277edo: Difference between revisions

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== Theory ==

277edo is a good 5-limit tuning; however, it is in[[consistent]] in the [[7-odd-limit]]. ~~The~~ equal temperament [[tempering out|tempers out]] 32805/32768 ([[schisma]]) and {{monzo| -11 -37 30 }} in the 5-limit.

277edo is a good [[5-limit]] tuning; however, it is in[[consistent]] in the [[7-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] 32805/32768 ([[schisma]]) and {{monzo| -11 -37 30 }} in the 5-limit.

The [[patent val]] {{val| 277 439 643 778 }} tempers out [[4375/4374]], [[65625/65536]], and 829440/823543 in the 7-limit; [[540/539]], [[6250/6237]], 15488/15435, and 35937/35840 in the 11-limit; [[625/624]], [[729/728]], [[1573/1568]], [[2080/2079]], and [[2200/2197]] in the 13-limit. It [[support]]s [[pontiac]].

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== 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

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| 0.1364

| 3.15

~~{{comma basis end}~~}

|}

=== 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

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| 498.19

| 4/3

| [[Helmholtz]]

| [[Helmholtz (temperament)|Helmholtz]]

~~{{rank~~-~~2 end}}~~

|}

~~{{orf}}~~

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

== Music ==

; [[Francium]]

* "Rizzardry" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/1NqjyKORN0c2AIOhTMMUK7 Spotify] | [https://francium223.bandcamp.com/track/rizzardry Bandcamp] | [https://www.youtube.com/watch?v=HZ67knYwALA YouTube] – in Zangaric, 277edo tuning

* "It's a Smell." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/35sVZfy1mDsPHZwjgh8Sql Spotify] | [https://francium223.bandcamp.com/track/its-a-smell Bandcamp] | [https://www.youtube.com/watch?v=L9Tn7n-THCM YouTube] – in Yerkesic, 277edo tuning

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|277}}
+{{ED intro}}
 == Theory ==
-edo is a good 5-limit tuning; however, it is in[[consistent]] in the [[7-odd-limit]]. The equal temperament [[tempering out|tempers out]] 32805/32768 ([[schisma]]) and {{monzo| -11 -37 30 }} in the 5-limit.
+edo is a good [[5-limit]] tuning; however, it is in[[consistent]] in the [[7-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] 32805/32768 ([[schisma]]) and {{monzo| -11 -37 30 }} in the 5-limit.
 The [[patent val]] {{val| 277 439 643 778 }} tempers out [[4375/4374]], [[65625/65536]], and 829440/823543 in the 7-limit; [[540/539]], [[6250/6237]], 15488/15435, and 35937/35840 in the 11-limit; [[625/624]], [[729/728]], [[1573/1568]], [[2080/2079]], and [[2200/2197]] in the 13-limit. It [[support]]s [[pontiac]].
@@ Line 16: / Line 16: @@
 == 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
@@ Line 31: / Line 40: @@
 | 0.1364
 | 3.15
-{{comma basis end}}
+|}
 === 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
@@ Line 40: / Line 56: @@
 | 498.19
 | 4/3
-| [[Helmholtz]]
+| [[Helmholtz (temperament)|Helmholtz]]
-{{rank-2 end}}
+|}
-{{orf}}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+== Music ==
+; [[Francium]]
+* "Rizzardry" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/1NqjyKORN0c2AIOhTMMUK7 Spotify] | [https://francium223.bandcamp.com/track/rizzardry Bandcamp] | [https://www.youtube.com/watch?v=HZ67knYwALA YouTube] – in Zangaric, 277edo tuning
+* "It's a Smell." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/35sVZfy1mDsPHZwjgh8Sql Spotify] | [https://francium223.bandcamp.com/track/its-a-smell Bandcamp] | [https://www.youtube.com/watch?v=L9Tn7n-THCM YouTube] – in Yerkesic, 277edo tuning