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== 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 supports [[amity]], [[trinity]] and [[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 ===
=== Prime harmonics ===
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| 2.3
| 2.3
| {{monzo| 734 -463 }}
| {{monzo| 734 -463 }}
| {{val| 463 734 }}
| {{mapping| 463 734 }}
| -0.1328
| -0.1328
| 0.1327
| 0.1327
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| 2.3.5
| 2.3.5
| 1600000/1594323, {{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
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| 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
Line 45: Line 45:
| 2.3.5.7.11
| 2.3.5.7.11
| 3025/3024, 4000/3993, 19712/19683, 117649/117612
| 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
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| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 676/675, 1716/1715, 3025/3024, 4000/3993, 4096/4095
| 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
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| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 442/441, 595/594, 676/675, 2500/2499, 3025/3024, 4096/4095
| 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
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|+Table of rank-2 temperaments by generator
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Periods<br>per 8ve
! Generator<br>(Reduced)
! Generator*
! Cents<br>(Reduced)
! Cents*
! Associated<br>Ratio
! Associated<br>Ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|31\463
| 31\463
|80.35
| 80.35
|22/21
| 22/21
|[[Undesemi]]
| [[Undesemi]]
|-
|-
|1
| 1
|51\463
| 51\463
|132.18
| 132.18
|27/25
| 27/25
|[[Astro]]
| [[Astro]]
|-
|-
|1
| 1
|131\463
| 131\463
|339.52
| 339.52
|243/200
| 243/200
|[[Amity]] (5-limit)
| [[Amity]] (5-limit)
|-
|-
|1
| 1
|176\463
| 176\463
|456.16
| 456.16
|125/96
| 125/96
|[[Qak]]
| [[Qak]]
|-
|-
|1
| 1
|198\463
| 198\463
|513.17
| 513.17
|121/90
| 121/90
|[[Trinity]] (463fg)
| [[Trinity]] (463fg)
|-
 
|}
|}


==Music==
== Music ==
*[https://www.youtube.com/watch?v=AsDaJXCBd_w For Amity] by Francium
; [[User:Francium|Francium]]
* [https://youtu.be/AsDaJXCBd_w?si=6BfHt5gYpCPD1oxq ''For Amity''] (2023) – amity in 463edo tuning
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