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463edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|463}}
{{ED intro}}
 
== Theory ==
== Theory ==
463et tempers out 184528125/184473632, 4096000/4084101, [[703125/702464]], 67108864/66976875, 95703125/95551488, 359661568/358722675 and 420175/419904 in the 7-limit; 161280/161051, 25165824/25109315, 820125/819896, 29296875/29218112, 1019215872/1019046875, [[4000/3993]], 759375/758912, 117649/117612, 2359296/2358125, [[6250/6237]], 369140625/369098752, [[200704/200475]], 283115520/282475249, 825000/823543, 180224/180075, 537109375/536870912, [[19712/19683]], [[3025/3024]], 199297406/199290375, 1362944/1361367, [[532400/531441]], 3294225/3294172 and [[1771561/1771470]] in the 11-limit. It provides the optimal patent val for the temperaments [[Amity]], [[Trinity]] until the [[11-limit]] and [[Hemfiness temperaments #Undesemi|Undesemi]].
The equal temperament [[tempering out|tempers out]] the [[amity comma]] in the 5-limit; 420175/419904 and [[703125/702464]] in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], [[19712/19683]], and 117649/117612 in the 11-limit. It [[support]]s [[amity]], [[trinity]] and [[undesemi]].
 
=== Prime harmonics ===
{{Harmonics in equal|463}}
 
=== Subsets and supersets ===
463edo is the 90th [[prime edo]].
463edo is the 90th [[prime edo]].
{{Harmonics in equal|463}}


==Regular temperament properties==
== Intervals ==
{{Main|Table of 463edo intervals}}
 
== 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" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
|-
![[TE error|Absolute]] (¢)
! rowspan="2" | [[Subgroup]]
![[TE simple badness|Relative]] (%)
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.3
| 2.3
|{{monzo|734 -463}}
| {{monzo| 734 -463 }}
|{{val|463 734}}
| {{mapping| 463 734 }}
| -0.1328
| −0.1328
| 0.1327
| 0.1327
| 5.12
| 5.12
|-
|-
|2.3.5
| 2.3.5
|{{monzo|9 -13 5}}, {{monzo|91 -12 -31}}
| 1600000/1594323, {{monzo| 91 -12 -31 }}
|{{val|463 734 1075}}
| {{mapping| 463 734 1075 }}
| -0.0689
| −0.0689
| 0.1411
| 0.1411
| 5.44
| 5.44
|-
|-
|2.3.5.7
| 2.3.5.7
|420175/419904, 703125/702464, 1600000/1594323
| 420175/419904, 703125/702464, 1600000/1594323
|{{val|463 734 1075 1300}}
| {{mapping| 463 734 1075 1300 }}
| -0.0966
| −0.0966
| 0.1313
| 0.1313
| 5.07
| 5.07
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|3025/3024, 6250/6237, 19712/19683, 180224/180075
| 3025/3024, 4000/3993, 19712/19683, 117649/117612
|{{val|463 734 1075 1300 1602}}
| {{mapping| 463 734 1075 1300 1602 }}
| -0.1197
| −0.1197
| 0.1262
| 0.1262
| 4.87
| 4.87
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|3025/3024, 1716/1715, 4096/4095, 676/675, 6250/6237
| 676/675, 1716/1715, 3025/3024, 4000/3993, 4096/4095
|{{val|463 734 1075 1300 1602 1713}}
| {{mapping| 463 734 1075 1300 1602 1713 }}
| -0.0643
| −0.0643
| 0.1691
| 0.1691
| 6.52
| 6.52
|-
|-
|2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
|442/441, 595/594, 1275/1274, 2601/2600, 3025/3024, 32955/32912, 45500/45441
| 442/441, 595/594, 676/675, 2500/2499, 3025/3024, 4096/4095
|{{val|463 734 1075 1300 1602 1713 1892}}
| {{mapping| 463 734 1075 1300 1602 1713 1892 }}
| -0.0103
| −0.0103
| 0.2051
| 0.2051
| 7.91
| 7.91
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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
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|131\463
| 31\463
|339.52
| 80.35
|243/200
| 22/21
|Amity
| [[Undesemi]]
|-
| 1
| 51\463
| 132.18
| 27/25
| [[Astro]]
|-
| 1
| 131\463
| 339.52
| 243/200
| [[Amity]] (5-limit)
|-
|-
|1
| 1
|198\463
| 176\463
|513.17
| 456.16
|168/125, 121/90
| 125/96
|Trinity
| [[Qak]]
|-
|-
|1
| 1
|31\463
| 198\463
|80.35
| 513.17
|8575/8192, 22/21
| 121/90
|Undesemi
| [[Trinity]] (463fg)
|}
|}
== Music ==
; [[Francium]]
* [https://youtu.be/AsDaJXCBd_w?si=6BfHt5gYpCPD1oxq ''For Amity''] (2023) – in Amity, 463edo tuning
* "SOUP" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/6VIDZVg571Fv4Ufzsw4UWV Spotify] | [https://francium223.bandcamp.com/track/soup Bandcamp] | [https://www.youtube.com/watch?v=U4okFGqPMkw YouTube] – in Undesemi, 463edo tuning
* "In the Field of Light Industry" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/10mz7Kh9ubilgDsbp4fiS1 Spotify] | [https://francium223.bandcamp.com/track/in-the-field-of-light-industry Bandcamp] | [https://www.youtube.com/watch?v=WvXQXaywf8o YouTube]
* "It's a Great Place To Be." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/24RX2WUoJ6vPHLoB5NrGTA Spotify] | [https://francium223.bandcamp.com/track/its-a-great-place-to-be Bandcamp] | [https://www.youtube.com/watch?v=iatqkX6MQ90 YouTube] – in Alphonsinic, 463edo tuning
[[Category:Listen]]
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