2777edo: Difference between revisions

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== 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 ===

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== Regular temperament properties ==

{| 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

| {{monzo|8803 -2777}}

| {{mapping|2777 8803}}

| -0.0081

| −0.0081

| 0.0081

| 1.87

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| {{monzo|146 -38 -11}}, {{monzo|-89 -21 67}}

| {{mapping|2777 8803 6448}}

| -0.0057

| −0.0057

| 0.0074

| 1.71

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| {{monzo|2 -10 14 -1}}, {{monzo|-1 -9 -3 13}}, {{monzo|-48 0 11 8}}

| {{mapping|2777 8803 6448 7796}}

| -0.0033

| −0.0033

| 0.0076

| 1.76

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| 151263/151250, 184549376/184528125, 35156250/35153041, 3487704605/3486784401

| {{mapping|2777 8803 6448 7796 9607}}

| -0.0066

| −0.0066

| 0.0095

| 2.20

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| 123201/123200, 6656/6655, 151263/151250, 8859375/8859136, 43061200/43046721

| {{mapping|2777 8803 6448 7796 9607 10276}}

| -0.0032

| −0.0032

| 0.0116

| 2.68

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| 12376/12375, 14400/14399, 123201/123200, 194481/194480, 4685824/4685625, 81331250/81310473

| {{mapping|2777 8803 6448 7796 9607 10276 11351}}

| -0.0045

| −0.0045

| 0.0112

| 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

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|2777}}
+{{ED intro}}
 == Theory ==
-edo 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]].
+edo 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 ===
@@ Line 13: / Line 13: @@
 == Regular temperament properties ==
 {| 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
 | {{monzo|8803 -2777}}
 | {{mapping|2777 8803}}
-| -0.0081
+| −0.0081
 | 0.0081
 | 1.87
@@ Line 32: / Line 33: @@
 | {{monzo|146 -38 -11}}, {{monzo|-89 -21 67}}
 | {{mapping|2777 8803 6448}}
-| -0.0057
+| −0.0057
 | 0.0074
 | 1.71
@@ Line 39: / Line 40: @@
 | {{monzo|2 -10 14 -1}}, {{monzo|-1 -9 -3 13}}, {{monzo|-48 0 11 8}}
 | {{mapping|2777 8803 6448 7796}}
-| -0.0033
+| −0.0033
 | 0.0076
 | 1.76
@@ Line 46: / Line 47: @@
 | 151263/151250, 184549376/184528125, 35156250/35153041, 3487704605/3486784401
 | {{mapping|2777 8803 6448 7796 9607}}
-| -0.0066
+| −0.0066
 | 0.0095
 | 2.20
@@ Line 53: / Line 54: @@
 | 123201/123200, 6656/6655, 151263/151250, 8859375/8859136, 43061200/43046721
 | {{mapping|2777 8803 6448 7796 9607 10276}}
-| -0.0032
+| −0.0032
 | 0.0116
 | 2.68
@@ Line 60: / Line 61: @@
 | 12376/12375, 14400/14399, 123201/123200, 194481/194480, 4685824/4685625, 81331250/81310473
 | {{mapping|2777 8803 6448 7796 9607 10276 11351}}
-| -0.0045
+| −0.0045
 | 0.0112
 | 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