Archytas clan: Difference between revisions

 

{{Mapping|legend=3| 1 0 0 6 | 0 1 0 -2 }}

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

[[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.  

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

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

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

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

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

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

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

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

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

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

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]].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mapping: {{mapping| 1 0 -12 6 -22 | 0 1 9 -2 16 }}

Mapping: {{mapping| 1 0 -12 6 -22 -17 | 0 1 9 -2 16 13 }}

Mapping: {{mapping| 1 0 -12 6 -22 26 | 0 1 9 -2 16 -14 }}

Mapping: {{mapping| 1 1 -3 4 -6 4 | 0 2 18 -4 32 -1 }}

Mapping: {{mapping| 1 0 -12 6 13 | 0 1 9 -2 -6 }}

Mapping: {{mapping| 1 0 -12 6 13 18 | 0 1 9 -2 -6 -9 }}

Mapping: {{mapping| 1 0 23 6 13 | 0 1 -13 -2 -6 }}

Mapping: {{mapping| 1 0 23 6 13 18 | 0 1 -13 -2 -6 -9 }}

Mapping: {{mapping| 1 0 23 6 -22 | 0 1 -13 -2 16 }}

Ultrapyth can be viewed as an extension of the excellent 2.3.7.13/5 [[the Biosphere #Oceanfront|oceanfront]] temperament, mapping the ~5/4 to +14 fifths as a double-augmented unison (C–C𝄪).

Mapping: {{mapping| 1 0 -20 6 21 | 0 1 14 -2 -11 }}

Mapping: {{mapping| 1 0 -20 6 21 -25 | 0 1 14 -2 -11 18 }}

Mapping: {{mapping| 1 0 -20 6 -38 | 0 1 14 -2 26 }}

Mapping: {{mapping| 1 0 -20 6 -38 -25 | 0 1 14 -2 26 18 }}

Mapping: {{mapping| 1 0 15 6 13 | 0 1 -8 -2 -6 }}

Mapping: {{mapping| 1 1 5 4 10 | 0 2 -9 -4 -22 }}

Mapping: {{mapping| 1 1 5 4 10 4 | 0 2 -9 -4 -22 -1 }}

Mapping: {{mapping| 1 1 5 4 2 | 0 2 -9 -4 5 }}

Mapping: {{mapping| 1 1 5 4 2 4 | 0 2 -9 -4 5 -1 }}

Mapping: {{mapping| 1 1 5 4 -1 | 0 2 -9 -4 15 }}

Mapping: {{mapping| 1 1 5 4 -1 4 | 0 2 -9 -4 15 -1 }}

Progress tempers out 392/375 and may be described as {{nowrap| 15 & 17c }}. It splits the perfect twelfth into three generators of ~10/7; its ploidacot is alpha-tricot. 32c-edo gives an obvious tuning.  

Mapping: {{mapping| 1 0 5 6 4 | 0 3 -5 -6 -1 }}

Mapping: {{mapping| 1 0 5 6 4 0 | 0 3 -5 -6 -1 7 }}

Mapping: {{mapping| 1 0 5 6 4 9 | 0 3 -5 -6 -1 -10 }}

Fervor tempers out 9704/9375 and may be described as {{nowrap| 25 & 27 }}. It splits the 6th harmonic into five generators of ~10/7; its ploidacot is beta-pentacot. 27edo is about as accurate as it can be tuned.  

Mapping: {{mapping| 1 -1 7 8 4 | 0 5 -9 -10 -1 }}

Mapping: {{mapping| 1 -1 7 8 4 12 | 0 5 -9 -10 -1 -16 }}

Sixix tempers out 3125/2916 and may be described as {{nowrap| 25 & 32 }}. It is related to the [[kleismic family]] in a way similar to the one between [[meantone]] and [[mavila]]. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction. Its ploidacot is gamma-pentacot.  

Mapping: {{mapping| 1 3 4 0 6 | 0 -5 -6 10 -9 }}

Mapping: {{mapping| 1 3 4 0 6 4 | 0 -5 -6 10 -9 -1 }}

Mapping: {{mapping| 1 3 4 0 6 4 1 | 0 -5 -6 10 -9 -1 11 }}

[[Category:Rank 2]]