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1861edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|1861}} == Theory == 1861et tempers out 369140625/369098752, 537109375/536870912 and 3025/3024 in the 11-limit; 1181640625/1181599328, 225000/224..."
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|1861}}
{{ED intro}}
 
== Theory ==
== Theory ==
1861et tempers out 369140625/369098752, 537109375/536870912 and [[3025/3024]] in the 11-limit; 1181640625/1181599328, 225000/224939, 78125/78078, 1610510000/1610497161, 8859375/8859136, [[4096/4095]], 196625/196608, 405769/405504, 10549994/10546875 and 91182091/91125000 in the 13-limit.
1861edo is only [[consistent]] to the [[5-odd-limit]], and the [[harmonic]] [[3/1|3]] is about halfway between its steps. It has a reasonable approximation of the 2.9.5.21.11 [[subgroup]].  
===Odd harmonics===
 
=== Odd harmonics ===
{{Harmonics in equal|1861}}
{{Harmonics in equal|1861}}
===Subsets and supersets===
1861edo is the 284th [[prime edo]].


==Regular temperament properties==
=== Subsets and supersets ===
1861edo is the 284th [[prime edo]]. 3722edo, which doubles it, provides a good correction to harmonics 3, 7, and 13.
 
== 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" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|2950 -1861}}
|{{val|1861 2950}}
| -0.0783
| 0.0783
| 12.14
|-
|2.3.5
|{{monzo|57 -55 13}}, {{monzo|91 -12 -31}}
|{{val|1861 2950 4321}}
| -0.0422
| 0.0818
| 12.69
|-
|-
|2.3.5.7
! rowspan="2" | [[Subgroup]]
|95703125/95551488, 359661568/358722675, 160163466183/160000000000
! rowspan="2" | [[Comma list]]
|{{val|1861 2950 4321 5224}}
! rowspan="2" | [[Mapping]]
| -0.0036
! rowspan="2" | Optimal<br />8ve stretch (¢)
| 0.0973
! colspan="2" | Tuning error
| 15.08
|-
|-
|2.3.5.7.11
! [[TE error|Absolute]] (¢)
|3025/3024, 19712/19683, 26796875/26763264, 102538515387/102400000000
! [[TE simple badness|Relative]] (%)
|{{val|1861 2950 4321 5224 6438}}
| -0.0028
| 0.0871
| 13.51
|-
|-
|2.3.5.7.11.13
| 2.9
|3025/3024, 4096/4095, 4459/4455, 765625/764478, 18302823/18279040
| {{monzo| -5899 1861 }}
|{{val|1861 2950 4321 5224 6438 6887}}
| {{mapping| 1861 5899 }}
| -0.0163
| +0.0234
| 0.0850
| 0.0234
| 13.18
| 3.63
|-
|2.3.5.7.11.13.17
|1225/1224, 2431/2430, 4096/4095, 4459/4455, 42500/42471, 22000363/21970000
|{{val|1861 2950 4321 5224 6438 6887 7607}}
| -0.0192
| 0.0790
| 12.25
|}
|}
== Scales ==
* [[Helayo14]]
== Music ==
; [[Francium]]
* "Happy Apocalypse!" from ''Helayo EP'' (2023) – [https://open.spotify.com/track/59RXlAsYgZynU6YFPfLAYg Spotify] | [https://francium223.bandcamp.com/track/happy-apocalypse Bandcamp] | [https://youtu.be/TD_ULM_Mwso?si=faP-SPfyf6ZmGWA9 YouTube] – helayo in 1861edo tuning
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/1861edo"