2777edo - Revision history

ArrowHead294 at 12:46, 21 February 2025

2025-02-21T12:46:46Z

← Older revision		Revision as of 12:46, 21 February 2025
Line 13:		Line 13:
	== 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" \| [[Subgroup]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \|Optimal<br>8ve ~~Stretch~~ (¢)		! rowspan="2" \| [[Mapping]]
	! colspan="2" \|Tuning ~~Error~~		! rowspan="2" \| Optimal<br />8ve stretch (¢)
	\|-		! colspan="2" \| Tuning error
	![[TE error\|Absolute]] (¢)		\|-
	![[TE simple badness\|Relative]] (%)		! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.9		\| 2.9
	\| {{monzo\|8803 -2777}}		\| {{monzo\|8803 -2777}}
	\| {{mapping\|2777 8803}}		\| {{mapping\|2777 8803}}
	\| -0.0081		\| −0.0081
	\| 0.0081		\| 0.0081
	\| 1.87		\| 1.87
Line 32:		Line 33:
	\| {{monzo\|146 -38 -11}}, {{monzo\|-89 -21 67}}		\| {{monzo\|146 -38 -11}}, {{monzo\|-89 -21 67}}
	\| {{mapping\|2777 8803 6448}}		\| {{mapping\|2777 8803 6448}}
	\| -0.0057		\| −0.0057
	\| 0.0074		\| 0.0074
	\| 1.71		\| 1.71
Line 39:		Line 40:
	\| {{monzo\|2 -10 14 -1}}, {{monzo\|-1 -9 -3 13}}, {{monzo\|-48 0 11 8}}		\| {{monzo\|2 -10 14 -1}}, {{monzo\|-1 -9 -3 13}}, {{monzo\|-48 0 11 8}}
	\| {{mapping\|2777 8803 6448 7796}}		\| {{mapping\|2777 8803 6448 7796}}
	\| -0.0033		\| −0.0033
	\| 0.0076		\| 0.0076
	\| 1.76		\| 1.76
Line 46:		Line 47:
	\| 151263/151250, 184549376/184528125, 35156250/35153041, 3487704605/3486784401		\| 151263/151250, 184549376/184528125, 35156250/35153041, 3487704605/3486784401
	\| {{mapping\|2777 8803 6448 7796 9607}}		\| {{mapping\|2777 8803 6448 7796 9607}}
	\| -0.0066		\| −0.0066
	\| 0.0095		\| 0.0095
	\| 2.20		\| 2.20
Line 53:		Line 54:
	\| 123201/123200, 6656/6655, 151263/151250, 8859375/8859136, 43061200/43046721		\| 123201/123200, 6656/6655, 151263/151250, 8859375/8859136, 43061200/43046721
	\| {{mapping\|2777 8803 6448 7796 9607 10276}}		\| {{mapping\|2777 8803 6448 7796 9607 10276}}
	\| -0.0032		\| −0.0032
	\| 0.0116		\| 0.0116
	\| 2.68		\| 2.68
Line 60:		Line 61:
	\| 12376/12375, 14400/14399, 123201/123200, 194481/194480, 4685824/4685625, 81331250/81310473		\| 12376/12375, 14400/14399, 123201/123200, 194481/194480, 4685824/4685625, 81331250/81310473
	\| {{mapping\|2777 8803 6448 7796 9607 10276 11351}}		\| {{mapping\|2777 8803 6448 7796 9607 10276 11351}}
	\| -0.0045		\| −0.0045
	\| 0.0112		\| 0.0112
	\| 2.59		\| 2.59

Francium: changed EDO intro to ED intro

2025-02-21T06:02:02Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:02, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|2777~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: +music

2024-12-01T12:49:13Z

+music

← Older revision		Revision as of 12:49, 1 December 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	2777edo is [[consistent]] to the [[7-odd-limit]] and its [[harmonic]] [[3/1\|3]] is about halfway its steps. Using the 2.9.5.7.11.13.17.23.29.31 [[subgroup]], it [[tempering out\|tempers out]] [[12376/12375]], [[14400/14399]], [[25025/25024]], [[123201/123200]], 20736/20735, [[194481/194480]], 16445/16443, 27625/27621 and 23716/23715. Using the ~~no-3-or-19~~ 23~~-limit~~ subgroup, it tempers out [[25025/25024]].		2777edo is [[consistent]] to the [[7-odd-limit]] and its [[harmonic]] [[3/1\|3]] is about halfway its steps. Using the 2.9.5.7.11.13.17.23.29.31 [[subgroup]], it [[tempering out\|tempers out]] [[12376/12375]], [[14400/14399]], [[25025/25024]], [[123201/123200]], 20736/20735, [[194481/194480]], 16445/16443, 27625/27621 and 23716/23715. Using the 2.5.7.11.13.17.23 subgroup, it tempers out [[25025/25024]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 64:		Line 64:
	\| 2.59		\| 2.59
	\|}		\|}

			== Music ==
			; [[Francium]]
			* "Joekalille" from ''Naughty Girl Era'' (2024) − [https://open.spotify.com/track/3JkOxSgwBe9dUtxNwI86qa Spotify] \| [https://francium223.bandcamp.com/track/joekalille Bandcamp] \| [https://www.youtube.com/watch?v=bIwZCmfz7HM YouTube] – joshuavoic in 2777edo

Francium: /* Theory */

2024-12-01T12:45:19Z

Theory

← Older revision		Revision as of 12:45, 1 December 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	2777edo is [[consistent]] to the [[7-odd-limit]] and its [[harmonic]] [[3/1\|3]] is about halfway its steps. Using the 2.9.5.7.11.13.17.23.29.31 [[subgroup]] it [[tempering out\|tempers out]] [[12376/12375]], [[14400/14399]], [[25025/25024]], [[123201/123200]], 20736/20735, [[194481/194480]], 16445/16443, 27625/27621 and 23716/23715. It [[~~support]]s [[joshuavoic~~]].		2777edo is [[consistent]] to the [[7-odd-limit]] and its [[harmonic]] [[3/1\|3]] is about halfway its steps. Using the 2.9.5.7.11.13.17.23.29.31 [[subgroup]], it [[tempering out\|tempers out]] [[12376/12375]], [[14400/14399]], [[25025/25024]], [[123201/123200]], 20736/20735, [[194481/194480]], 16445/16443, 27625/27621 and 23716/23715. Using the no-3-or-19 23-limit subgroup, it tempers out [[25025/25024]].

	=== Odd harmonics ===		=== Odd harmonics ===

Francium: Created page with "{{Infobox ET}} {{EDO intro|2777}} == Theory == 2777edo is consistent to the 7-odd-limit and its harmonic 3 is about halfway its steps. Using the 2.9.5.7.1..."

2024-10-17T15:26:38Z

Created page with "{{Infobox ET}} {{EDO intro|2777}} == Theory == 2777edo is consistent to the 7-odd-limit and its harmonic 3 is about halfway its steps. Using the 2.9.5.7.1..."

New page

{{Infobox ET}}
{{EDO intro|2777}}

== Theory ==
2777edo is [[consistent]] to the [[7-odd-limit]] and its [[harmonic]] [[3/1|3]] is about halfway its steps. Using the 2.9.5.7.11.13.17.23.29.31 [[subgroup]] it [[tempering out|tempers out]] [[12376/12375]], [[14400/14399]], [[25025/25024]], [[123201/123200]], 20736/20735, [[194481/194480]], 16445/16443, 27625/27621 and 23716/23715. It [[support]]s [[joshuavoic]].

=== Odd harmonics ===
{{Harmonics in equal|2777}}

=== Subsets and supersets ===
2777edo is the 404th [[prime EDO]]. [[5554edo]], which doubles it, gives a good correction to the harmonic 3.

== 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]] (%)
|-
| 2.9
| {{monzo|8803 -2777}}
| {{mapping|2777 8803}}
| -0.0081
| 0.0081
| 1.87
|-
| 2.9.5
| {{monzo|146 -38 -11}}, {{monzo|-89 -21 67}}
| {{mapping|2777 8803 6448}}
| -0.0057
| 0.0074
| 1.71
|-
| 2.9.5.7
| {{monzo|2 -10 14 -1}}, {{monzo|-1 -9 -3 13}}, {{monzo|-48 0 11 8}}
| {{mapping|2777 8803 6448 7796}}
| -0.0033
| 0.0076
| 1.76
|-
| 2.9.5.7.11
| 151263/151250, 184549376/184528125, 35156250/35153041, 3487704605/3486784401
| {{mapping|2777 8803 6448 7796 9607}}
| -0.0066
| 0.0095
| 2.20
|-
| 2.9.5.7.11.13
| 123201/123200, 6656/6655, 151263/151250, 8859375/8859136, 43061200/43046721
| {{mapping|2777 8803 6448 7796 9607 10276}}
| -0.0032
| 0.0116
| 2.68
|-
| 2.9.5.7.11.13.17
| 12376/12375, 14400/14399, 123201/123200, 194481/194480, 4685824/4685625, 81331250/81310473
| {{mapping|2777 8803 6448 7796 9607 10276 11351}}
| -0.0045
| 0.0112
| 2.59
|}