1193edo: Difference between revisions

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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! 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
| 2.3
| {{monzo| 1891 -1193 }}
| {{monzo| 1891 -1193 }}
| {{mapping| 1193 1891 }}
| {{mapping| 1193 1891 }}
| -0.0443
| &minus;0.0443
| 0.0443
| 0.0443
| 4.41
| 4.41
Line 32: Line 24:
| {{monzo| 10 -40 -23 }}, {{monzo| 77 -31 -12 }}
| {{monzo| 10 -40 -23 }}, {{monzo| 77 -31 -12 }}
| {{mapping| 1193 1891 2770 }}
| {{mapping| 1193 1891 2770 }}
| -0.0209
| &minus;0.0209
| 0.0491
| 0.0491
| 4.88
| 4.88
Line 39: Line 31:
| 2401/2400, {{monzo| -13 -12 15 -1 }}, {{monzo| 41 -15 -5 -2 }}
| 2401/2400, {{monzo| -13 -12 15 -1 }}, {{monzo| 41 -15 -5 -2 }}
| {{mapping| 1193 1891 2770 3349 }}
| {{mapping| 1193 1891 2770 3349 }}
| -0.000028
| &minus;0.000028
| 0.0558
| 0.0558
| 5.55
| 5.55
Line 53: Line 45:
| 2401/2400, 3025/3024, 4096/4095, 78125/78078, 114345/114244
| 2401/2400, 3025/3024, 4096/4095, 78125/78078, 114345/114244
| {{mapping| 1193 1891 2770 3349 4127 4415 }}
| {{mapping| 1193 1891 2770 3349 4127 4415 }}
| -0.0121
| &minus;0.0121
| 0.0617
| 0.0617
| 6.14
| 6.14
Line 63: Line 55:
| 0.0664
| 0.0664
| 6.60
| 6.60
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio
! Temperaments
|-
|-
| 1
| 1
Line 91: Line 77:
| 768/625
| 768/625
| [[Dodifo]]
| [[Dodifo]]
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}


== Music ==
== Music ==
; [[User:Francium|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
* "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] &ndash; 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
* ''1193'' (2024) &ndash; [https://open.spotify.com/album/4lJGqEt76mFGRbxWQmT6vo Spotify] | [https://francium223.bandcamp.com/album/1193 bandcamp] | [https://www.youtube.com/playlist?list=PLLZE7hMjEXRatIUXyBQyjNvDsiV40JAmk YouTube] &ndash; 4-piece EP in 1193edo


[[Category:Listen]]
[[Category:Listen]]

Revision as of 03:17, 16 November 2024

← 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

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

Template:Comma basis begin |- | 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 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 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 Template:Rank-2 end Template:Orf

Music

Francium
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