Tour of regular temperaments: Difference between revisions

Line 636:

A wide-open field. These are regular temperaments of various ranks which temper [[just intonation subgroups]].

== Commatic realms ~~of 11-limit and 13-limit commas~~ ==

== Commatic realms ==

By a ''commatic realm'' is meant the whole collection of regular temperaments of various ranks and for both full groups and [[subgroups]] tempering out a given comma. For some commas, looking at the full commatic realm seems the best approach to discussing associated temperaments.

~~; [[Orgonia|Orgonia or Satrilu-aruru]]~~

~~: Orgonia is the commatic realm of the [[11-limit]] comma 65536/65219 = {{monzo| 16 0 0 -2 -3 }}, the [[orgonisma]].~~

; [[The Biosphere|The Biosphere or Thozogu]]

: The Biosphere is the name given to the commatic realm of the [[13-limit]] comma 91/90.

; [[Marveltwin|Marveltwin or Thoyoyo]]

: This is the commatic realm of the 13-limit comma 325/324, the [[marveltwin comma]].

; [[The Archipelago|The Archipelago or Bithogu]]

The Archipelago is a name which has been given to the commatic realm of the 13-limit comma 676/675 = {{monzo| 2 -3 -2 0 0 2 }}, the [[island comma]].

: The Archipelago is a name which has been given to the commatic realm of the 13-limit comma 676/675 = {{monzo| 2 -3 -2 0 0 2 }}, the [[island comma]].

; [[The Jacobins|The Jacobins or Thotrilu-agu]]

: This is the commatic realm of the 13-limit comma 6656/6655, the [[jacobin comma]].

; [[~~Marveltwin~~|~~Marveltwin~~ or ~~Thoyoyo~~]]

; [[Stellar remnants]]

: This is the commatic realm of the 13-limit comma ~~325~~/~~324~~, the [[~~marveltwin comma~~]].

: This is the commatic realm of [[7777/7776]], the pulsar comma.

; [[Orgonia|Orgonia or Satrilu-aruru]]

: This is the commatic realm of the 11-limit comma 65536/65219 = {{monzo| 16 0 0 -2 -3 }}, the [[orgonisma]].

; [[The Nexus]]

; [[The Nexus|The Nexus or Tribilo]]

: This is the commatic realm of the 11-limit comma 1771561/1769472 = {{monzo| -16 -3 0 0 6 }}, the [[nexus comma]].

; [[The Quartercache]]

; [[The Quartercache|The Quartercache or Saquinlu-azo]]

: This is the commatic realm of the 11-limit comma 117440512/117406179 = {{monzo| 24 -6 0 1 -5 }}, the [[quartisma]].

== Miscellaneous other temperaments ==

; [[Limmic temperaments]]

: Various subgroup temperaments all tempering out the limma, 256/243.

@@ Line 636: / Line 636: @@
 A wide-open field. These are regular temperaments of various ranks which temper [[just intonation subgroups]].
-== Commatic realms of 11-limit and 13-limit commas ==
+== Commatic realms ==
 By a ''commatic realm'' is meant the whole collection of regular temperaments of various ranks and for both full groups and [[subgroups]] tempering out a given comma. For some commas, looking at the full commatic realm seems the best approach to discussing associated temperaments.
-; [[Orgonia|Orgonia or Satrilu-aruru]]
-: Orgonia is the commatic realm of the [[11-limit]] comma 65536/65219 = {{monzo| 16 0 0 -2 -3 }}, the [[orgonisma]].
 ; [[The Biosphere|The Biosphere or Thozogu]]
 : The Biosphere is the name given to the commatic realm of the [[13-limit]] comma 91/90.
+; [[Marveltwin|Marveltwin or Thoyoyo]]
+: This is the commatic realm of the 13-limit comma 325/324, the [[marveltwin comma]].
 ; [[The Archipelago|The Archipelago or Bithogu]]
-The Archipelago is a name which has been given to the commatic realm of the 13-limit comma 676/675 = {{monzo| 2 -3 -2 0 0 2 }}, the [[island comma]].
+: The Archipelago is a name which has been given to the commatic realm of the 13-limit comma 676/675 = {{monzo| 2 -3 -2 0 0 2 }}, the [[island comma]].
+; [[The Jacobins|The Jacobins or Thotrilu-agu]]
+: This is the commatic realm of the 13-limit comma 6656/6655, the [[jacobin comma]].
-; [[Marveltwin|Marveltwin or Thoyoyo]]
+; [[Stellar remnants]]
-: This is the commatic realm of the 13-limit comma 325/324, the [[marveltwin comma]].
+: This is the commatic realm of [[7777/7776]], the pulsar comma.
+; [[Orgonia|Orgonia or Satrilu-aruru]]
+: This is the commatic realm of the 11-limit comma 65536/65219 = {{monzo| 16 0 0 -2 -3 }}, the [[orgonisma]].
-; [[The Nexus]]
+; [[The Nexus|The Nexus or Tribilo]]
 : This is the commatic realm of the 11-limit comma 1771561/1769472 = {{monzo| -16 -3 0 0 6 }}, the [[nexus comma]].
-; [[The Quartercache]]
+; [[The Quartercache|The Quartercache or Saquinlu-azo]]
 : This is the commatic realm of the 11-limit comma 117440512/117406179 = {{monzo| 24 -6 0 1 -5 }}, the [[quartisma]].
 == Miscellaneous other temperaments ==
 ; [[Limmic temperaments]]
 : Various subgroup temperaments all tempering out the limma, 256/243.