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 ==

{| class="wikitable center-4 center-5 center-6"

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list~~|Comma List~~]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve ~~Stretch~~ (¢)

! rowspan="2" | Optimal 8ve stretch (¢)

! colspan="2" | Tuning ~~Error~~

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)

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| {{monzo| -439 277 }}

| {{mapping| 277 439 }}

| 0.0473

| +0.0473

| 0.0473

| 1.09

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| 32805/32768, {{monzo| -11 -37 30 }}

| {{mapping| 277 439 643 }}

| 0.1398

| +0.1398

| 0.1364

| 3.15

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=== Rank-2 temperaments ===

{| 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 per 8ve

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ratio*

! Associated ratio*

! Temperaments

|-

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| 498.19

| 4/3

| [[Helmholtz]]

| [[Helmholtz (temperament)|Helmholtz]]

|}

<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 />* [[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 17: / Line 17: @@
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! 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 simple badness|Relative]] (%)
@@ Line 29: / Line 30: @@
 | {{monzo| -439 277 }}
 | {{mapping| 277 439 }}
-| 0.0473
+| +0.0473
 | 0.0473
 | 1.09
@@ Line 36: / Line 37: @@
 | 32805/32768, {{monzo| -11 -37 30 }}
 | {{mapping| 277 439 643 }}
-| 0.1398
+| +0.1398
 | 0.1364
 | 3.15
@@ Line 43: / Line 44: @@
 === Rank-2 temperaments ===
 {| 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
+|-
+! Periods<br />per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>ratio*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 54: / Line 56: @@
 | 498.19
 | 4/3
-| [[Helmholtz]]
+| [[Helmholtz (temperament)|Helmholtz]]
 |}
-<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 />* [[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