190edo: Difference between revisions

Line 1:

'''190edo''' divides the octave into 190 equal parts of size 6.316 ~~cents~~ each. It 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 [[~~Gamelismic_clan#Unidec|~~unidec]], the 118~~&190~~ 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 ~~three~~ 11-limit temperament [[~~Gamelismic_family#Portent|~~portent]], which tempers out 385/384 and 441/440, and [[~~Gamelismic_family#Gamelan|~~gamelan]], the rank ~~three~~ 7-limit temperament which tempers out 1029/1024, as well as [[~~Chromatic_pairs#Slendric|~~slendric]], the 2.3.7 subgroup temperament featured ~~below~~. 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 [[~~Gamelismic_clan#Unidec|~~ekadash ~~temperament~~]] and the rank ~~three~~ [[~~Gamelismic_family#Portent|~~portentous ~~temperament~~]].

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 size 6.316 [[cent]]s 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 ===

== Music ==

* [http://micro.soonlabel.com/tuning-survey/daily20111026-the-11th-slendric-fanfare.mp3 The 11th Slendric Fanfare]

* [http://micro.soonlabel.com/tuning-survey/daily20111026-16-slendric-virgins.mp3 16 Slendric Virgins] by [[~~Chris_Vaisvil|~~Chris Vaisvil]]

* [http://micro.soonlabel.com/tuning-survey/daily20111026-16-slendric-virgins.mp3 16 Slendric Virgins] by [[Chris Vaisvil]]

~~[[Category:ekadash]]~~

~~[[Category:gamelan]]~~

~~[[Category:gamelismic]]~~

~~[[Category:portent]]~~

~~[[Category:portentous]]~~

~~[[Category:unidec~~]]

~~{{todo| cleanup | improve linking }}~~

[[Category:Equal divisions of the octave]]

[[Category:Unidec]]

[[Category:Ekadash]]

[[Category:Gamelan]]

[[Category:Portent]]

[[Category:Portentous]]

@@ Line 1: / Line 1: @@
-'''190edo''' divides the octave into 190 equal parts of size 6.316 cents each. It 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 [[Gamelismic_clan#Unidec|unidec]], the 118&amp;190 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 three 11-limit temperament [[Gamelismic_family#Portent|portent]], which tempers out 385/384 and 441/440, and [[Gamelismic_family#Gamelan|gamelan]], the rank three 7-limit temperament which tempers out 1029/1024, as well as [[Chromatic_pairs#Slendric|slendric]], the 2.3.7 subgroup temperament featured below. 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 [[Gamelismic_clan#Unidec|ekadash temperament]] and the rank three [[Gamelismic_family#Portent|portentous temperament]].
+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 size 6.316 [[cent]]s each.
+== Theory ==
+edo 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 ===
+{{Primes in edo|190}}
 == Music ==
 * [http://micro.soonlabel.com/tuning-survey/daily20111026-the-11th-slendric-fanfare.mp3 The 11th Slendric Fanfare]
-* [http://micro.soonlabel.com/tuning-survey/daily20111026-16-slendric-virgins.mp3 16 Slendric Virgins] by [[Chris_Vaisvil|Chris Vaisvil]]
+* [http://micro.soonlabel.com/tuning-survey/daily20111026-16-slendric-virgins.mp3 16 Slendric Virgins] by [[Chris Vaisvil]]
-[[Category:ekadash]]
-[[Category:gamelan]]
-[[Category:gamelismic]]
-[[Category:portent]]
-[[Category:portentous]]
-[[Category:unidec]]
-{{todo| cleanup | improve linking }}
+[[Category:Equal divisions of the octave]]
+[[Category:Unidec]]
+[[Category:Ekadash]]
+[[Category:Gamelan]]
+[[Category:Portent]]
+[[Category:Portentous]]