1489edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
1489edo is [[consistent]] to the [[21-odd-limit]]. | 1489edo is [[consistent]] to the [[21-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[3025/3024]] in the 11-limit; [[4225/4224]] and [[256000/255879]] in the 13-limit; [[2500/2499]], [[5985/5984]], and [[57375/57344]] in the 17-limit; [[6175/6174]] in the 19-limit. Using the 2.3.11.17.19.37 [[subgroup]]<!-- explain why this subgroup is good to consider -->, it tempers out [[3553/3552]]. It [[support]]s [[qak]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 13: | Line 13: | ||
== 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" |[[Comma list | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" |Optimal<br>8ve | ! rowspan="2" | [[Mapping]] | ||
! colspan="2" |Tuning | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
|- | ! colspan="2" | Tuning error | ||
![[TE error|Absolute]] (¢) | |- | ||
![[TE simple badness|Relative]] (%) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo|-2360 1489}} | | {{monzo|-2360 1489}} | ||
| {{mapping|1489 2360}} | | {{mapping|1489 2360}} | ||
| 0.0023 | | +0.0023 | ||
| 0.0023 | | 0.0023 | ||
| 0.29 | | 0.29 | ||
| Line 32: | Line 33: | ||
| {{monzo|54 -37 2}}, {{monzo|-73 -14 41}} | | {{monzo|54 -37 2}}, {{monzo|-73 -14 41}} | ||
| {{mapping|1489 2360 3457}} | | {{mapping|1489 2360 3457}} | ||
| 0.0422 | | +0.0422 | ||
| 0.0564 | | 0.0564 | ||
| 7.00 | | 7.00 | ||
| Line 39: | Line 40: | ||
| 420175/419904, 703125/702464, {{monzo|49 -27 7 -8}} | | 420175/419904, 703125/702464, {{monzo|49 -27 7 -8}} | ||
| {{mapping|1489 2360 3457 4180}} | | {{mapping|1489 2360 3457 4180}} | ||
| 0.0425 | | +0.0425 | ||
| 0.0488 | | 0.0488 | ||
| 6.06 | | 6.06 | ||
| Line 46: | Line 47: | ||
| 3025/3024, 759375/758912, 420175/419904, 32768000000/32750405919 | | 3025/3024, 759375/758912, 420175/419904, 32768000000/32750405919 | ||
| {{mapping|1489 2360 3457 4180 5151}} | | {{mapping|1489 2360 3457 4180 5151}} | ||
| 0.0384 | | +0.0384 | ||
| 0.0444 | | 0.0444 | ||
| 5.51 | | 5.51 | ||
| Line 53: | Line 54: | ||
| 3025/3024, 4225/4224, 91125/91091, 256000/255879, 420175/419904 | | 3025/3024, 4225/4224, 91125/91091, 256000/255879, 420175/419904 | ||
| {{mapping|1489 2360 3457 4180 5151 5510}} | | {{mapping|1489 2360 3457 4180 5151 5510}} | ||
| 0.0303 | | +0.0303 | ||
| 0.0444 | | 0.0444 | ||
| 5.51 | | 5.51 | ||
| Line 60: | Line 61: | ||
| 3025/3024, 2500/2499, 4225/4224, 56595/56576, 57375/57344, 256000/255879 | | 3025/3024, 2500/2499, 4225/4224, 56595/56576, 57375/57344, 256000/255879 | ||
| {{mapping|1489 2360 3457 4180 5151 5510 6086}} | | {{mapping|1489 2360 3457 4180 5151 5510 6086}} | ||
| 0.0325 | | +0.0325 | ||
| 0.0414 | | 0.0414 | ||
| 5.14 | | 5.14 | ||
|} | |} | ||
== Music == | |||
; [[Francium]] | |||
* "Hum During Funerals" from ''I Want To'' (2025) – [https://open.spotify.com/track/04UFLrEWXC3lMYCApQGJd1 Spotify] | [https://francium223.bandcamp.com/track/hum-during-funerals Bandcamp] | [https://www.youtube.com/watch?v=0sMj7ylaVO0 YouTube] – in Meranic, 1489edo tuning | |||