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1193edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|1193}} == Theory == 1193et tempers out 2401/2400 in the 7-limit; 117440512/117406179, 26214400/26198073, 151263/151250, 369140625/369098752,..."
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|1193}}
{{ED intro}}
 
== Theory ==
== Theory ==
1193et tempers out [[2401/2400]] in the 7-limit; [[117440512/117406179]], 26214400/26198073, 151263/151250, 369140625/369098752, 537109375/536870912, [[3025/3024]], [[41503/41472]] and 781258401/781250000 in the 11-limit. It provides the optimal patent val for the [[Gross]] temperament.
1193edo is [[consistent]] to the [[11-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] {{monzo| 144 -22 -47 }} (gross comma) in the 5-limit; [[2401/2400]] in the 7-limit; [[3025/3024]], [[41503/41472]], 151263/151250, 17561600/17537553, 26214400/26198073, 95703125/95664294, and [[117440512/117406179]] in the 11-limit.  
 
=== Prime harmonics ===
{{Harmonics in equal|1193}}
 
=== Subsets and supersets ===
1193edo is the 196th [[prime edo]].
1193edo is the 196th [[prime edo]].
{{Harmonics in equal|1193}}


==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" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
|-
![[TE error|Absolute]] (¢)
! rowspan="2" | [[Subgroup]]
![[TE simple badness|Relative]] (%)
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
|-
|2.3
! [[TE error|Absolute]] (¢)
|{{monzo|1891 -1193}}
! [[TE simple badness|Relative]] (%)
|{{val|1193 1891}}
|-
| -0.0443
| 2.3
| {{monzo| 1891 -1193 }}
| {{mapping| 1193 1891 }}
| −0.0443
| 0.0443
| 0.0443
| 4.40
| 4.41
|-
|-
|2.3.5
| 2.3.5
|{{monzo|10 -40 -23}}, {{monzo|77 -31 -12}}
| {{monzo| 10 -40 -23 }}, {{monzo| 77 -31 -12 }}
|{{val|1193 1891 2770}}
| {{mapping| 1193 1891 2770 }}
| -0.0209
| −0.0209
| 0.0491
| 0.0491
| 4.88
| 4.88
|-
|-
|2.3.5.7
| 2.3.5.7
|2401/2400, {{monzo|-13 -12 15 -1}}, {{monzo|-18 -13 13 3}}, {{monzo|36 -16 -7 2}}
| 2401/2400, {{monzo| -13 -12 15 -1 }}, {{monzo| 41 -15 -5 -2 }}
|{{val|1193 1891 2770 3349}}
| {{mapping| 1193 1891 2770 3349 }}
| -0.000028
| −0.000028
| 0.0558
| 0.0558
| 5.55
| 5.55
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|2401/2400, 3025/3024, 41503/41472, 151263/151250, 26214400/26198073
| 2401/2400, 3025/3024, 17561600/17537553, 95703125/95664294
|{{val|1193 1891 2770 3349 4127}}
| {{mapping| 1193 1891 2770 3349 4127 }}
| +0.0059
| +0.0059
| 0.0513
| 0.0513
| 5.10
| 5.10
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|2401/2400, 3025/3024, 154880/154791, 1071875/1070784, 1960000/1957527, 5175625/5174928
| 2401/2400, 3025/3024, 4096/4095, 78125/78078, 114345/114244
|{{val|1193 1891 2770 3349 4127 4415}}
| {{mapping| 1193 1891 2770 3349 4127 4415 }}
| -0.0121
| −0.0121
| 0.0617
| 0.0617
| 6.13
| 6.14
|-
|-
|2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
|2401/2400, 2431/2430, 2601/2600, 3025/3024, 8624/8619, 12376/12375, 37180/37179, 42500/42471, 47432/47385, 122825/122694, 154880/154791
| 2401/2400, 2431/2430, 2601/2600, 3025/3024, 4096/4095, 42500/42471
|{{val|1193 1891 2770 3349 4127 4415 4876}}
| {{mapping| 1193 1891 2770 3349 4127 4415 4876 }}
| +0.0017
| +0.0017
| 0.0664
| 0.0664
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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
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|91\1193
| 91\1193
|91.533948
| 91.534
|{{monzo|144 -22 -47}}
| {{monzo| 144 -22 -47 }}
|Gross
| [[Gross]]
|-
| 1
| 257\1193
| 258.508
| 125/108
| [[Lafa]]
|-
| 1
| 355\1193
| 357.083
| 768/625
| [[Dodifo]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
== Music ==
; [[User:Francium|Francium]]
* "I Made A Gross Mistake" from ''Gross Temperament EP'' (2023) [https://open.spotify.com/track/1hLYQFf1K97uv4jOAaGzgS Spotify] | [https://francium223.bandcamp.com/track/i-made-a-gross-mistake Bandcamp] | [https://www.youtube.com/watch?v=FRdrzOkAKic YouTube] – gross in 1193edo
* ''1193'' (2024) – [https://open.spotify.com/album/4lJGqEt76mFGRbxWQmT6vo Spotify] | [https://francium223.bandcamp.com/album/1193 bandcamp] | [https://www.youtube.com/playlist?list=PLLZE7hMjEXRatIUXyBQyjNvDsiV40JAmk YouTube] – 4-piece EP in 1193edo
[[Category:Listen]]
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