277edo: Difference between revisions

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'''277EDO''' is the [[EDO|equal division of the octave]] into 277 parts of 4.3321 [[cent]]s each. It tempers out 32805/32768 (schisma) and |-11 -37 30> in the 5-limit. Using the patent val, it 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. Using the 277d val, it tempers out 1029/1024, 10976/10935, and 48828125/48771072 in the 7-limit; 385/384, 441/440, 19712/19683, and 234375/234256 in the 11-limit; 625/624, 847/845, 1001/1000, and 1575/1573 in the 13-limit. The patent val [[support]]s the [[pontiac]], and the 277d val supports the [[guiron]] and the [[widefourth]].

~~277EDO~~ is the ~~59th~~ [[~~prime EDO~~]].

== Theory ==

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.

[[~~Category:Equal divisions of~~ the ~~octave~~|~~###~~]]

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]].

[[~~Category~~:~~Prime EDO~~]]

The 277d val {{val| 277 439 643 '''777''' }} tempers out [[1029/1024]], [[10976/10935]], and 48828125/48771072 in the 7-limit; [[385/384]], [[441/440]], [[19712/19683]], and 234375/234256 in the 11-limit; 625/624, [[847/845]], [[1001/1000]], and [[1575/1573]] in the 13-limit. It supports [[guiron]] and [[widefourth]].

=== Prime harmonics ===

=== Subsets and supersets ===

277edo is the 59th [[prime edo]].

== Regular temperament properties ==

{| 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

| {{monzo| -439 277 }}

| {{mapping| 277 439 }}

| +0.0473

| 0.0473

| 1.09

|-

| 2.3.5

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

| {{mapping| 277 439 643 }}

| +0.1398

| 0.1364

| 3.15

|}

=== Rank-2 temperaments ===

{| 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

| 115\277

| 498.19

| 4/3

| [[Helmholtz (temperament)|Helmholtz]]

|}

<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}}
-'''277EDO''' is the [[EDO|equal division of the octave]] into 277 parts of 4.3321 [[cent]]s each. It tempers out 32805/32768 (schisma) and |-11 -37 30&gt; in the 5-limit. Using the patent val, it 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. Using the 277d val, it tempers out 1029/1024, 10976/10935, and 48828125/48771072 in the 7-limit; 385/384, 441/440, 19712/19683, and 234375/234256 in the 11-limit; 625/624, 847/845, 1001/1000, and 1575/1573 in the 13-limit. The patent val [[support]]s the [[pontiac]], and the 277d val supports the [[guiron]] and the [[widefourth]].
+{{ED intro}}
-EDO is the 59th [[prime EDO]].
+== Theory ==
+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.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+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]].
-[[Category:Prime EDO]]
+The 277d val {{val| 277 439 643 '''777''' }} tempers out [[1029/1024]], [[10976/10935]], and 48828125/48771072 in the 7-limit; [[385/384]], [[441/440]], [[19712/19683]], and 234375/234256 in the 11-limit; 625/624, [[847/845]], [[1001/1000]], and [[1575/1573]] in the 13-limit. It supports [[guiron]] and [[widefourth]].
+=== Prime harmonics ===
+{{Harmonics in equal|277}}
+=== Subsets and supersets ===
+edo is the 59th [[prime edo]].
+== Regular temperament properties ==
+{| 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
+| {{monzo| -439 277 }}
+| {{mapping| 277 439 }}
+| +0.0473
+| 0.0473
+| 1.09
+|-
+| 2.3.5
+| 32805/32768, {{monzo| -11 -37 30 }}
+| {{mapping| 277 439 643 }}
+| +0.1398
+| 0.1364
+| 3.15
+|}
+=== Rank-2 temperaments ===
+{| 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
+| 115\277
+| 498.19
+| 4/3
+| [[Helmholtz (temperament)|Helmholtz]]
+|}
+<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