1193edo: Difference between revisions

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{{novelty}}{{stub}}{{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 supports 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 ===
=== 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" | [[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| 1891 -1193 }}
| {{monzo| 1891 -1193 }}
| {{val| 1193 1891 }}
| {{mapping| 1193 1891 }}
| -0.0443
| −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
Line 38: Line 39:
| 2.3.5.7
| 2.3.5.7
| 2401/2400, {{monzo| -13 -12 15 -1 }}, {{monzo| 41 -15 -5 -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
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| 2.3.5.7.11
| 2.3.5.7.11
| 2401/2400, 3025/3024, 17561600/17537553, 95703125/95664294
| 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
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| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 2401/2400, 3025/3024, 4096/4095, 78125/78078, 114345/114244
| 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, 4096/4095, 42500/42471
| 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
|91.534
| 91.534
|{{monzo|144 -22 -47}}
| {{monzo| 144 -22 -47 }}
|[[Gross]]
| [[Gross]]
|-
|-
|1
| 1
|257\1193
| 257\1193
|258.508
| 258.508
|125/108
| 125/108
|[[Lafa]]
| [[Lafa]]
|-
|-
|1
| 1
|355\1193
| 355\1193
|357.083
| 357.083
|768/625
| 768/625
|[[Dodifo]]
| [[Dodifo]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct


== Music ==
== Music ==
* [https://www.youtube.com/watch?v=FRdrzOkAKic I Made A Gross Mistake] by Francium
; [[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]]

Latest revision as of 06:13, 21 February 2025

← 1192edo 1193edo 1194edo →
Prime factorization 1193 (prime)
Step size 1.00587 ¢ 
Fifth 698\1193 (702.096 ¢)
Semitones (A1:m2) 114:89 (114.7 ¢ : 89.52 ¢)
Consistency limit 11
Distinct consistency limit 11

1193 equal divisions of the octave (abbreviated 1193edo or 1193ed2), also called 1193-tone equal temperament (1193tet) or 1193 equal temperament (1193et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1193 equal parts of about 1.01 ¢ each. Each step represents a frequency ratio of 21/1193, or the 1193rd root of 2.

Theory

1193edo is consistent to the 11-odd-limit. As an equal temperament, it tempers out [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

Approximation of prime harmonics in 1193edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.141 -0.061 -0.175 -0.103 +0.378 -0.345 +0.224 +0.393 +0.431 -0.358
Relative (%) +0.0 +14.0 -6.0 -17.4 -10.2 +37.5 -34.3 +22.2 +39.1 +42.9 -35.6
Steps
(reduced) 		1193
(0) 		1891
(698) 		2770
(384) 		3349
(963) 		4127
(548) 		4415
(836) 		4876
(104) 		5068
(296) 		5397
(625) 		5796
(1024) 		5910
(1138)

Subsets and supersets

1193edo is the 196th prime edo.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [1891 -1193⟩ [⟨1193 1891]] −0.0443 0.0443 4.41
2.3.5 [10 -40 -23⟩, [77 -31 -12⟩ [⟨1193 1891 2770]] −0.0209 0.0491 4.88
2.3.5.7 2401/2400, [-13 -12 15 -1⟩, [41 -15 -5 -2⟩ [⟨1193 1891 2770 3349]] −0.000028 0.0558 5.55
2.3.5.7.11 2401/2400, 3025/3024, 17561600/17537553, 95703125/95664294 [⟨1193 1891 2770 3349 4127]] +0.0059 0.0513 5.10
2.3.5.7.11.13 2401/2400, 3025/3024, 4096/4095, 78125/78078, 114345/114244 [⟨1193 1891 2770 3349 4127 4415]] −0.0121 0.0617 6.14
2.3.5.7.11.13.17 2401/2400, 2431/2430, 2601/2600, 3025/3024, 4096/4095, 42500/42471 [⟨1193 1891 2770 3349 4127 4415 4876]] +0.0017 0.0664 6.60

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
1 91\1193 91.534 [144 -22 -47⟩ Gross
1 257\1193 258.508 125/108 Lafa
1 355\1193 357.083 768/625 Dodifo

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

Music

Francium
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