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 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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=== Subsets and supersets ===
=== Subsets and supersets ===
463edo is the 90th [[prime edo]].
463edo is the 90th [[prime edo]].
== Intervals ==
{{Main|Table of 463edo intervals}}


== 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]]
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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
| 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
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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
| 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
| 31\463
| 80.35
| 22/21
| [[Undesemi]]
|-
| 1
| 51\463
| 132.18
| 27/25
| [[Astro]]
|-
|-
| 1
| 1
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| 339.52
| 339.52
| 243/200
| 243/200
| [[Amity]]
| [[Amity]] (5-limit)
|-
| 1
| 176\463
| 456.16
| 125/96
| [[Qak]]
|-
|-
| 1
| 1
| 198\463
| 198\463
| 513.17
| 513.17
| 168/125, 121/90
| 121/90
| [[Trinity]]
| [[Trinity]] (463fg)
|-
| 1
| 31\463
| 80.35
| 22/21
| [[Undesemi]]
|}
|}
== 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]]

Latest revision as of 14:26, 23 February 2025

← 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

463 equal divisions of the octave (abbreviated 463edo or 463ed2), also called 463-tone equal temperament (463tet) or 463 equal temperament (463et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 463 equal parts of about 2.59 ¢ each. Each step represents a frequency ratio of 21/463, or the 463rd root of 2.

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.

Intervals

Main article: Table of 463edo intervals

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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