193edo: Difference between revisions

Line 1:

~~The '''193 equal divisions of the octave''' ('''193edo'''), or the '''193(-tone) equal temperament''' ('''193tet''', '''193et''') when viewed from a [[regular temperament]] perspective, is the [[~~EDO|~~equal division of the octave]] into~~ 193 ~~parts of about 6.22 [[cent]]s each.~~

== Theory ==

193edo provides the [[optimal patent val]] for the [[sqrtphi]] temperament in the 13-, 17- and 19-~~limits~~, and for the 13-limit [[Swetismic temperaments #Minos|minos]] and [[Mirkwai family #Indra|vish]] temperaments~~. It is the 44th [[prime edo]]~~.

193edo provides the [[optimal patent val]] for the [[sqrtphi]] temperament in the 13-, 17- and 19-limit, and for the 13-limit [[Swetismic temperaments #Minos|minos]] and [[Mirkwai family #Indra|vish]] temperaments.

=== Prime harmonics ===

=== Miscellaneous properties ===

193edo is the 44th [[prime edo]].

== Regular temperament properties ==

Line 82:

Line 85:

| 99.48

| 18/17

| [[Quindromeda family#Quintakwai|Quintakwai]]/[[Quindromeda family#Quintakwoid|~~Quintakwoid~~]]

| [[Quindromeda family#Quintakwai|Quintakwai]] / [[Quindromeda family#Quintakwoid|quintakwoid]]

|-

| 1

Line 133:

Line 136:

|}

==Scales==

== Scales ==

*Approximation of sqrt (π): '''159\193''' (988.60104 cents), and of φ: '''134\193''' (833.16062 cents), both inside in the [[7L 2s|superdiatonic]] scale: 25 25 25 9 25 25 25 25 9

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The '''193 equal divisions of the octave''' ('''193edo'''), or the '''193(-tone) equal temperament''' ('''193tet''', '''193et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 193 parts of about 6.22 [[cent]]s each.
+{{EDO intro|193}}
 == Theory ==
-edo provides the [[optimal patent val]] for the [[sqrtphi]] temperament in the 13-, 17- and 19-limits, and for the 13-limit [[Swetismic temperaments #Minos|minos]] and [[Mirkwai family #Indra|vish]] temperaments. It is the 44th [[prime edo]].
+edo provides the [[optimal patent val]] for the [[sqrtphi]] temperament in the 13-, 17- and 19-limit, and for the 13-limit [[Swetismic temperaments #Minos|minos]] and [[Mirkwai family #Indra|vish]] temperaments.
 === Prime harmonics ===
-{{Harmonics in equal|193}}
+{{Harmonics in equal|193|columns=11}}
+=== Miscellaneous properties ===
+edo is the 44th [[prime edo]].
 == Regular temperament properties ==
@@ Line 82: / Line 85: @@
 | 99.48
 | 18/17
-| [[Quindromeda family#Quintakwai|Quintakwai]]/[[Quindromeda family#Quintakwoid|Quintakwoid]]
+| [[Quindromeda family#Quintakwai|Quintakwai]] / [[Quindromeda family#Quintakwoid|quintakwoid]]
 |-
 | 1
@@ Line 133: / Line 136: @@
 |}
-==Scales==
+== Scales ==
 *Approximation of sqrt (π): '''159\193''' (988.60104 cents), and of φ: '''134\193''' (833.16062 cents), both inside in the [[7L 2s|superdiatonic]] scale: 25 25 25 9 25 25 25 25 9