4224~~, ~~14400~~/~~14399~~, ~~6175~~/~~6174~~, 61965/61952		\| 4225/4224, 4375/4374, 5985/5984, 6175/6174, 6656/6655, 12376/12375, 61965/61952
	\| {{~~mapping~~\|1889 2994 4386 5303 6535 6990 7721 8024}}		\| {{Mapping\| 1889 2994 4386 5303 6535 6990 7721 8024 }}
	\| +0.0167		\| +0.0167
	\| 0.0226		\| 0.0226
Line 79:		Line 79:
	\|+ 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 88:		Line 88:
	\| 392\1889		\| 392\1889
	\| 249.021		\| 249.021
	\| {{~~monzo~~\|-26 18 1}}		\| {{Monzo\| -26 18 1 }}
	\| [[Monzismic]]		\| [[Monzismic]]
	\|-		\|-
Line 97:		Line 97:
	\| [[Semidimi]]		\| [[Semidimi]]
	\|}		\|}
	<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: +interval chapter

2025-03-02T14:46:29Z

+interval chapter

← Older revision		Revision as of 14:46, 2 March 2025
Line 9:		Line 9:
	=== Subsets and supersets ===		=== Subsets and supersets ===
	1889edo is the 290th [[prime edo]].		1889edo is the 290th [[prime edo]].

			== Intervals ==
			{{Main\|Table of 1889edo intervals}}

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

ArrowHead294 at 14:10, 20 February 2025

2025-02-20T14:10:36Z

← Older revision		Revision as of 14:10, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1889~~}}		{{ED intro}}
	== Theory ==		== Theory ==
	1889edo is strong in the [[23-limit]], though [[1578edo\|1578]], which among other things has a lower 23-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], rather puts it in the shade. It is distinctly [[consistent]] through the 27-odd-limit, but not, unlike 1578, to the 29-odd-limit. Even so, it should be noted that it supplies the [[optimal patent val]] for the 7-limit [[monzismic]] temperament.		1889edo is strong in the [[23-limit]], though [[1578edo\|1578]], which among other things has a lower 23-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], rather puts it in the shade. It is distinctly [[consistent]] through the 27-odd-limit, but not, unlike 1578, to the 29-odd-limit. Even so, it should be noted that it supplies the [[optimal patent val]] for the 7-limit [[monzismic]] temperament.
Line 12:		Line 12:
	== 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" \|[[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		! rowspan="2" \| [[Subgroup]]
	\|{{monzo\|2994 -1889}}		! rowspan="2" \| [[Comma list]]
	\|{{mapping\|1889 2994}}		! rowspan="2" \| [[Mapping]]
	\| -0.0012		! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
			\|-
			\| 2.3
			\| {{monzo\|2994 -1889}}
			\| {{mapping\|1889 2994}}
			\| −0.0012
	\| 0.0012		\| 0.0012
	\| 0.19		\| 0.19
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|54 -37 2}}, {{monzo\|-66 -36 53}}		\| {{monzo\|54 -37 2}}, {{monzo\|-66 -36 53}}
	\|{{mapping\|1889 2994 4386}}		\| {{mapping\|1889 2994 4386}}
	\| +0.0104		\| +0.0104
	\| 0.0163		\| 0.0163
	\| 2.57		\| 2.57
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|4375/4374, 3955078125/3954653486, {{monzo\|-57 16 10 3}}		\| 4375/4374, 3955078125/3954653486, {{monzo\|-57 16 10 3}}
	\|{{mapping\|1889 2994 4386 5303}}		\| {{mapping\|1889 2994 4386 5303}}
	\| +0.0131		\| +0.0131
	\| 0.0149		\| 0.0149
	\| 2.35		\| 2.35
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|4375/4374, 151263/151250, 820125/819896, 1879453125/1879048192		\| 4375/4374, 151263/151250, 820125/819896, 1879453125/1879048192
	\|{{mapping\|1889 2994 4386 5303 6535}}		\| {{mapping\|1889 2994 4386 5303 6535}}
	\| +0.0055		\| +0.0055
	\| 0.0201		\| 0.0201
	\| 3.16		\| 3.16
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|4375/4374, 4225/4224, 6656/6655, 4100625/4100096, 151263/151250		\| 4375/4374, 4225/4224, 6656/6655, 4100625/4100096, 151263/151250
	\|{{mapping\|1889 2994 4386 5303 6535 6990}}		\| {{mapping\|1889 2994 4386 5303 6535 6990}}
	\| +0.0084		\| +0.0084
	\| 0.0194		\| 0.0194
	\| 3.05		\| 3.05
	\|-		\|-
	\|2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\|4375/4374, 12376/12375, 4225/4224, 14400/14399, 14875/14872, 194481/194480		\| 4375/4374, 12376/12375, 4225/4224, 14400/14399, 14875/14872, 194481/194480
	\|{{mapping\|1889 2994 4386 5303 6535 6990 7721}}		\| {{mapping\|1889 2994 4386 5303 6535 6990 7721}}
	\| +0.0120		\| +0.0120
	\| 0.0200		\| 0.0200
	\| 3.15		\| 3.15
	\|-		\|-
	\|2.3.5.7.11.13.17.19		\| 2.3.5.7.11.13.17.19
	\|4375/4374, 12376/12375, 5985/5984, 4225/4224, 14400/14399, 6175/6174, 61965/61952		\| 4375/4374, 12376/12375, 5985/5984, 4225/4224, 14400/14399, 6175/6174, 61965/61952
	\|{{mapping\|1889 2994 4386 5303 6535 6990 7721 8024}}		\| {{mapping\|1889 2994 4386 5303 6535 6990 7721 8024}}
	\| +0.0167		\| +0.0167
	\| 0.0226		\| 0.0226
Line 73:		Line 74:
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		\|-
	! Generator~~<br>(reduced)~~*		! Periods<br />per 8ve
	! Cents~~<br>(reduced)~~*		! Generator*
	! Associated<br>~~Ratio~~*		! Cents*
			! Associated<br />ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|392\1889		\| 392\1889
	\|249.021		\| 249.021
	\|{{monzo\|-26 18 1}}		\| {{monzo\|-26 18 1}}
	\|[[Monzismic]]		\| [[Monzismic]]
	\|-		\|-
	\|1		\| 1
	\|707\1889		\| 707\1889
	\|449.127		\| 449.127
	\|35/27		\| 35/27
	\|[[Semidimi]]		\| [[Semidimi]]
	\|}		\|}
			<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

Francium: +music

2024-11-10T14:40:45Z

+music

← Older revision		Revision as of 14:40, 10 November 2024
Line 92:		Line 92:
	\|[[Semidimi]]		\|[[Semidimi]]
	\|}		\|}

			== Music ==
			; [[Francium]]
			* "Scoop" from ''Scoop'' (2024) – [https://open.spotify.com/track/7stqQkZKeaaonzwH2rnhzH Spotify] \| [https://francium223.bandcamp.com/track/scoop Bandcamp] \| [https://www.youtube.com/watch?v=387kUkmHIrk YouTube]

	[[Category:Monzismic]]		[[Category:Monzismic]]

Eliora: sectioning

2023-12-02T11:18:13Z

sectioning

← Older revision		Revision as of 11:18, 2 December 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1889}}		{{EDO intro\|1889}}
			== Theory ==
	1889edo is strong in the [[23-limit]], though [[1578edo\|1578]], which among other things has a lower 23-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], rather puts it in the shade. It is distinctly [[consistent]] through the 27-odd-limit, but not, unlike 1578, to the 29-odd-limit. Even so, it should be noted that it supplies the [[optimal patent val]] for the 7-limit [[monzismic]] temperament.		1889edo is strong in the [[23-limit]], though [[1578edo\|1578]], which among other things has a lower 23-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], rather puts it in the shade. It is distinctly [[consistent]] through the 27-odd-limit, but not, unlike 1578, to the 29-odd-limit. Even so, it should be noted that it supplies the [[optimal patent val]] for the 7-limit [[monzismic]] temperament.

Francium: /* Regular temperament properties */

2023-12-01T15:13:28Z

Regular temperament properties

← Older revision		Revision as of 15:13, 1 December 2023
Line 26:		Line 26:
	\| -0.0012		\| -0.0012
	\| 0.0012		\| 0.0012
	\| 0.~~1889~~		\| 0.19
	\|-		\|-
	\|2.3.5		\|2.3.5