1019edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
1019edo is [[consistent]] to the [[17-odd-limit]], [[ | 1019edo is [[consistent]] to the [[17-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[3025/3024]] and [[1771561/1771470]] in the 11-limit; [[1716/1715]] and [[4096/4095]] in the 13-limit; and [[1275/1274]], [[2500/2499]] and 3536379/3536000 in the 17-limit. Using the 2.3.5.11.17.29.43 [[subgroup]], it tempers out [[17545/17544]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
1019edo is the 171st [[prime | 1019edo is the 171st [[prime edo]]. | ||
== 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|-1615 1019}} | | {{monzo| -1615 1019 }} | ||
| {{mapping|1019 1615}} | | {{mapping| 1019 1615 }} | ||
| +0.0285 | | +0.0285 | ||
| 0.0285 | | 0.0285 | ||
| Line 30: | Line 31: | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo|-31 43 -16}}, {{monzo|-68 18 17}} | | {{monzo| -31 43 -16 }}, {{monzo| -68 18 17 }} | ||
| {{mapping|1019 1615 2366}} | | {{mapping| 1019 1615 2366 }} | ||
| +0.0266 | | +0.0266 | ||
| 0.0235 | | 0.0235 | ||
| Line 38: | Line 39: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 703125/702464, 14348907/14336000, 283115520/282475249 | | 703125/702464, 14348907/14336000, 283115520/282475249 | ||
| {{mapping|1019 1615 2366 2861}} | | {{mapping| 1019 1615 2366 2861 }} | ||
| | | −0.0121 | ||
| 0.0700 | | 0.0700 | ||
| 5.94 | | 5.94 | ||
|- | |- | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 3025/3024, 759375/758912 | | 3025/3024, 180224/180075, 759375/758912, 14348907/14336000 | ||
| {{mapping|1019 1615 2366 2861 3525}} | | {{mapping| 1019 1615 2366 2861 3525 }} | ||
| +0.0013 | | +0.0013 | ||
| 0.0681 | | 0.0681 | ||
| Line 51: | Line 52: | ||
|- | |- | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 3025/3024, | | 1716/1715, 3025/3024, 4096/4095, 216513/216320, 540000/539539 | ||
| {{mapping|1019 1615 2366 2861 3525 3771}} | | {{mapping| 1019 1615 2366 2861 3525 3771 }} | ||
| | | −0.0123 | ||
| 0.0692 | | 0.0692 | ||
| 5.88 | | 5.88 | ||
|- | |- | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 1275/1274, 3025/3024 | | 1275/1274, 1716/1715, 2500/2499, 3025/3024, 4096/4095, 3536379/3536000 | ||
| {{mapping|1019 1615 2366 2861 3525 3771 4165}} | | {{mapping| 1019 1615 2366 2861 3525 3771 4165 }} | ||
| | | −0.0054 | ||
| 0.0662 | | 0.0662 | ||
| 5.62 | | 5.62 | ||
|} | |} | ||
== Music == | |||
; [[Francium]] | |||
* "Enjoy to Read Many Books" from ''I Want To'' (2025) – [https://open.spotify.com/track/1HVplNgMA7SoxFnfKVko58 Spotify] | [https://francium223.bandcamp.com/track/enjoy-to-read-many-books Bandcamp] | [https://www.youtube.com/watch?v=USNzpQnR2CQ YouTube] – in Manheimic, 1019edo tuning | |||