897edo: Difference between revisions
m Adopt template: Factorization; misc. cleanup |
→Regular temperament properties: countritonic -> ragitritonic |
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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 27: | Line 28: | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| 33 -34 9 }}, {{monzo| 70 -9 -24 }} | ||
| {{ | | {{Mapping| 897 1422 2083 }} | ||
| | | −0.1255 | ||
| 0.0996 | | 0.0996 | ||
| 7.44 | | 7.44 | ||
| Line 35: | Line 36: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 250047/250000, 67108864/66976875, 28824005/28697814 | | 250047/250000, 67108864/66976875, 28824005/28697814 | ||
| {{ | | {{Mapping| 897 1422 2083 2518 }} (897) | ||
| | | −0.0706 | ||
| 0.1283 | | 0.1283 | ||
| 9.59 | | 9.59 | ||
| Line 42: | Line 43: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 3025/3024, 5632/5625, 102487/102400, 28824005/28697814 | | 3025/3024, 5632/5625, 102487/102400, 28824005/28697814 | ||
| {{ | | {{Mapping| 897 1422 2083 2518 3103 }} (897) | ||
| | | −0.0480 | ||
| 0.1234 | | 0.1234 | ||
| 9.22 | | 9.22 | ||
| Line 49: | Line 50: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 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) | ||
| | | −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 74: | Line 76: | ||
| 588.63 | | 588.63 | ||
| 128/91 | | 128/91 | ||
| [[ | | [[Ragitritonic]] (897df) | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 82: | Line 84: | ||
| [[Avicenna (temperament)|Avicenna]] (897) | | [[Avicenna (temperament)|Avicenna]] (897) | ||
|} | |} | ||
<nowiki>* | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|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]] | |||