897edo: Difference between revisions
m Adopt template: Factorization; misc. cleanup |
m changed EDO intro to ED intro |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
| Line 29: | Line 30: | ||
| {{monzo| 33 -34 9 }}, {{monzo| 70 -9 -24 }} | | {{monzo| 33 -34 9 }}, {{monzo| 70 -9 -24 }} | ||
| {{mapping| 897 1422 2083 }} | | {{mapping| 897 1422 2083 }} | ||
| | | −0.1255 | ||
| 0.0996 | | 0.0996 | ||
| 7.44 | | 7.44 | ||
| Line 36: | Line 37: | ||
| 250047/250000, 67108864/66976875, 28824005/28697814 | | 250047/250000, 67108864/66976875, 28824005/28697814 | ||
| {{mapping| 897 1422 2083 2518 }} (897) | | {{mapping| 897 1422 2083 2518 }} (897) | ||
| | | −0.0706 | ||
| 0.1283 | | 0.1283 | ||
| 9.59 | | 9.59 | ||
| Line 43: | Line 44: | ||
| 3025/3024, 5632/5625, 102487/102400, 28824005/28697814 | | 3025/3024, 5632/5625, 102487/102400, 28824005/28697814 | ||
| {{mapping| 897 1422 2083 2518 3103 }} (897) | | {{mapping| 897 1422 2083 2518 3103 }} (897) | ||
| | | −0.0480 | ||
| 0.1234 | | 0.1234 | ||
| 9.22 | | 9.22 | ||
| Line 50: | Line 51: | ||
| 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814 | | 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814 | ||
| {{mapping| 897 1422 2083 2518 3103 3319 }} (897) | | {{mapping| 897 1422 2083 2518 3103 3319 }} (897) | ||
| | | −0.0222 | ||
| 0.1265 | | 0.1265 | ||
| 9.46 | | 9.46 | ||
| Line 57: | Line 58: | ||
=== 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 | |- | ||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 82: | Line 84: | ||
| [[Avicenna (temperament)|Avicenna]] (897) | | [[Avicenna (temperament)|Avicenna]] (897) | ||
|} | |} | ||
<nowiki>* | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||
; [[User:Francium|Francium]] | ; [[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''] (2023) – 3-, 13-, and 23edo polymicrotonal | ||
[[Category:Listen]] | |||