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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|897}}
{{ED intro}}


897et tempers out [[250047/250000]] in the 7-limit, and [[5632/5625]], [[3025/3024]] in the 11-limit.
== Theory ==
897edo shares the same approximation to [[3/1|harmonic 3]] with [[299edo]]. It has sharp approximations to [[5/1|5]] and flat ones starting with [[7/1|7]]. In the 13-limit at least, we want to consider the [[patent val]] {{val| 897 1422 2083 '''2518''' '''3103''' '''3319''' }} as well as the 897def [[val]] {{val| 897 1422 2083 '''2519''' '''3104''' '''3320''' }}.  


===Odd harmonics===
The patent val tempers out [[250047/250000]] in the 7-limit; [[3025/3024]], [[5632/5625]], 42592/42525, 102487/102400, [[131072/130977]], 160083/160000, and 172032/171875 in the 11-limit; [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.
 
The 897def val tempers out [[4375/4374]] in the 7-limit; [[4000/3993]], 46656/46585, and 172032/171875 in the 11-limit; [[1716/1715]], and [[10648/10647]] in the 13-limit.
 
=== Odd harmonics ===
{{Harmonics in equal|897}}
{{Harmonics in equal|897}}


==Music==
=== Subsets and supersets ===
Since 897 factors into {{factorization|897}}, 897edo has subset edos {{EDOs| 3, 13, 23, 39, 69, and 299 }}.
 
== 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]] (%)
|-
| 2.3.5
| {{monzo| 33 -34 9 }}, {{monzo| 70 -9 -24 }}
| {{mapping| 897 ​1422​ 2083​ }}
| −0.1255
| 0.0996
| 7.44
|-
| 2.3.5.7
| 250047/250000, 67108864/66976875, 28824005/28697814
| {{mapping| 897​ 1422 ​2083 ​2518 }} (897)
| −0.0706
| 0.1283
| 9.59
|-
| 2.3.5.7.11
| 3025/3024, 5632/5625, 102487/102400, 28824005/28697814
| {{mapping| 897 ​1422​ 2083 ​2518 ​3103 }} (897)
| −0.0480
| 0.1234
| 9.22
|-
| 2.3.5.7.11.13
| 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814
| {{mapping| 897​ 1422 ​2083 ​2518​ 3103​ 3319 }} (897)
| −0.0222
| 0.1265
| 9.46
|}
 
=== 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
| 419\897
| 560.54
| 864/625
| [[Whoosh]]
|-
| 1
| 440\897
| 588.63
| 128/91
| [[Countritonic]] (897df)
|-
| 3
| 103\897
| 137.79
| 13/12
| [[Avicenna (temperament)|Avicenna]] (897)
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 
== Music ==
; [[User:Francium|Francium]]
* [https://www.youtube.com/watch?v=opR71xbJ-PQ ''13|3|23''] (2023) – 3-, 13-, and 23edo polymicrotonal


*[https://www.youtube.com/watch?v=opR71xbJ-PQ 13|3|23] by Francium
[[Category:Listen]]
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