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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|190}}
{{ED intro}}


== Theory ==
== Theory ==
190edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]] with a flat tendency, as [[harmonic]]s 3 through 13 are all tuned flat.  
190edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]] with a flat tendency, as [[harmonic]]s 3 through 13 are all tuned flat.  


The equal temperament is interesting because of the utility of its approximations; it [[tempering out|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 [[625/624]], [[729/728]], [[847/845]], [[1001/1000]] and [[1575/1573]], and provides the optimal patent val for the [[ekadash]] temperament and the rank-3 [[portentous]] temperament.
190edo is interesting because of the utility of its approximations; it [[tempering out|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 {{nowrap|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 [[625/624]], [[729/728]], [[847/845]], [[1001/1000]] and [[1575/1573]], and provides the optimal patent val for the [[ekadash]] temperament and the rank-3 [[portentous]] temperament.


The 190g [[val]] shows us a smooth path to the even higher limits. This extension tempers out [[289/288]], [[561/560]], [[595/594]] in the 17-limit; [[343/342]], [[476/475]], [[495/494]] in the 19-limit; and [[391/390]], [[529/528]] in the 23-limit.  
The 190g [[val]] shows us a smooth path to the even higher limits. This extension tempers out [[289/288]], [[561/560]], [[595/594]] in the 17-limit; [[343/342]], [[476/475]], [[495/494]] in the 19-limit; and [[391/390]], [[529/528]] in the 23-limit.  
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! rowspan="2" | [[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
|-
|-
Line 28: Line 28:
|-
|-
| 2.3
| 2.3
| {{monzo| -301 190 }}
| {{Monzo| -301 190 }}
| {{mapping| 190 301 }}
| {{Mapping| 190 301 }}
| +0.285
| +0.285
| 0.285
| 0.285
Line 36: Line 36:
| 2.3.5
| 2.3.5
| 2109375/2097152, {{monzo| -7 22 -12 }}
| 2109375/2097152, {{monzo| -7 22 -12 }}
| {{mapping| 190 301 441 }}
| {{Mapping| 190 301 441 }}
| +0.341
| +0.341
| 0.246
| 0.246
Line 43: Line 43:
| 2.3.5.7
| 2.3.5.7
| 1029/1024, 4375/4374, 235298/234375
| 1029/1024, 4375/4374, 235298/234375
| {{mapping| 190 301 441 533 }}
| {{Mapping| 190 301 441 533 }}
| +0.479
| +0.479
| 0.321
| 0.321
Line 50: Line 50:
| 2.3.5.7.11
| 2.3.5.7.11
| 385/384, 441/440, 4375/4374, 234375/234256
| 385/384, 441/440, 4375/4374, 234375/234256
| {{mapping| 190 301 441 533 657 }}
| {{Mapping| 190 301 441 533 657 }}
| +0.490
| +0.490
| 0.288
| 0.288
Line 57: Line 57:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 385/384, 441/440, 625/624, 729/728, 847/845
| 385/384, 441/440, 625/624, 729/728, 847/845
| {{mapping| 190 301 441 533 657 703 }}
| {{Mapping| 190 301 441 533 657 703 }}
| +0.432
| +0.432
| 0.293
| 0.293
Line 64: Line 64:
| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 289/288, 385/384, 441/440, 561/560, 625/624, 847/845
| 289/288, 385/384, 441/440, 561/560, 625/624, 847/845
| {{mapping| 190 301 441 533 657 703 776 }} (190g)
| {{Mapping| 190 301 441 533 657 703 776 }} (190g)
| +0.507
| +0.507
| 0.327
| 0.327
Line 71: Line 71:
| 2.3.5.7.11.13.17.19
| 2.3.5.7.11.13.17.19
| 289/288, 343/342, 385/384, 441/440, 476/475, 495/494, 847/845
| 289/288, 343/342, 385/384, 441/440, 476/475, 495/494, 847/845
| {{mapping| 190 301 441 533 657 703 776 807 }} (190g)
| {{Mapping| 190 301 441 533 657 703 776 807 }} (190g)
| +0.463
| +0.463
| 0.327
| 0.327
Line 78: Line 78:
| 2.3.5.7.11.13.17.19.23
| 2.3.5.7.11.13.17.19.23
| 289/288, 343/342, 385/384, 391/390, 441/440, 476/475, 495/494, 529/528
| 289/288, 343/342, 385/384, 391/390, 441/440, 476/475, 495/494, 529/528
| {{mapping| 190 301 441 533 657 703 776 807 859 }} (190g)
| {{Mapping| 190 301 441 533 657 703 776 807 859 }} (190g)
| +0.486
| +0.486
| 0.315
| 0.315
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|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
! Periods<br />per 8ve
! Periods<br>per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br />ratio*
! Associated<br>ratio*
! Temperament
! Temperament
|-
|-
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|-
|-
| 2
| 2
| 59\190<br />(36\190)
| 59\190<br>(36\190)
| 372.63<br />(227.37)
| 372.63<br>(227.37)
| 26/21<br />(297/260)
| 26/21<br>(297/260)
| [[Essence]]
| [[Essence]]
|-
|-
| 2
| 2
| 71\190<br />(24\190)
| 71\190<br>(24\190)
| 448.42<br />(151.58)
| 448.42<br>(151.58)
| 35/27<br />(12/11)
| 35/27<br>(12/11)
| [[Neusec]]
| [[Neusec]]
|-
|-
| 5
| 5
| 79\190<br />(3\190)
| 79\190<br>(3\190)
| 498.95<br />(18.95)
| 498.95<br>(18.95)
| 4/3<br />(81/80)
| 4/3<br>(81/80)
| [[Pental (temperament)|Pental]]
| [[Quintile]]
|-
|-
| 10
| 10
| 50\190<br />(7\190)
| 50\190<br>(7\190)
| 315.79<br />(45.79)
| 315.79<br>(45.79)
| 6/5<br />(40/39)
| 6/5<br>(40/39)
| [[Deca]]
| [[Deca]]
|-
|-
| 10
| 10
| 79\190<br />(3\190)
| 79\190<br>(3\190)
| 498.95<br />(18.95)
| 498.95<br>(18.95)
| 4/3<br />(81/80)
| 4/3<br>(81/80)
| [[Decal]]
| [[Decile]]
|-
|-
| 19
| 19
| 79\190<br />(1\190)
| 79\190<br>(1\190)
| 498.95<br />(6.32)
| 498.95<br>(6.32)
| 4/3<br />(225/224)
| 4/3<br>(225/224)
| [[Enneadecal]]
| [[Enneadecal]]
|-
|-
| 38
| 38
| 79\190<br />(1\190)
| 79\190<br>(1\190)
| 265.26<br />(6.32)
| 265.26<br>(6.32)
| 4/3<br />(225/224)
| 4/3<br>(225/224)
| [[Hemienneadecal]]
| [[Hemienneadecal]]
|-
|-
| 38
| 38
| 42\190<br />(2\190)
| 42\190<br>(2\190)
| 265.26<br />(12.63)
| 265.26<br>(12.63)
| 500/429<br />(144/143)
| 500/429<br>(144/143)
| [[Semihemienneadecal]]
| [[Semihemienneadecal]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct


== Scales ==
== Scales ==
Retrieved from "https://en.xen.wiki/w/190edo"