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557edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|557}} ==Theory== 557et tempers out 645700815/645657712, 2460375/2458624, 65625/65536 and 420175/419904 in the 7-limit; 820125/819896, 209715..."
 
Francium (talk | contribs)
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m changed EDO intro to ED intro
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|557}}
{{ED intro}}
==Theory==
 
557et tempers out [[645700815/645657712]], 2460375/2458624, [[65625/65536]] and 420175/419904 in the 7-limit; 820125/819896, 2097152/2096325, [[4000/3993]], 78675968/78594219, [[536870912/535869675]], 180224/180075, 1375/1372, 184549376/184528125, [[19712/19683]], 43923/43904, 20614528/20588575 and 322102/321489 in the 11-limit.
== Theory ==
===Prime harmonics===
557edo is only [[consistent]] to the [[5-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out|tempers out]] {{monzo| 3 -18 11 }} (quartonic comma) and {{monzo| -74 13 23 }} (sesesix comma), as well as {{monzo| 77 -31 -12 }} (lafa comma) in the 5-limit; [[65625/65536]], 420175/419904 and 2460375/2458624 in the 7-limit; 1375/1372, [[4000/3993]], [[19712/19683]], 43923/43904, 180224/180075, and 322102/321489 in the 11-limit. It [[support]]s [[fifthplus]], although [[171edo]] is better suited for that purpose.
 
=== Prime harmonics ===
{{Harmonics in equal|557}}
{{Harmonics in equal|557}}
===Subsets and supersets===
 
557edo is the 102nd [[prime EDO]].
=== Subsets and supersets ===
==Regular temperament properties==
557edo is the 102nd [[prime edo]].
 
== 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|883 -557}}
! rowspan="2" | [[Comma list]]
|{{val|557 883}}
! rowspan="2" | [[Mapping]]
| -0.1195
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 883 -557 }}
| {{mapping| 557 883 }}
| −0.1195
| 0.1195
| 0.1195
| 5.55
| 5.55
|-
|-
|2.3.5
| 2.3.5
|{{monzo|3 -18 11}}, {{monzo|-74 13 23}}
| {{monzo| 3 -18 11 }}, {{monzo| -74 13 23 }}
|{{val|557 883 1293}}
| {{mapping| 557 883 1293 }}
| +0.0174
| +0.0174
| 0.2169
| 0.2169
| 10.07
| 10.07
|}
|}
===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
|228\557
| 228\557
|491.203
| 491.203
|4/3
| 3645/2744
|[[Sesesix]]
| [[Fifthplus]]
|}
|}
==Scales==
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 
== Scales ==
* [[Laz5]]
* [[Laz5]]
* [[Laz9]]
* [[Laz9]]
== Music ==
; [[Francium]]
* "Are You A Youth Medium?" from ''Questions'' (2024) – [https://open.spotify.com/track/4S3oY6c2VRNHBrYD16owoF Spotify] | [https://francium223.bandcamp.com/track/are-you-a-youth-medium Bandcamp] | [https://www.youtube.com/watch?v=OAxdvEZJ-8M YouTube] – sidi in 557edo tuning
Retrieved from "https://en.xen.wiki/w/557edo"