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1559edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|1559}} == Theory == 1559edo is consistent to the 9-odd-limit. Using the patent val, it tempers out 43046721/43025920, 78125000/781218..."
 
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}}
{{EDO intro|1559}}
{{ED intro}}


== Theory ==
== Theory ==
1559edo is [[consistent]] to the [[9-odd-limit]]. Using the patent val, it tempers out [[43046721/43025920]], [[78125000/78121827]] and {{monzo|32 1 -6 -7}} in the 7-limit, [[3025/3024]], 180224/180075, 50014503/50000000 and 56953125/56942116 in the 11-limit. It [[support]]s [[luna]].
1559edo is [[consistent]] to the [[9-odd-limit]]. Using the [[patent val]], it [[tempering out|tempers out]] {{monzo| 38 -2 -15 }} (luna comma) and {{monzo| 71 -99 37 }} (raider comma) in the 5-limit; [[43046721/43025920]], [[78125000/78121827]] and {{monzo| 32 1 -6 -7 }} in the 7-limit, [[3025/3024]], 180224/180075, 50014503/50000000 and 56953125/56942116 in the 11-limit.  


=== Prime harmonics ===
=== Prime harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
1559edo is the 246th [[prime EDO]].
1559edo is the 246th [[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|Comma List]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Comma list]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! rowspan="2" | [[Mapping]]
! colspan="2" |Tuning Error
! 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|2471 -1559}}
| {{monzo| 2471 -1559 }}
| {{mapping|1559 2471}}
| {{mapping| 1559 2471 }}
| -0.0106
| −0.0106
| 0.0106
| 0.0106
| 1.38
| 1.38
|-
|-
| 2.3.5
| 2.3.5
| {{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
| −0.0196
| 0.0155
| 0.0155
| 2.01
| 2.01
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| 2.3.5.7
| 2.3.5.7
| 43046721/43025920, 78125000/78121827, 12884901888/12867859375
| 43046721/43025920, 78125000/78121827, 12884901888/12867859375
| {{mapping|1559 2471 3620 4377}}
| {{mapping| 1559 2471 3620 4377 }}
| -0.0376
| −0.0376
| 0.0339
| 0.0339
| 4.40
| 4.40
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| 2.3.5.7.11
| 2.3.5.7.11
| 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
| −0.0188
| 0.0483
| 0.0483
| 6.27
| 6.27
|-
|-
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 3025/3024, 1716/1715, 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
| −0.0162
| 0.0445
| 0.0445
| 5.78
| 5.78
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=== 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>Ratio*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
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| [[Raider]]
| [[Raider]]
|}
|}
<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 ==
; [[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


<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
[[Category:Listen]]
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