227edo: Difference between revisions

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== Theory ==

~~The equal temperament~~ [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 61 -37 -1 }} in the 5-limit; [[5120/5103]], [[65625/65536]], and 117649/116640 in the 7-limit, so that it [[support]]s [[countercata]]. In the 11-limit, it tempers out [[385/384]], [[2200/2187]], [[3388/3375]], and 12005/11979, so that it provides the [[optimal patent val]] for 11-limit countercata. In the 13-limit, it tempers out [[325/324]], [[352/351]], [[625/624]], [[676/675]], and [[847/845]], and again supplies a good tuning for 13-limit countercata, although [[140edo]] tunes it better in this case.

227et [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 61 -37 -1 }} in the [[5-limit]]; [[5120/5103]], [[65625/65536]], and 117649/116640 in the [[7-limit]], so that it [[support]]s [[countercata]]. In the [[11-limit]], it tempers out [[385/384]], [[2200/2187]], [[3388/3375]], and [[12005/11979]], so that it provides the [[optimal patent val]] for 11-limit countercata. In the [[13-limit]], it tempers out [[325/324]], [[352/351]], [[625/624]], [[676/675]], and [[847/845]], and again supplies a good tuning for 13-limit countercata, although [[140edo]] tunes it better in this case.

227edo is accurate for the [[13/1|13th harmonic]], as the denominator of a convergent to log213, after [[10edo|10]] and before [[5231edo|5231]].

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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| 360 -227 }}

| {{mapping| 227 360 }}

| -0.3561

| −0.3561

| 0.3560

| 6.73

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| 15625/15552, {{monzo| 61 -37 -1 }}

| {{mapping| 227 360 527 }}

| -0.1785

| −0.1785

| 0.3842

| 7.27

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| 5120/5103, 15625/15552, 117649/116640

| {{mapping| 227 360 527 637 }}

| -0.0071

| −0.0071

| 0.4461

| 8.44

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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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| [[Undecental]]

|}

<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 ==

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* "Cuckoo Cucumber" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/4WSc7cTf1ctWIiOXjTSAmc Spotify] | [https://francium223.bandcamp.com/track/cuckoo-cucumber Bandcamp] | [https://www.youtube.com/watch?v=po7hrgzSeb8 YouTube]

* "Did You Put Resistors In My Brain?" from ''Questions'' (2024) – [https://open.spotify.com/track/3QS6mj3GAMSmfJuQSsOE7Y Spotify] | [https://francium223.bandcamp.com/track/did-you-put-resistors-in-my-brain Bandcamp] | [https://www.youtube.com/watch?v=-FzOGzpxPv4 YouTube]

* "Too Bad Homeboy" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6VPup7pwSC10c0VzsBU4PG Spotify] | [https://francium223.bandcamp.com/track/too-bad-homeboy Bandcamp] | [https://www.youtube.com/watch?v=Y246sdIRbwQ YouTube]

[[Category:Countercata]]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|227}}
+{{ED intro}}
 == Theory ==
-The equal temperament [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 61 -37 -1 }} in the 5-limit; [[5120/5103]], [[65625/65536]], and 117649/116640 in the 7-limit, so that it [[support]]s [[countercata]]. In the 11-limit, it tempers out [[385/384]], [[2200/2187]], [[3388/3375]], and 12005/11979, so that it provides the [[optimal patent val]] for 11-limit countercata. In the 13-limit, it tempers out [[325/324]], [[352/351]], [[625/624]], [[676/675]], and [[847/845]], and again supplies a good tuning for 13-limit countercata, although [[140edo]] tunes it better in this case.
+et [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 61 -37 -1 }} in the [[5-limit]]; [[5120/5103]], [[65625/65536]], and 117649/116640 in the [[7-limit]], so that it [[support]]s [[countercata]]. In the [[11-limit]], it tempers out [[385/384]], [[2200/2187]], [[3388/3375]], and [[12005/11979]], so that it provides the [[optimal patent val]] for 11-limit countercata. In the [[13-limit]], it tempers out [[325/324]], [[352/351]], [[625/624]], [[676/675]], and [[847/845]], and again supplies a good tuning for 13-limit countercata, although [[140edo]] tunes it better in this case.
 edo is accurate for the [[13/1|13th harmonic]], as the denominator of a convergent to log<sub>2</sub>13, after [[10edo|10]] and before [[5231edo|5231]].
@@ Line 18: / Line 18: @@
 == 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 30: / Line 31: @@
 | {{monzo| 360 -227 }}
 | {{mapping| 227 360 }}
-| -0.3561
+| −0.3561
 | 0.3560
 | 6.73
@@ Line 37: / Line 38: @@
 | 15625/15552, {{monzo| 61 -37 -1 }}
 | {{mapping| 227 360 527 }}
-| -0.1785
+| −0.1785
 | 0.3842
 | 7.27
@@ Line 44: / Line 45: @@
 | 5120/5103, 15625/15552, 117649/116640
 | {{mapping| 227 360 527 637 }}
-| -0.0071
+| −0.0071
 | 0.4461
 | 8.44
@@ Line 72: / Line 73: @@
 === 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 97: / Line 99: @@
 | [[Undecental]]
 |}
-<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 ==
@@ Line 104: / Line 106: @@
 * "Cuckoo Cucumber" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/4WSc7cTf1ctWIiOXjTSAmc Spotify] | [https://francium223.bandcamp.com/track/cuckoo-cucumber Bandcamp] | [https://www.youtube.com/watch?v=po7hrgzSeb8 YouTube]
 * "Did You Put Resistors In My Brain?" from ''Questions'' (2024) – [https://open.spotify.com/track/3QS6mj3GAMSmfJuQSsOE7Y Spotify] | [https://francium223.bandcamp.com/track/did-you-put-resistors-in-my-brain Bandcamp] | [https://www.youtube.com/watch?v=-FzOGzpxPv4 YouTube]
+* "Too Bad Homeboy" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6VPup7pwSC10c0VzsBU4PG Spotify] | [https://francium223.bandcamp.com/track/too-bad-homeboy Bandcamp] | [https://www.youtube.com/watch?v=Y246sdIRbwQ YouTube]
 [[Category:Countercata]]
 [[Category:Listen]]