1559edo: Difference between revisions
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m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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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]] (¢) | ||
! [[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
| Line 25: | Line 26: | ||
| {{monzo| 2471 -1559 }} | | {{monzo| 2471 -1559 }} | ||
| {{mapping| 1559 2471 }} | | {{mapping| 1559 2471 }} | ||
| | | −0.0106 | ||
| 0.0106 | | 0.0106 | ||
| 1.38 | | 1.38 | ||
| Line 32: | Line 33: | ||
| {{monzo| 38 -2 -15 }}, {{monzo| 71 -99 37 }} | | {{monzo| 38 -2 -15 }}, {{monzo| 71 -99 37 }} | ||
| {{mapping| 1559 2471 3620 }} | | {{mapping| 1559 2471 3620 }} | ||
| | | −0.0196 | ||
| 0.0155 | | 0.0155 | ||
| 2.01 | | 2.01 | ||
| Line 39: | Line 40: | ||
| 43046721/43025920, 78125000/78121827, 12884901888/12867859375 | | 43046721/43025920, 78125000/78121827, 12884901888/12867859375 | ||
| {{mapping| 1559 2471 3620 4377 }} | | {{mapping| 1559 2471 3620 4377 }} | ||
| | | −0.0376 | ||
| 0.0339 | | 0.0339 | ||
| 4.40 | | 4.40 | ||
| Line 46: | Line 47: | ||
| 3025/3024, 180224/180075, 50014503/50000000, 56953125/56942116 | | 3025/3024, 180224/180075, 50014503/50000000, 56953125/56942116 | ||
| {{mapping| 1559 2471 3620 4377 5393 }} | | {{mapping| 1559 2471 3620 4377 5393 }} | ||
| | | −0.0188 | ||
| 0.0483 | | 0.0483 | ||
| 6.27 | | 6.27 | ||
| Line 53: | Line 54: | ||
| 1716/1715, 3025/3024, 4096/4095, 492128/492075, 5282739/5281250 | | 1716/1715, 3025/3024, 4096/4095, 492128/492075, 5282739/5281250 | ||
| {{mapping| 1559 2471 3620 4377 5393 5769 }} | | {{mapping| 1559 2471 3620 4377 5393 5769 }} | ||
| | | −0.0162 | ||
| 0.0445 | | 0.0445 | ||
| 5.78 | | 5.78 | ||
| Line 60: | Line 61: | ||
=== 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 79: | Line 81: | ||
| [[Raider]] | | [[Raider]] | ||
|} | |} | ||
<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 == | ||
; [[Francium]] | ; [[Francium]] | ||
* "confluenceprettype" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/0jCzkUrwVEHevs7xAWgsvh Spotify] | [https://francium223.bandcamp.com/track/confluenceprettype Bandcamp] | [https://www.youtube.com/watch?v=4rxv7ec4BEM YouTube] – luna[25] in 1559edo tuning | * "confluenceprettype" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/0jCzkUrwVEHevs7xAWgsvh Spotify] | [https://francium223.bandcamp.com/track/confluenceprettype Bandcamp] | [https://www.youtube.com/watch?v=4rxv7ec4BEM YouTube] – luna[25] in 1559edo tuning | ||
[[Category:Listen]] | |||