1193edo: Difference between revisions

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== 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.
1193et tempers out [[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. It supports the [[gross]] temperament.


=== Prime harmonics ===
=== Prime harmonics ===
Line 24: Line 24:
| 2.3
| 2.3
| {{monzo| 1891 -1193 }}
| {{monzo| 1891 -1193 }}
| {{val| 1193 1891 }}
| {{mapping| 1193 1891 }}
| -0.0443
| -0.0443
| 0.0443
| 0.0443
Line 31: Line 31:
| 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
Line 38: Line 38:
| 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
Line 45: Line 45:
| 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
Line 52: Line 52:
| 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
Line 59: Line 59:
| 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
Line 69: 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*
! Cents<br>(Reduced)
! Cents*
! Associated<br>Ratio
! 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>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct


== Music ==
== Music ==
* [https://www.youtube.com/watch?v=FRdrzOkAKic I Made A Gross Mistake] by Francium
; [[User:Francium|Francium]]
* [https://www.youtube.com/watch?v=FRdrzOkAKic ''I Made A Gross Mistake''] (2023)

Revision as of 13:04, 17 October 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; 3025/3024, 41503/41472, 151263/151250, 17561600/17537553, 26214400/26198073, 95703125/95664294, and 117440512/117406179 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⟩, [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 6.13
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 it is distinct

Music

Francium
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