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}}
{{EDO intro|1193}}
== 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.
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.
 
=== 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" | [[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" | [[Comma list|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]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.3
| 2.3
|{{monzo|1891 -1193}}
| {{monzo| 1891 -1193 }}
|{{val|1193 1891}}
| {{val| 1193 1891 }}
| -0.0443
| -0.0443
| 0.0443
| 0.0443
| 4.40
| 4.40
|-
|-
|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}}
| {{val| 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| -18 -13 13 3 }}, {{monzo| 36 -16 -7 2 }}
|{{val|1193 1891 2770 3349}}
| {{val|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, 41503/41472, 151263/151250, 26214400/26198073
|{{val|1193 1891 2770 3349 4127}}
| {{val| 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, 154880/154791, 1071875/1070784, 1960000/1957527, 5175625/5174928
|{{val|1193 1891 2770 3349 4127 4415}}
| {{val| 1193 1891 2770 3349 4127 4415 }}
| -0.0121
| -0.0121
| 0.0617
| 0.0617
| 6.13
| 6.13
|-
|-
|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, 8624/8619, 12376/12375, 37180/37179, 42500/42471, 47432/47385, 122825/122694, 154880/154791
|{{val|1193 1891 2770 3349 4127 4415 4876}}
| {{val|1193 1891 2770 3349 4127 4415 4876}}
| +0.0017
| +0.0017
| 0.0664
| 0.0664
Line 64: Line 69:
|+Table of rank-2 temperaments by generator
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Periods<br>per 8ve
! Generator<br>(reduced)
! Generator<br>(Reduced)
! Cents<br>(reduced)
! Cents<br>(Reduced)
! Associated<br>ratio
! Associated<br>Ratio
! Temperaments
! Temperaments
|-
|-
|1
| 1
|91\1193
| 91\1193
|91.533948
| 91.533948
|{{monzo|144 -22 -47}}
| {{monzo|144 -22 -47}}
|Gross
| Gross
|}
|}

Revision as of 13:10, 7 April 2023

← 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

Template:EDO intro

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.

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 4.40
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⟩, [-18 -13 13 3⟩, [36 -16 -7 2⟩ ⟨1193 1891 2770 3349] -0.000028 0.0558 5.55
2.3.5.7.11 2401/2400, 3025/3024, 41503/41472, 151263/151250, 26214400/26198073 ⟨1193 1891 2770 3349 4127] +0.0059 0.0513 5.10
2.3.5.7.11.13 2401/2400, 3025/3024, 154880/154791, 1071875/1070784, 1960000/1957527, 5175625/5174928 ⟨1193 1891 2770 3349 4127 4415] -0.0121 0.0617 6.13
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 ⟨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
(Reduced) 		Cents
(Reduced) 		Associated
Ratio 		Temperaments
1 91\1193 91.533948 [144 -22 -47⟩ Gross
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