463edo: Difference between revisions

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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 ===
Line 24: Line 24:
| 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

Revision as of 06:50, 3 November 2023

← 462edo 463edo 464edo →
Prime factorization 463 (prime)
Step size 2.59179 ¢ 
Fifth 271\463 (702.376 ¢)
Semitones (A1:m2) 45:34 (116.6 ¢ : 88.12 ¢)
Consistency limit 11
Distinct consistency limit 11

Template:EDO intro

Theory

The equal temperament 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 supports amity, trinity and undesemi.

Prime harmonics

Approximation of prime harmonics in 463edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.42 -0.14 +0.50 +0.73 -0.79 -1.28 +0.54 -1.06 -0.64 +0.54
Relative (%) +0.0 +16.2 -5.3 +19.5 +28.3 -30.4 -49.5 +21.0 -40.9 -24.5 +20.7
Steps
(reduced) 		463
(0) 		734
(271) 		1075
(149) 		1300
(374) 		1602
(213) 		1713
(324) 		1892
(40) 		1967
(115) 		2094
(242) 		2249
(397) 		2294
(442)

Subsets and supersets

463edo is the 90th prime edo.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢) 		Tuning Error
Absolute (¢) Relative (%)
2.3 [734 -463⟩ [⟨463 734]] -0.1328 0.1327 5.12
2.3.5 1600000/1594323, [91 -12 -31⟩ [⟨463 734 1075]] -0.0689 0.1411 5.44
2.3.5.7 420175/419904, 703125/702464, 1600000/1594323 [⟨463 734 1075 1300]] -0.0966 0.1313 5.07
2.3.5.7.11 3025/3024, 4000/3993, 19712/19683, 117649/117612 [⟨463 734 1075 1300 1602]] -0.1197 0.1262 4.87
2.3.5.7.11.13 676/675, 1716/1715, 3025/3024, 4000/3993, 4096/4095 [⟨463 734 1075 1300 1602 1713]] -0.0643 0.1691 6.52
2.3.5.7.11.13.17 442/441, 595/594, 676/675, 2500/2499, 3025/3024, 4096/4095 [⟨463 734 1075 1300 1602 1713 1892]] -0.0103 0.2051 7.91

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
Ratio* 		Temperaments
1 31\463 80.35 22/21 Undesemi
1 51\463 132.18 27/25 Astro
1 131\463 339.52 243/200 Amity (5-limit)
1 176\463 456.16 125/96 Qak
1 198\463 513.17 121/90 Trinity (463fg)

Music

Francium
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