1277edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave" to "Octave-reduced form, reduced to the first half-octave"

2026-03-13T13:34:34Z

Text replacement - "Octave-reduced form, reduced to the first half-octave" to "Octave-reduced form, reduced to the first half-octave"

← Older revision		Revision as of 13:34, 13 March 2026
Line 80:		Line 80:
	\| [[Supermajor (temperament)\|Supermajor]]		\| [[Supermajor (temperament)\|Supermajor]]
	\|}		\|}
	<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[Normal forms\|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 form]] in parentheses if distinct

	== Music ==		== Music ==

FloraC: Cleanup

2025-10-27T13:18:03Z

Cleanup

← Older revision		Revision as of 13:18, 27 October 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1277edo is [[consistent]] to the [[11-odd-limit]]. ~~The~~ equal temperament [[tempering out\|tempers out]] [[4375/4374]], 52734375/52706752, 645700815/645657712 ([[starscape comma]]) and {{monzo\| 51 -13 -1 -10 }} ([[technologisma]]) in the 7-limit; 151263/151250, 759375/758912, and 2097152/2096325 in the 11-limit. It [[support]]s [[monzismic]], [[supermajor]], [[revopent]], as well as the rank-3 temperament [[bragi]].		1277edo is [[consistent]] to the [[11-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] [[4375/4374]], 52734375/52706752, 645700815/645657712 ([[starscape comma]]) and {{monzo\| 51 -13 -1 -10 }} ([[technologisma]]) in the 7-limit; 151263/151250, 759375/758912, and 2097152/2096325 in the 11-limit. It [[support]]s [[monzismic]], [[supermajor (temperament)\|supermajor]], [[revopent]], as well as the rank-3 temperament [[bragi]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 17:		Line 17:
	! 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 24:		Line 24:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| 2024 -1277 }}		\| {{Monzo\| 2024 -1277 }}
	\| {{~~mapping~~\| 1277 2024 }}		\| {{Mapping\| 1277 2024 }}
	\| −0.0009		\| −0.0009
	\| 0.0009		\| 0.0009
Line 31:		Line 31:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| 54 -37 2 }}, {{monzo\| -67 -9 35 }}		\| {{Monzo\| 54 -37 2 }}, {{monzo\| -67 -9 35 }}
	\| {{~~mapping~~\| 1277 2024 2965 }}		\| {{Mapping\| 1277 2024 2965 }}
	\| +0.0132		\| +0.0132
	\| 0.0199		\| 0.0199
Line 39:		Line 39:
	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, 52734375/52706752, {{monzo\| 51 -13 -1 -10 }}		\| 4375/4374, 52734375/52706752, {{monzo\| 51 -13 -1 -10 }}
	\| {{~~mapping~~\| 1277 2024 2965 3585 }}		\| {{Mapping\| 1277 2024 2965 3585 }}
	\| +0.0093		\| +0.0093
	\| 0.0186		\| 0.0186
Line 46:		Line 46:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 4375/4374, 151263/151250, 759375/758912, 2097152/2096325		\| 4375/4374, 151263/151250, 759375/758912, 2097152/2096325
	\| {{~~mapping~~\| 1277 2024 2965 3585 4418 }}		\| {{Mapping\| 1277 2024 2965 3585 4418 }}
	\| −0.0092		\| −0.0092
	\| 0.0405		\| 0.0405
Line 56:		Line 56:
	\|+ 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 65:		Line 65:
	\| 265\1277		\| 265\1277
	\| 249.021		\| 249.021
	\| {{~~monzo~~\| -27 11 3 1 }}		\| {{Monzo\| -27 11 3 1 }}
	\| [[Monzismic]]		\| [[Monzismic]]
	\|-		\|-
Line 78:		Line 78:
	\| 435.082		\| 435.082
	\| 9/7		\| 9/7
	\| [[Supermajor]]		\| [[Supermajor (temperament)\|Supermajor]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[Normal ~~lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[Normal forms\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "mututhery" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] \| [https://francium223.bandcamp.com/track/mututhery Bandcamp] \| [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] – in Monzismic[19], 1277edo tuning		* "mututhery" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] \| [https://francium223.bandcamp.com/track/mututhery Bandcamp] \| [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] – in Monzismic[19], 1277edo tuning
	* "Makeup Is Soothing." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/6SJHf64ENaPnzQKlnO315x Spotify] \| [https://francium223.bandcamp.com/track/makeup-is-soothing Bandcamp] \| [https://www.youtube.com/watch?v=zw1oavPPnqU YouTube] – in ~~Aunusic~~, 1277edo tuning		* "Makeup Is Soothing." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/6SJHf64ENaPnzQKlnO315x Spotify] \| [https://francium223.bandcamp.com/track/makeup-is-soothing Bandcamp] \| [https://www.youtube.com/watch?v=zw1oavPPnqU YouTube] – in aunusic, 1277edo tuning

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

Francium: changed EDO intro to ED intro

2025-02-19T18:09:44Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:09, 19 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1277~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: /* Music */ +music

2025-02-16T13:11:57Z

Music: +music

← Older revision		Revision as of 13:11, 16 February 2025
Line 84:		Line 84:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "mututhery" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] \| [https://francium223.bandcamp.com/track/mututhery Bandcamp] \| [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] – ~~monzismic~~[19] in 1277edo tuning		* "mututhery" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] \| [https://francium223.bandcamp.com/track/mututhery Bandcamp] \| [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] – in Monzismic[19], 1277edo tuning
			* "Makeup Is Soothing." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/6SJHf64ENaPnzQKlnO315x Spotify] \| [https://francium223.bandcamp.com/track/makeup-is-soothing Bandcamp] \| [https://www.youtube.com/watch?v=zw1oavPPnqU YouTube] – in Aunusic, 1277edo tuning

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

ArrowHead294 at 18:03, 15 January 2025

2025-01-15T18:03:08Z

← Older revision		Revision as of 18:03, 15 January 2025
Line 26:		Line 26:
	\| {{monzo\| 2024 -1277 }}		\| {{monzo\| 2024 -1277 }}
	\| {{mapping\| 1277 2024 }}		\| {{mapping\| 1277 2024 }}
	\| ~~−0~~.0009		\| −0.0009
	\| 0.0009		\| 0.0009
	\| 0.10		\| 0.10
Line 47:		Line 47:
	\| 4375/4374, 151263/151250, 759375/758912, 2097152/2096325		\| 4375/4374, 151263/151250, 759375/758912, 2097152/2096325
	\| {{mapping\| 1277 2024 2965 3585 4418 }}		\| {{mapping\| 1277 2024 2965 3585 4418 }}
	\| ~~−0~~.0092		\| −0.0092
	\| 0.0405		\| 0.0405
	\| 4.31		\| 4.31
Line 80:		Line 80:
	\| [[Supermajor]]		\| [[Supermajor]]
	\|}		\|}
	<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]]
	* "mututhery" from ''albumwithoutspaces'' (2024) ~~–~~ [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] \| [https://francium223.bandcamp.com/track/mututhery Bandcamp] \| [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] ~~–~~ monzismic[19] in 1277edo tuning		* "mututhery" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] \| [https://francium223.bandcamp.com/track/mututhery Bandcamp] \| [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] – monzismic[19] in 1277edo tuning

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

ArrowHead294: Partial undo

2024-11-16T13:04:14Z

Partial undo

← Older revision		Revision as of 13:04, 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 41:		Line 50:
	\| 0.0405		\| 0.0405
	\| 4.31		\| 4.31
	~~{{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 63:		Line 79:
	\| 9/7		\| 9/7
	\| [[Supermajor]]		\| [[Supermajor]]
	~~{{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 02:41, 16 November 2024

2024-11-16T02:41:40Z

← Older revision		Revision as of 02:41, 16 November 2024
Line 69:		Line 69:
	; [[Francium]]		; [[Francium]]
	* "mututhery" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] \| [https://francium223.bandcamp.com/track/mututhery Bandcamp] \| [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] – monzismic[19] in 1277edo tuning		* "mututhery" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] \| [https://francium223.bandcamp.com/track/mututhery Bandcamp] \| [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] – monzismic[19] in 1277edo tuning

			[[Category:Listen]]

ArrowHead294 at 02:41, 16 November 2024

2024-11-16T02:41:29Z

← Older revision		Revision as of 02:41, 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\| 2024 -1277 }}		\| {{monzo\| 2024 -1277 }}
	\| {{mapping\| 1277 2024 }}		\| {{mapping\| 1277 2024 }}
	\| -0.0009		\| −0.0009
	\| 0.0009		\| 0.0009
	\| 0.10		\| 0.10
Line 46:		Line 38:
	\| 4375/4374, 151263/151250, 759375/758912, 2097152/2096325		\| 4375/4374, 151263/151250, 759375/758912, 2097152/2096325
	\| {{mapping\| 1277 2024 2965 3585 4418 }}		\| {{mapping\| 1277 2024 2965 3585 4418 }}
	\| -0.0092		\| −0.0092
	\| 0.0405		\| 0.0405
	\| 4.31		\| 4.31
	\|}		{{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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	\| 9/7		\| 9/7
	\| [[Supermajor]]		\| [[Supermajor]]
	\|}		{{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]]
	* "mututhery" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] \| [https://francium223.bandcamp.com/track/mututhery Bandcamp] \| [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] – monzismic[19] in 1277edo tuning		* "mututhery" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] \| [https://francium223.bandcamp.com/track/mututhery Bandcamp] \| [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] – monzismic[19] in 1277edo tuning

Francium: +music

2024-06-09T13:07:29Z

+music

← Older revision		Revision as of 13:07, 9 June 2024
Line 79:		Line 79:
	\|}		\|}
	<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]]
			* "mututhery" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6EUbC14BVFJ20b1C4cCOFe Spotify] \| [https://francium223.bandcamp.com/track/mututhery Bandcamp] \| [https://www.youtube.com/watch?v=0j7yaypCOts YouTube] – monzismic[19] in 1277edo tuning

FloraC: Review. The listing of temps was particularly lame.

2024-05-17T10:56:34Z

Review. The listing of temps was particularly lame.

← Older revision		Revision as of 10:56, 17 May 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1277edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out\|tempers out]] [[4375/4374]], 52734375/52706752 and {{monzo\|51 -13 -1 -10}} in the 7-limit; ~~4375~~/~~4374~~, 759375/758912, ~~151263/151250~~ and 2097152/2096325 in the 11-limit. It [[support]]s [[~~nanismic~~]], [[~~nanic]], [[ragismic]], [[bragi]], [[revopentic~~]], [[revopent]], ~~[[sasaquinbizo~~-~~atriyo]],~~ [[~~starscape]], [[nommismic]], [[technologismic]], [[supermajor]] and [[monzismic~~]].		1277edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out\|tempers out]] [[4375/4374]], 52734375/52706752, 645700815/645657712 ([[starscape comma]]) and {{monzo\| 51 -13 -1 -10 }} ([[technologisma]]) in the 7-limit; 151263/151250, 759375/758912, and 2097152/2096325 in the 11-limit. It [[support]]s [[monzismic]], [[supermajor]], [[revopent]], as well as the rank-3 temperament [[bragi]].

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

	=== Subsets and supersets ===		=== Subsets and supersets ===
	1277edo is the 206th [[prime ~~EDO~~]].		1277edo is the 206th [[prime edo]]. [[2554edo]], which divides the edostep in two, is the smallest edo [[distinctly consistent]] through the [[41-odd-limit]], and provides correction for harmonics 11 through 41.

	[[2554edo]], which divides the edostep in two, is the smallest ~~EDO~~ [[distinctly consistent]] through the [[41-odd-limit]], ~~hence~~ provides correction for harmonics 11 through 41.

	== 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\|2024 -1277}}		\| {{monzo\| 2024 -1277 }}
	\|{{mapping\|1277 2024}}		\| {{mapping\| 1277 2024 }}
	\| -0.0009		\| -0.0009
	\| 0.0009		\| 0.0009
	\| 0.10		\| 0.10
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|54 -37 2}}, {{monzo\|-67 -9 35}}		\| {{monzo\| 54 -37 2 }}, {{monzo\| -67 -9 35 }}
	\|{{mapping\|1277 2024 2965}}		\| {{mapping\| 1277 2024 2965 }}
	\| +0.0132		\| +0.0132
	\| 0.0199		\| 0.0199
	\| 2.12		\| 2.12
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|4375/4374, 52734375/52706752, {{monzo\|51 -13 -1 -10}}		\| 4375/4374, 52734375/52706752, {{monzo\| 51 -13 -1 -10 }}
	\|{{mapping\|1277 2024 2965 3585}}		\| {{mapping\| 1277 2024 2965 3585 }}
	\| +0.0093		\| +0.0093
	\| 0.0186		\| 0.0186
	\| 1.98		\| 1.98
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|4375/4374, 759375/758912~~, 151263/151250~~, 2097152/2096325		\| 4375/4374, 151263/151250, 759375/758912, 2097152/2096325
	\|{{mapping\|1277 2024 2965 3585 4418}}		\| {{mapping\| 1277 2024 2965 3585 4418 }}
	\| -0.0092		\| -0.0092
	\| 0.0405		\| 0.0405
Line 62:		Line 60:
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|265\1277		\| 265\1277
	\|249.021		\| 249.021
	\|{{monzo\|-27 11 3 1}}		\| {{monzo\| -27 11 3 1 }}
	\|[[Monzismic]]		\| [[Monzismic]]
	\|-		\|-
	\|1		\| 1
	\|380\1277		\| 380\1277
	\|357.087		\| 357.087
	\|768/625		\| 768/625
	\|[[Dodifo]]		\| [[Dodifo]]
	\|-		\|-
	\|1		\| 1
	\|463\1277		\| 463\1277
	\|435.082		\| 435.082
	\|9/7		\| 9/7
	\|[[Supermajor]]		\| [[Supermajor]]
	\|}		\|}

	<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