3889edo: Difference between revisions

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=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|3889}}
{{Harmonics in equal|3889|columns=11}}
{{Harmonics in equal|3889|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 3889edo (continued)}}


=== Subsets and supersets ===
=== Subsets and supersets ===
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|-
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[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]] (¢)
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|-
|-
| 2.3
| 2.3
| {{monzo|6164 -3889}}
| {{Monzo| 6164 -3889 }}
| {{mapping|3889 6164}}
| {{Mapping| 3889 6164 }}
| −0.0079
| −0.0079
| 0.0079
| 0.0079
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|-
|-
| 2.3.5
| 2.3.5
| {{monzo|-90 -15 49}}, {{monzo|56 -91 38}}
| {{Monzo| -90 -15 49 }}, {{monzo| 56 -91 38 }}
| {{mapping|3889 6164 9030}}
| {{Mapping| 3889 6164 9030 }}
| −0.0062
| −0.0062
| 0.0068
| 0.0068
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|-
|-
| 2.3.5.7
| 2.3.5.7
| {{monzo|-4 17 1 -9}}, {{monzo|2 -20 14 -1}}, {{monzo|46 -14 -3 -6}}
| {{Monzo| -4 17 1 -9 }}, {{monzo| 2 -20 14 -1 }}, {{monzo| 46 -14 -3 -6 }}
| {{mapping|3889 6164 9030 10918}}
| {{Mapping| 3889 6164 9030 10918 }}
| −0.0101
| −0.0101
| 0.0089
| 0.0089
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| 2.3.5.7.11
| 2.3.5.7.11
| 21437500/21434787, 47265625/47258883, 56953125/56942116, 104857600/104825259
| 21437500/21434787, 47265625/47258883, 56953125/56942116, 104857600/104825259
| {{mapping|3889 6164 9030 10918 13454}}
| {{Mapping| 3889 6164 9030 10918 13454 }}
| −0.0129
| −0.0129
| 0.0098
| 0.0098
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|-
|-
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 123201/123200, 6656/6655, 1990656/1990625, 492128/492075, 29046875/29042496
| 6656/6655, 123201/123200, 492128/492075, 1990656/1990625, 29046875/29042496
| {{mapping|3889 6164 9030 10918 13454 14391}}
| {{Mapping| 3889 6164 9030 10918 13454 14391 }}
| −0.0106
| −0.0106
| 0.0103
| 0.0103
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| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 12376/12375, 14400/14399, 123201/123200, 37180/37179, 1990656/1990625, 361250/361179
| 12376/12375, 14400/14399, 123201/123200, 37180/37179, 1990656/1990625, 361250/361179
| {{mapping|3889 6164 9030 10918 13454 14391 15896}}
| {{Mapping| 3889 6164 9030 10918 13454 14391 15896 }}
| −0.0075
| −0.0075
| 0.0121
| 0.0121
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|+ style="font-size: 105%;" | 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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| 602\3889
| 602\3889
| 185.755
| 185.755
| {{monzo|24 4 -13}}
| {{Monzo| 24 4 -13 }}
| [[Pirate]]
| [[Pirate]]
|}
|}
<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 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


== Music ==
== Music ==
; [[Francium]]
; [[Francium]]
* "Don't Stop Interrupting People" from ''Don't'' (2025) – [https://open.spotify.com/track/2W1M2taD9SRU2MIz7YqpxQ Spotify] | [https://francium223.bandcamp.com/track/dont-stop-interrupting-people Bandcamp] | [https://www.youtube.com/watch?v=nOoXjJ6dqhk YouTube]
* "Don't Stop Interrupting People" from ''Don't'' (2025) – [https://open.spotify.com/track/2W1M2taD9SRU2MIz7YqpxQ Spotify] | [https://francium223.bandcamp.com/track/dont-stop-interrupting-people Bandcamp] | [https://www.youtube.com/watch?v=nOoXjJ6dqhk YouTube]

Revision as of 14:31, 17 April 2026

← 3888edo 3889edo 3890edo →
Prime factorization 3889 (prime)
Step size 0.308563 ¢ 
Fifth 2275\3889 (701.98 ¢)
Semitones (A1:m2) 369:292 (113.9 ¢ : 90.1 ¢)
Consistency limit 27
Distinct consistency limit 27

3889 equal divisions of the octave (abbreviated 3889edo or 3889ed2), also called 3889-tone equal temperament (3889tet) or 3889 equal temperament (3889et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3889 equal parts of about 0.309 ¢ each. Each step represents a frequency ratio of 21/3889, or the 3889th root of 2.

Theory

3889edo is consistent to the 27-odd-limit, tempering out 12376/12375, 14400/14399, 6175/6174, 8625/8624, 89376/89375, 123201/123200, 1549184/1549125 and 1990656/1990625 in the 23-limit. It is strong in the 2.3.5.7.13.17.19.23.31 subgroup, tempering out 6175/6174, 14365/14364, 426496/426465, 52326/52325, 52003/52000, 1549184/1549125, 1990656/1990625 and 22816/22815. The equal temperament also tempers out 19251/19250 in the 2.3.5.7.11.23.31 subgroup and 5440/5439 in the 2.3.5.7.17.37 subgroup.

Prime harmonics

Approximation of prime harmonics in 3889edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.025 +0.007 +0.061 +0.083 -0.003 -0.044 -0.059 -0.041 +0.096 +0.040
Relative (%) +0.0 +8.1 +2.2 +19.7 +27.0 -1.0 -14.3 -19.0 -13.2 +31.2 +13.1
Steps
(reduced) 		3889
(0) 		6164
(2275) 		9030
(1252) 		10918
(3140) 		13454
(1787) 		14391
(2724) 		15896
(340) 		16520
(964) 		17592
(2036) 		18893
(3337) 		19267
(3711)
Approximation of prime harmonics in 3889edo (continued)
Harmonic 37 41 43 47 53 59 61 67 71 73 79
Error Absolute (¢) +0.134 +0.148 +0.079 +0.063 +0.036 +0.124 +0.112 -0.006 -0.113 -0.070 -0.124
Relative (%) +43.6 +48.0 +25.6 +20.4 +11.7 +40.1 +36.2 -2.1 -36.7 -22.8 -40.3
Steps
(reduced) 		20260
(815) 		20836
(1391) 		21103
(1658) 		21602
(2157) 		22276
(2831) 		22878
(3433) 		23065
(3620) 		23591
(257) 		23916
(582) 		24072
(738) 		24515
(1181)

Subsets and supersets

3889edo is the 539th prime edo.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [6164 -3889⟩ [⟨3889 6164]] −0.0079 0.0079 2.56
2.3.5 [-90 -15 49⟩, [56 -91 38⟩ [⟨3889 6164 9030]] −0.0062 0.0068 2.20
2.3.5.7 [-4 17 1 -9⟩, [2 -20 14 -1⟩, [46 -14 -3 -6⟩ [⟨3889 6164 9030 10918]] −0.0101 0.0089 2.88
2.3.5.7.11 21437500/21434787, 47265625/47258883, 56953125/56942116, 104857600/104825259 [⟨3889 6164 9030 10918 13454]] −0.0129 0.0098 3.18
2.3.5.7.11.13 6656/6655, 123201/123200, 492128/492075, 1990656/1990625, 29046875/29042496 [⟨3889 6164 9030 10918 13454 14391]] −0.0106 0.0103 3.34
2.3.5.7.11.13.17 12376/12375, 14400/14399, 123201/123200, 37180/37179, 1990656/1990625, 361250/361179 [⟨3889 6164 9030 10918 13454 14391 15896]] −0.0075 0.0121 3.92

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
1 602\3889 185.755 [24 4 -13⟩ Pirate

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

Music

Francium
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