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3889edo: Difference between revisions

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== Theory ==
== 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.
3889edo is [[consistent]] to the [[27-odd-limit]], and except for [[29/19]] and its [[octave complement]], it is consistent to the [[31-odd-limit]].
 
As an equal temperament, it [[tempering out|tempers out]] the [[pirate comma]], the [[starscape comma]], and the [[quartisma]]. Some of the simpler commas it tempers out in the higher limits include [[6656/6655]], [[123201/123200]] and [[1990656/1990625]] in the [[13-limit]]; [[12376/12375]], [[14400/14399]] in the [[17-limit]]; [[5776/5775]], [[6175/6174]], 14365/14364, 23409/23408, 28900/28899, 43681/43680 in the [[19-limit]]; [[5083/5082]], 7866/7865, and 8625/8624 in the [[23-limit]].  


=== 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}}
| 645700815/645657712, {{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
| 1771875/1771561, 3294225/3294172, 14348907/14348180, 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, 823680/823543, 1990656/1990625
| {{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
| 6656/6655, 12376/12375, 28561/28560, 37180/37179, 361250/361179, 937125/937024
| {{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 lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|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]
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