Archytas clan: Difference between revisions

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The second comma in the comma list defines which [[7-limit]] family member we are looking at:

* [[#Schism|Schism]] adds [[360/343]], for a tuning around [[12edo]];

* [[Dominant ~~(temperament)~~|Dominant]] adds [[36/35]], for a tuning between [[12edo]] and [[17edo|17c-edo]];

* [[Meantone family #Dominant|Dominant]] adds [[36/35]], for a tuning between [[12edo]] and [[17edo|17c-edo]];

* [[#Quasisuper|Quasisuper]] adds [[2430/2401]], for a tuning between 17c-edo and [[22edo]];

* [[#Superpyth|Superpyth]] adds [[245/243]], for a tuning between 22edo and [[27edo]];

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These all use the same generators as archy.

[[686/675]] gives beatles~~, splitting~~ the fifth in two. [[8748/8575]] gives immunized, splitting the twelfth in two. [[50/49]] gives pajara with a semioctave period. [[392/375]] gives progress, splitting the twelfth in three. [[250/243]] gives porcupine, splitting the fourth in three. [[126/125]] gives augene with a 1/3-octave period. [[4375/4374]] gives modus, splitting the fifth in four. [[3125/3024]] gives brightstone. [[9604/9375]] gives fervor. [[3125/2916]] gives sixix. [[3125/3087]] gives passion. Those split the generator in five in various ways. [[28/27]] gives blackwood with a 1/5-octave period. Finally, [[15625/15552]] gives catalan, splitting the twelfth in six.

[[25/24]] gives dichotic. [[686/675]] gives beatles. Those split the fifth in two. [[8748/8575]] gives immunized, splitting the twelfth in two. [[50/49]] gives pajara with a semioctave period. [[392/375]] gives progress, splitting the twelfth in three. [[250/243]] gives porcupine, splitting the fourth in three. [[126/125]] gives augene with a 1/3-octave period. [[4375/4374]] gives modus, splitting the fifth in four. [[3125/3024]] gives brightstone. [[9604/9375]] gives fervor. [[3125/2916]] gives sixix. [[3125/3087]] gives passion. Those split the generator in five in various ways. [[28/27]] gives blackwood with a 1/5-octave period. Finally, [[15625/15552]] gives catalan, splitting the twelfth in six.

Temperaments discussed elsewhere are:

* ''[[Mother]]'' (+[[16/15]]) → [[Father family #Mother|Father family]]

* ''[[Mother]]'' (+16/15) → [[Father family #Mother|Father family]]

* [[Dominant (temperament)|Dominant]] (+[[36/35]]) → [[Meantone family #Dominant|Meantone family]]

* [[Dominant (temperament)|Dominant]] (+36/35) → [[Meantone family #Dominant|Meantone family]]

* ''[[Medusa]]'' (+[[15/14]]) → [[Very low accuracy temperaments #Medusa|Very low accuracy temperaments]]

* ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa|Very low accuracy temperaments]]

* ''[[~~Immunized~~]]'' (+[[8748/8575]]) → [[Immunity family #Immunized|Immunity family]]

* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]]

* [[Pajara]] (+[[50/49]]) → [[Diaschismic family #Pajara|Diaschismic family]]

* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized|Immunity family]]

* [[Augene]] (+[[126/125]]) → [[Augmented family #Septimal augmented (augene)|Augmented family]]

* [[Pajara]] (+50/49) → [[Diaschismic family #Pajara|Diaschismic family]]

* [[Porcupine]] (+[[250/243]]) → [[Porcupine family #Septimal porcupine|Porcupine family]]

* [[Augene]] (+126/125) → [[Augmented family #Septimal augmented (augene)|Augmented family]]

* ''[[Modus]]'' (+[[4375/4374]]) → [[Tetracot family #Modus|Tetracot family]]

* [[Porcupine]] (+250/243) → [[Porcupine family #Septimal porcupine|Porcupine family]]

* ''[[Brightstone]]'' (+[[3125/3024]]) → [[Magic family #Brightstone|Magic family]]

* [[Modus]] (+4375/4374) → [[Tetracot family #Modus|Tetracot family]]

* ''[[Passion]]'' (+[[3125/3087]]) → [[Passion family #Septimal passion|Passion family]]

* ''[[Brightstone]]'' (+3125/3024) → [[Magic family #Brightstone|Magic family]]

* [[Blackwood]] (+[[28/27]]) → [[Limmic temperaments #Blackwood|Limmic temperaments]]

* ''[[Passion]]'' (+3125/3087) → [[Passion family #Septimal passion|Passion family]]

* ''[[Catalan]]'' (+[[15625/15552]]) → [[Kleismic family #Catalan|Kleismic family]]

* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]]

* ''[[Catalan]]'' (+15625/15552) → [[Kleismic family #Catalan|Kleismic family]]

Considered below are superpyth, quasisuper, ultrapyth, quasiultra, schism, beatles, progress, fervor, and sixix.

==== Subgroup extensions ====

Omitting prime 5, archy can be extended to the 2.3.7.11 subgroup by identifying 11/8 as a diminished fourth (C–G♭). This is called supra, given right below. Discussed elsewhere is [[suhajira]] of the [[~~neutral~~ clan #Suhajira|~~neutral~~ clan]].

Omitting prime 5, archy can be extended to the 2.3.7.11 subgroup by identifying 11/8 as a diminished fourth (C–G♭). This is called supra, given right below. Discussed elsewhere is [[suhajira]] of the [[rastmic clan #Suhajira|rastmic clan]].

=== Supra ===

@@ Line 33: / Line 33: @@
 The second comma in the comma list defines which [[7-limit]] family member we are looking at:
 * [[#Schism|Schism]] adds [[360/343]], for a tuning around [[12edo]];
-* [[Dominant (temperament)|Dominant]] adds [[36/35]], for a tuning between [[12edo]] and [[17edo|17c-edo]];
+* [[Meantone family #Dominant|Dominant]] adds [[36/35]], for a tuning between [[12edo]] and [[17edo|17c-edo]];
 * [[#Quasisuper|Quasisuper]] adds [[2430/2401]], for a tuning between 17c-edo and [[22edo]];
 * [[#Superpyth|Superpyth]] adds [[245/243]], for a tuning between 22edo and [[27edo]];
@@ Line 42: / Line 42: @@
 These all use the same generators as archy.
-[[686/675]] gives beatles, splitting the fifth in two. [[8748/8575]] gives immunized, splitting the twelfth in two. [[50/49]] gives pajara with a semioctave period. [[392/375]] gives progress, splitting the twelfth in three. [[250/243]] gives porcupine, splitting the fourth in three. [[126/125]] gives augene with a 1/3-octave period. [[4375/4374]] gives modus, splitting the fifth in four. [[3125/3024]] gives brightstone. [[9604/9375]] gives fervor. [[3125/2916]] gives sixix. [[3125/3087]] gives passion. Those split the generator in five in various ways. [[28/27]] gives blackwood with a 1/5-octave period. Finally, [[15625/15552]] gives catalan, splitting the twelfth in six.
+[[25/24]] gives dichotic. [[686/675]] gives beatles. Those split the fifth in two. [[8748/8575]] gives immunized, splitting the twelfth in two. [[50/49]] gives pajara with a semioctave period. [[392/375]] gives progress, splitting the twelfth in three. [[250/243]] gives porcupine, splitting the fourth in three. [[126/125]] gives augene with a 1/3-octave period. [[4375/4374]] gives modus, splitting the fifth in four. [[3125/3024]] gives brightstone. [[9604/9375]] gives fervor. [[3125/2916]] gives sixix. [[3125/3087]] gives passion. Those split the generator in five in various ways. [[28/27]] gives blackwood with a 1/5-octave period. Finally, [[15625/15552]] gives catalan, splitting the twelfth in six.
 Temperaments discussed elsewhere are:
-* ''[[Mother]]'' (+[[16/15]]) → [[Father family #Mother|Father family]]
+* ''[[Mother]]'' (+16/15) → [[Father family #Mother|Father family]]
-* [[Dominant (temperament)|Dominant]] (+[[36/35]]) → [[Meantone family #Dominant|Meantone family]]
+* [[Dominant (temperament)|Dominant]] (+36/35) → [[Meantone family #Dominant|Meantone family]]
-* ''[[Medusa]]'' (+[[15/14]]) → [[Very low accuracy temperaments #Medusa|Very low accuracy temperaments]]
+* ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa|Very low accuracy temperaments]]
-* ''[[Immunized]]'' (+[[8748/8575]]) → [[Immunity family #Immunized|Immunity family]]
+* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]]
-* [[Pajara]] (+[[50/49]]) → [[Diaschismic family #Pajara|Diaschismic family]]
+* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized|Immunity family]]
-* [[Augene]] (+[[126/125]]) → [[Augmented family #Septimal augmented (augene)|Augmented family]]
+* [[Pajara]] (+50/49) → [[Diaschismic family #Pajara|Diaschismic family]]
-* [[Porcupine]] (+[[250/243]]) → [[Porcupine family #Septimal porcupine|Porcupine family]]
+* [[Augene]] (+126/125) → [[Augmented family #Septimal augmented (augene)|Augmented family]]
-* ''[[Modus]]'' (+[[4375/4374]]) → [[Tetracot family #Modus|Tetracot family]]
+* [[Porcupine]] (+250/243) → [[Porcupine family #Septimal porcupine|Porcupine family]]
-* ''[[Brightstone]]'' (+[[3125/3024]]) → [[Magic family #Brightstone|Magic family]]
+* [[Modus]] (+4375/4374) → [[Tetracot family #Modus|Tetracot family]]
-* ''[[Passion]]'' (+[[3125/3087]]) → [[Passion family #Septimal passion|Passion family]]
+* ''[[Brightstone]]'' (+3125/3024) → [[Magic family #Brightstone|Magic family]]
-* [[Blackwood]] (+[[28/27]]) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
+* ''[[Passion]]'' (+3125/3087) → [[Passion family #Septimal passion|Passion family]]
-* ''[[Catalan]]'' (+[[15625/15552]]) → [[Kleismic family #Catalan|Kleismic family]]
+* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
+* ''[[Catalan]]'' (+15625/15552) → [[Kleismic family #Catalan|Kleismic family]]
 Considered below are superpyth, quasisuper, ultrapyth, quasiultra, schism, beatles, progress, fervor, and sixix.
 ==== Subgroup extensions ====
-Omitting prime 5, archy can be extended to the 2.3.7.11 subgroup by identifying 11/8 as a diminished fourth (C–G♭). This is called supra, given right below. Discussed elsewhere is [[suhajira]] of the [[neutral clan #Suhajira|neutral clan]].
+Omitting prime 5, archy can be extended to the 2.3.7.11 subgroup by identifying 11/8 as a diminished fourth (C–G♭). This is called supra, given right below. Discussed elsewhere is [[suhajira]] of the [[rastmic clan #Suhajira|rastmic clan]].
 === Supra ===