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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|227}}
{{ED intro}}
 
== Theory ==
== Theory ==
The equal temperament 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 13th harmonic, as the denominator of a convergent to log<sub>2</sub>13, after [[10edo|10]] and before [[5231edo|5231]].
227edo 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]].


=== Prime harmonics ===
=== Prime harmonics ===
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227edo is the 49th [[prime edo]].
227edo is the 49th [[prime edo]].


==Regular temperament properties==
== Intervals ==
{{Main|Table of 227edo intervals}}
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|-
|2.3
! rowspan="2" | [[Subgroup]]
|{{monzo|360 -227}}
! rowspan="2" | [[Comma list]]
|{{val|227 360}}
! rowspan="2" | [[Mapping]]
| -0.3561
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 360 -227 }}
| {{mapping| 227 360 }}
| −0.3561
| 0.3560
| 0.3560
| 6.73
| 6.73
|-
|-
|2.3.5
| 2.3.5
|15625/15552, {{monzo|61 -37 -1}}
| 15625/15552, {{monzo| 61 -37 -1 }}
|{{val|227 360 527}}
| {{mapping| 227 360 527 }}
| -0.1785
| −0.1785
| 0.3842
| 0.3842
| 7.27
| 7.27
|-
|-
|2.3.5.7
| 2.3.5.7
|5120/5103, 15625/15552, 65625/65536
| 5120/5103, 15625/15552, 117649/116640
|{{val|227 360 527 637}}
| {{mapping| 227 360 527 637 }}
| -0.0071
| −0.0071
| 0.4461
| 0.4461
| 8.44
| 8.44
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|385/384, 2200/2187, 3388/3375, 5120/5103
| 385/384, 2200/2187, 3388/3375, 12005/11979
|{{val|227 360 527 637 785}}
| {{mapping| 227 360 527 637 785 }}
| +0.0832
| +0.0832
| 0.4380
| 0.4380
| 8.29
| 8.29
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|325/324, 352/351, 385/384, 625/624, 847/845
| 325/324, 352/351, 385/384, 625/624, 12005/11979
|{{val|227 360 527 637 785 840}}
| {{mapping| 227 360 527 637 785 840 }}
| +0.0693
| +0.0693
| 0.4010
| 0.4010
| 7.59
| 7.59
|-
|-
|2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
|352/351, 595/594, 715/714, 847/845, 1001/1000, 3185/3179
| 325/324, 352/351, 385/384, 595/594, 625/624, 3185/3179
|{{val|227 360 527 637 785 840 928}}
| {{mapping| 227 360 527 637 785 840 928 }}
| +0.0324
| +0.0324
| 0.3821
| 0.3821
| 7.23
| 7.23
|}
|}
=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| 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
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|25\227
| 25\227
|132.16
| 132.16
|{{monzo|-38 5 13}}
| 121/112
|[[Astro]] / [[kastro]]
| [[Kastro]]
|-
|-
|1
| 1
|60\227
| 60\227
|317.18
| 317.18
|6/5
| 6/5
|[[Hanson]] / [[countercata]]
| [[Countercata]]
|-
|-
|1
| 1
|94\227
| 94\227
|496.92
| 496.92
|4/3
| 4/3
|[[Undecental]]
| [[Undecental]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
== Music ==
; [[Francium]]
* "little hope" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1J6VKSGTkTRFs75WlEb6GP Spotify] | [https://francium223.bandcamp.com/track/little-hope Bandcamp] | [https://www.youtube.com/watch?v=juMfOpUu25I YouTube]
* "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:Countercata]]
[[Category:Listen]]
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