2053edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|2053}} == Theory == 2053edo is consistent to the 5-odd-limit, its harmonic 7 is exactly between its steps. The equal temperamen..."
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|2053}}
{{ED intro}}


== Theory ==
== Theory ==
2053edo is [[consistent]] to the [[5-odd-limit]], its [[harmonic]] [[7/1|7]] is exactly between its steps. The equal temperament is strong in the 2.3.5.13.19.23.31 [[subgroup]], [[tempering out]] 359424/359375, 22816/22815, 96876/96875, 497705/497664, 4784000/4782969 and 369664/369603. Using the 2.3.5.13.19.37 subgroup, it tempers out [[7696/7695]].
2053edo is [[consistent]] to the [[5-odd-limit]], its [[harmonic]] [[7/1|7]] is exactly between its steps. It is strong in the 2.3.5.13.19.23.31 [[subgroup]], [[tempering out]] 359424/359375, 22816/22815, 96876/96875, 497705/497664, 4784000/4782969, and 369664/369603. Using the 2.3.5.13.19.37 subgroup, it tempers out [[7696/7695]].


=== Prime harmonics ===
=== Prime harmonics ===
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== 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
| {{monzo|3254 -2053}}
| {{monzo|3254 -2053}}
| {{mapping|2053 3254}}
| {{mapping|2053 3254}}
| -0.0133
| −0.0133
| 0.0133
| 0.0133
| 2.28
| 2.28
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| {{monzo|37 25 -33}}, {{monzo|93 -66 5}}
| {{monzo|37 25 -33}}, {{monzo|93 -66 5}}
| {{mapping|2053 3254 4767}}
| {{mapping|2053 3254 4767}}
| -0.0157
| −0.0157
| 0.0114
| 0.0114
| 1.95
| 1.95
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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
|-
! Periods<br />per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br>Ratio*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
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| [[Whoosh]]
| [[Whoosh]]
|}
|}
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct


<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
== Music ==
; [[Francium]]
* "Willie Dustice" from ''Don't Give Your Kids These Names!'' (2025) − [https://open.spotify.com/track/6t8HM9dCOjxDuNb5xO9Bma Spotify] | [https://francium223.bandcamp.com/track/willie-dustice Bandcamp] | [https://www.youtube.com/watch?v=Osjql2cB9XU YouTube] − in Liebic, 2053edo tuning

Latest revision as of 13:31, 13 March 2026

← 2052edo 2053edo 2054edo →
Prime factorization 2053 (prime)
Step size 0.58451 ¢ 
Fifth 1201\2053 (701.997 ¢)
Semitones (A1:m2) 195:154 (114 ¢ : 90.01 ¢)
Consistency limit 5
Distinct consistency limit 5

2053 equal divisions of the octave (abbreviated 2053edo or 2053ed2), also called 2053-tone equal temperament (2053tet) or 2053 equal temperament (2053et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2053 equal parts of about 0.585 ¢ each. Each step represents a frequency ratio of 21/2053, or the 2053rd root of 2.

Theory

2053edo is consistent to the 5-odd-limit, its harmonic 7 is exactly between its steps. It is strong in the 2.3.5.13.19.23.31 subgroup, tempering out 359424/359375, 22816/22815, 96876/96875, 497705/497664, 4784000/4782969, and 369664/369603. Using the 2.3.5.13.19.37 subgroup, it tempers out 7696/7695.

Prime harmonics

Approximation of prime harmonics in 2053edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.042 +0.048 -0.292 -0.125 -0.002 +0.256 +0.003 +0.074 -0.254 +0.020
Relative (%) +0.0 +7.2 +8.2 -50.0 -21.3 -0.3 +43.9 +0.5 +12.7 -43.5 +3.5
Steps
(reduced) 		2053
(0) 		3254
(1201) 		4767
(661) 		5763
(1657) 		7102
(943) 		7597
(1438) 		8392
(180) 		8721
(509) 		9287
(1075) 		9973
(1761) 		10171
(1959)

Subsets and supersets

2053edo is the 310th prime edo. 4106edo, which doubles it, gives a good correction to the harmonic 7.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [3254 -2053⟩ [⟨2053 3254]] −0.0133 0.0133 2.28
2.3.5 [37 25 -33⟩, [93 -66 5⟩ [⟨2053 3254 4767]] −0.0157 0.0114 1.95

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
1 959\2053 560.546 864/625 Whoosh

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct

Music

Francium
  • "Willie Dustice" from Don't Give Your Kids These Names! (2025) − Spotify | Bandcamp | YouTube − in Liebic, 2053edo tuning
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