190edo: Difference between revisions

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=== Prime harmonics ===
=== Prime harmonics ===
{{Primes in edo|190}}
{{Primes in edo|190}}
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| -301 190 }}
| [{{val| 190 301 }}]
| +0.285
| 0.285
| 4.51
|-
| 2.3.5
| 2109375/2097152, {{monzo| -7 22 -12 }}
| [{{val| 190 301 441 }}]
| +0.341
| 0.246
| 3.89
|-
| 2.3.5.7
| 1029/1024, 4375/4374, 235298/234375
| [{{val| 190 301 441 533 }}]
| +0.479
| 0.321
| 5.07
|-
| 2.3.5.7.11
| 385/384, 441/440, 4375/4374, 234375/234256
| [{{val| 190 301 441 533 657 }}]
| +0.490
| 0.288
| 4.55
|-
| 2.3.5.7.11.13
| 385/384, 441/440, 729/728, 847/845, 1001/1000
| [{{val| 190 301 441 533 657 703 }}]
| +0.432
| 0.293
| 4.63
|}
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per octave
! Generator<br>(reduced)
! Cents<br>(reduced)
! Associated<br>ratio
! Temperaments
|-
| 1
| 37\190
| 233.68
| 8/7
| [[Slendric]]
|-
| 1
| 43\190
| 271.58
| 75/64
| [[Orson]] / [[sabric]]
|-
| 1
| 49\190
| 309.47
| 448/375
| [[Triwell]]
|-
| 1
| 71\190
| 448.42
| 35/27
| [[Semidimfourth]]
|-
| 1
| 83\190
| 524.21
| 65/48
| [[Widefourth]]
|-
| 2
| 28\190
| 176.84
| 195/176
| [[Quatracot]]
|-
| 2
| 29\190
| 183.16
| 10/9
| [[Unidec]] / ekadash
|-
| 2
| 59\190<br>(36\190)
| 372.63<br>(227.37)
| 26/21<br>(297/260)
| [[Essence]]
|-
| 2
| 71\190<br>(24\190)
| 448.42<br>(151.58)
| 35/27<br>(12/11)
| [[Neusec]]
|-
| 5
| 79\190<br>(3\190)
| 498.95<br>(18.95)
| 4/3<br>(81/80)
| [[Pental]]
|-
| 10
| 50\190<br>(7\190)
| 315.79<br>(45.79)
| 6/5<br>(40/39)
| [[Deca]]
|-
| 10
| 79\190<br>(3\190)
| 498.95<br>(18.95)
| 4/3<br>(81/80)
| [[Decal]]
|-
| 19
| 79\190<br>(1\190)
| 498.95<br>(6.32)
| 4/3<br>(225/224)
| [[Enneadecal]]
|-
| 38
| 79\190<br>(1\190)
| 498.95<br>(6.32)
| 4/3<br>(225/224)
| [[Hemienneadecal]]
|}


== Scales ==
== Scales ==

Revision as of 14:12, 11 November 2021

← 189edo 190edo 191edo →
Prime factorization 2 × 5 × 19
Step size 6.31579 ¢ 
Fifth 111\190 (701.053 ¢)
Semitones (A1:m2) 17:15 (107.4 ¢ : 94.74 ¢)
Consistency limit 15
Distinct consistency limit 15

The 190 equal divisions of the octave (190edo) or 190(-tone) equal temperament (190tet, 190et) when view from a regular temperament perspective, divides the octave into 190 equal parts of about 6.32 cents each.

Theory

190edo is interesting because of the utility of its approximations; it tempers out 1029/1024, 4375/4374, 385/384, 441/440, 3025/3024 and 9801/9800. It provides the optimal patent val for both the 7- and 11-limit versions of unidec, the 72 & 118 temperament, which tempers out 1029/1024, 4375/4374, and in the 11-limit, 385/384 and 441/440. It also provides the optimal patent val for the rank-3 11-limit temperament portent, which tempers out 385/384 and 441/440, and gamelan, the rank-3 7-limit temperament which tempers out 1029/1024, as well as slendric, the 2.3.7 subgroup temperament featured in the #Music section. In the 13-limit, 190et tempers out 847/845, 625/624, 729/728, 1575/1573 and 1001/1000, and provides the optimal patent val for the ekadash temperament and the rank-3 portentous temperament.

Prime harmonics

Script error: No such module "primes_in_edo".

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [-301 190⟩ [⟨190 301]] +0.285 0.285 4.51
2.3.5 2109375/2097152, [-7 22 -12⟩ [⟨190 301 441]] +0.341 0.246 3.89
2.3.5.7 1029/1024, 4375/4374, 235298/234375 [⟨190 301 441 533]] +0.479 0.321 5.07
2.3.5.7.11 385/384, 441/440, 4375/4374, 234375/234256 [⟨190 301 441 533 657]] +0.490 0.288 4.55
2.3.5.7.11.13 385/384, 441/440, 729/728, 847/845, 1001/1000 [⟨190 301 441 533 657 703]] +0.432 0.293 4.63

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per octave 		Generator
(reduced) 		Cents
(reduced) 		Associated
ratio 		Temperaments
1 37\190 233.68 8/7 Slendric
1 43\190 271.58 75/64 Orson / sabric
1 49\190 309.47 448/375 Triwell
1 71\190 448.42 35/27 Semidimfourth
1 83\190 524.21 65/48 Widefourth
2 28\190 176.84 195/176 Quatracot
2 29\190 183.16 10/9 Unidec / ekadash
2 59\190
(36\190) 		372.63
(227.37) 		26/21
(297/260) 		Essence
2 71\190
(24\190) 		448.42
(151.58) 		35/27
(12/11) 		Neusec
5 79\190
(3\190) 		498.95
(18.95) 		4/3
(81/80) 		Pental
10 50\190
(7\190) 		315.79
(45.79) 		6/5
(40/39) 		Deca
10 79\190
(3\190) 		498.95
(18.95) 		4/3
(81/80) 		Decal
19 79\190
(1\190) 		498.95
(6.32) 		4/3
(225/224) 		Enneadecal
38 79\190
(1\190) 		498.95
(6.32) 		4/3
(225/224) 		Hemienneadecal

Scales

Music

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