3643edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|3643}} == Theory == 3643edo is consistent to the 15-odd-limit, tempering out 123201/123200, 6656/6655, 1016064/1015625, 655473/..."
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|3643}}
{{ED intro}}


== Theory ==
== Theory ==
Line 13: Line 13:
== 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" |[[Comma list|Comma List]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Comma list]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! rowspan="2" | [[Mapping]]
! colspan="2" |Tuning Error
! rowspan="2" | Optimal<br />8ve stretch (¢)
|-
! colspan="2" | Tuning error
![[TE error|Absolute]] (¢)
|-
![[TE simple badness|Relative]] (%)
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
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| {{monzo|22 33 -32}}, {{monzo|199 -86 -27}}
| {{monzo|22 33 -32}}, {{monzo|199 -86 -27}}
| {{mapping|3643 5774 8459}}
| {{mapping|3643 5774 8459}}
| -0.0089
| −0.0089
| 0.0154
| 0.0154
| 4.68
| 4.68
Line 39: Line 40:
| {{monzo|-9 5 -8 7}}, {{monzo|3 -24 3 10}}, {{monzo|43 -1 -13 -4}}
| {{monzo|-9 5 -8 7}}, {{monzo|3 -24 3 10}}, {{monzo|43 -1 -13 -4}}
| {{mapping|3643 5774 8459 10227}}
| {{mapping|3643 5774 8459 10227}}
| -0.0010
| −0.0010
| 0.0192
| 0.0192
| 5.83
| 5.83
Line 46: Line 47:
| 117649/117612, 50014503/50000000, 520224768/519921875, 234365481/234256000
| 117649/117612, 50014503/50000000, 520224768/519921875, 234365481/234256000
| {{mapping|3643 5774 8459 10227 12603}}
| {{mapping|3643 5774 8459 10227 12603}}
| -0.0063
| −0.0063
| 0.0202
| 0.0202
| 6.13
| 6.13
Line 53: Line 54:
| 123201/123200, 6656/6655, 1016064/1015625, 655473/655360, 2250423/2249728
| 123201/123200, 6656/6655, 1016064/1015625, 655473/655360, 2250423/2249728
| {{mapping|3643 5774 8459 10227 12603 13481}}
| {{mapping|3643 5774 8459 10227 12603 13481}}
| -0.0097
| −0.0097
| 0.0199
| 0.0199
| 6.04
| 6.04
Line 60: Line 61:
| 12376/12375, 14400/14399, 123201/123200, 1796256/1795625, 637637/637500, 2100875/2100384
| 12376/12375, 14400/14399, 123201/123200, 1796256/1795625, 637637/637500, 2100875/2100384
| {{mapping|3643 5774 8459 10227 12603 13481 14891}}
| {{mapping|3643 5774 8459 10227 12603 13481 14891}}
| -0.0126
| −0.0126
| 0.0197
| 0.0197
| 5.98
| 5.98
|}
|}
== Music ==
; [[Francium]]
* "Don't Make a Difference" from ''Don't'' (2025) – [https://open.spotify.com/track/1sRKpCbUmknJfUsYlpqvbW Spotify] | [https://francium223.bandcamp.com/track/dont-make-a-difference Bandcamp] | [https://www.youtube.com/watch?v=6C515dSWG3E YouTube]

Latest revision as of 11:57, 3 July 2025

← 3642edo 3643edo 3644edo →
Prime factorization 3643 (prime)
Step size 0.329399 ¢ 
Fifth 2131\3643 (701.949 ¢)
Semitones (A1:m2) 345:274 (113.6 ¢ : 90.26 ¢)
Consistency limit 15
Distinct consistency limit 15

3643 equal divisions of the octave (abbreviated 3643edo or 3643ed2), also called 3643-tone equal temperament (3643tet) or 3643 equal temperament (3643et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3643 equal parts of about 0.329 ¢ each. Each step represents a frequency ratio of 21/3643, or the 3643rd root of 2.

Theory

3643edo is consistent to the 15-odd-limit, tempering out 123201/123200, 6656/6655, 1016064/1015625, 655473/655360 and 2250423/2249728 in the 13-limit. It supports 9177/9176 in the 2.3.7.19.23.31.37 subgroup.

Prime harmonics

Approximation of prime harmonics in 3643edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.006 +0.071 -0.064 +0.096 +0.098 +0.123 -0.066 -0.111 +0.124 -0.045
Relative (%) +0.0 -1.8 +21.6 -19.4 +29.1 +29.8 +37.3 -20.0 -33.6 +37.5 -13.7
Steps
(reduced) 		3643
(0) 		5774
(2131) 		8459
(1173) 		10227
(2941) 		12603
(1674) 		13481
(2552) 		14891
(319) 		15475
(903) 		16479
(1907) 		17698
(3126) 		18048
(3476)

Subsets and supersets

3643edo is the 510th prime edo.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [-5774 3643⟩ [⟨3643 5774]] +0.0019 0.0019 0.58
2.3.5 [22 33 -32⟩, [199 -86 -27⟩ [⟨3643 5774 8459]] −0.0089 0.0154 4.68
2.3.5.7 [-9 5 -8 7⟩, [3 -24 3 10⟩, [43 -1 -13 -4⟩ [⟨3643 5774 8459 10227]] −0.0010 0.0192 5.83
2.3.5.7.11 117649/117612, 50014503/50000000, 520224768/519921875, 234365481/234256000 [⟨3643 5774 8459 10227 12603]] −0.0063 0.0202 6.13
2.3.5.7.11.13 123201/123200, 6656/6655, 1016064/1015625, 655473/655360, 2250423/2249728 [⟨3643 5774 8459 10227 12603 13481]] −0.0097 0.0199 6.04
2.3.5.7.11.13.17 12376/12375, 14400/14399, 123201/123200, 1796256/1795625, 637637/637500, 2100875/2100384 [⟨3643 5774 8459 10227 12603 13481 14891]] −0.0126 0.0197 5.98

Music

Francium
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