463edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|463}} == Theory == 463et tempers out 184528125/184473632, 4096000/4084101, 703125/702464, 67108864/66976875, 95703125/95551488, 359661568/358722..."
 
Correction (it's not the OPV for amity or trinity)
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|463}}
{{EDO intro|463}}
== 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]].
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]].
 
=== 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==
== 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|Comma List]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
! colspan="2" | Tuning Error
|-
|-
![[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.3
| 2.3
|{{monzo|734 -463}}
| {{monzo| 734 -463 }}
|{{val|463 734}}
| {{val| 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}}
| {{monzo| 9 -13 5 }}, {{monzo| 91 -12 -31 }}
|{{val|463 734 1075}}
| {{val| 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}}
| {{val| 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, 6250/6237, 19712/19683, 180224/180075
|{{val|463 734 1075 1300 1602}}
| {{val| 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
| 3025/3024, 1716/1715, 4096/4095, 676/675, 6250/6237
|{{val|463 734 1075 1300 1602 1713}}
| {{val| 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, 1275/1274, 2601/2600, 3025/3024, 32955/32912, 45500/45441
|{{val|463 734 1075 1300 1602 1713 1892}}
| {{val| 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<br>(Reduced)
! Cents<br>(reduced)
! Cents<br>(Reduced)
! Associated<br>ratio
! Associated<br>Ratio
! Temperaments
! Temperaments
|-
|-
|1
| 1
|131\463
| 131\463
|339.52
| 339.52
|243/200
| 243/200
|Amity
| [[Amity]]
|-
|-
|1
| 1
|198\463
| 198\463
|513.17
| 513.17
|168/125, 121/90
| 168/125, 121/90
|Trinity
| [[Trinity]]
|-
|-
|1
| 1
|31\463
| 31\463
|80.35
| 80.35
|8575/8192, 22/21
| 22/21
|Undesemi
| [[Undesemi]]
|}
|}

Revision as of 04:19, 13 April 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

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.

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 [9 -13 5⟩, [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, 6250/6237, 19712/19683, 180224/180075 ⟨463 734 1075 1300 1602] -0.1197 0.1262 4.87
2.3.5.7.11.13 3025/3024, 1716/1715, 4096/4095, 676/675, 6250/6237 ⟨463 734 1075 1300 1602 1713] -0.0643 0.1691 6.52
2.3.5.7.11.13.17 442/441, 595/594, 1275/1274, 2601/2600, 3025/3024, 32955/32912, 45500/45441 ⟨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
(Reduced) 		Cents
(Reduced) 		Associated
Ratio 		Temperaments
1 131\463 339.52 243/200 Amity
1 198\463 513.17 168/125, 121/90 Trinity
1 31\463 80.35 22/21 Undesemi
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