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Line 11: Line 11:
[[Comma list]]: 64/63
[[Comma list]]: 64/63


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


{{Mapping|legend=5| 1 0 0 6 | 0 1 0 -2 }}
: mapping generators: ~2, ~3
: mapping generators: ~2, ~3


Line 42: Line 41:
These all use the same generators as archy.  
These all use the same generators as archy.  


[[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.  
[[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 semi-octave period. [[392/375]] gives progress. [[6125/5832]] gives kangaroo. Those split 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. [[15625/15552]] gives catalan, splitting the twelfth in six. Finally, [[28/27]] gives blackwood and [[17496/16807]] gives [[gothic]], reducing the intervals of 3 and 7 to the same chain of 1/5- and 1/17-octave periods, respectively.  


Temperaments discussed elsewhere are:  
Temperaments discussed elsewhere are:  
* ''[[Phlegyas]]'' (+10/9) → [[Very low accuracy temperaments #Phlegyas|Very low accuracy temperaments]]
* ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa|Very low accuracy temperaments]]
* ''[[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]]
* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]]
* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]]
* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized|Immunity family]]
* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized|Immunity family]]
Line 56: Line 56:
* ''[[Brightstone]]'' (+3125/3024) → [[Magic family #Brightstone|Magic family]]
* ''[[Brightstone]]'' (+3125/3024) → [[Magic family #Brightstone|Magic family]]
* ''[[Passion]]'' (+3125/3087) → [[Passion family #Septimal passion|Passion 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]]
* ''[[Catalan]]'' (+15625/15552) → [[Kleismic family #Catalan|Kleismic family]]
* [[Blackwood]] (+28/27) → [[Blackwood family #Blackwood|Blackwood family]]
* ''[[Gothic]]'' (+17496/16807) → [[17th-octave temperaments #Gothic|17th-octave temperaments]]


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


==== Subgroup extensions ====
==== 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 [[rastmic clan #Suhajira|rastmic 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 in [[#Subgroup extensions_2|#Subgroup extensions]]. Discussed elsewhere is [[suhajira]] of the [[rastmic clan #Suhajira|rastmic clan]].
 
=== Supra ===
Subgroup: 2.3.7.11
 
Comma list: 64/63, 99/98
 
Subgroup-val mapping: {{mapping| 1 0 6 13 | 0 1 -2 -6 }}
 
Gencom mapping: {{mapping| 1 0 0 6 13 | 0 1 0 -2 -6 }}
 
Optimal tunings:
* WE: ~2 = 1197.2650{{c}}, ~3/2 = 705.5803{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 707.4981{{c}}
 
{{Optimal ET sequence|legend=0| 5, 12, 17, 39d, 56d }}
 
Badness (Sintel): 0.352
 
Scales: [[supra7]], [[supra12]]
 
==== Supraphon ====
This extension maps [[13/11]] to the minor third (C–E♭), [[12/11]][[~]][[14/13]] to the augmented unison (C–C♯), and [[13/12]] to the diminished third (C–E𝄫).
 
Subgroup: 2.3.7.11.13
 
Comma list: 64/63, 78/77, 99/98
 
Subgroup-val mapping: {{mapping| 1 0 6 13 18 | 0 1 -2 -6 -9 }}
 
Gencom mapping: {{mapping| 1 0 0 6 13 18 | 0 1 0 -2 -6 -9 }}
 
Optimal tunings:
* WE: ~2 = 1197.1909{{c}}, ~3/2 = 704.4836{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 706.4289{{c}}
 
{{Optimal ET sequence|legend=0| 12f, 17 }}
 
Badness (Sintel): 0.498
 
Scales: [[supra7]], [[supra12]]


== Superpyth ==
== Superpyth ==
Line 133: Line 94:
Comma list: 64/63, 100/99, 245/243
Comma list: 64/63, 100/99, 245/243


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


Optimal tunings:  
Optimal tunings:  
Line 148: Line 109:
Comma list: 64/63, 78/77, 91/90, 100/99
Comma list: 64/63, 78/77, 91/90, 100/99


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


Optimal tunings:  
Optimal tunings:  
Line 163: Line 124:
Comma list: 64/63, 100/99, 144/143, 245/243
Comma list: 64/63, 100/99, 144/143, 245/243


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


Optimal tunings:  
Optimal tunings:  
Line 178: Line 139:
Comma list: 64/63, 100/99, 169/168, 245/243
Comma list: 64/63, 100/99, 169/168, 245/243


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


Optimal tunings:  
Optimal tunings:  
Line 195: Line 156:
Comma list: 55/54, 64/63, 99/98
Comma list: 55/54, 64/63, 99/98


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


Optimal tunings:  
Optimal tunings:  
Line 210: Line 171:
Comma list: 55/54, 64/63, 65/63, 99/98
Comma list: 55/54, 64/63, 65/63, 99/98


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


Optimal tunings:  
Optimal tunings:  
Line 246: Line 207:
Comma list: 64/63, 99/98, 121/120
Comma list: 64/63, 99/98, 121/120


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


Optimal tunings:  
Optimal tunings:  
Line 261: Line 222:
Comma list: 64/63, 78/77, 91/90, 121/120
Comma list: 64/63, 78/77, 91/90, 121/120


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


Optimal tunings:  
Optimal tunings:  
Line 276: Line 237:
Comma list: 55/54, 64/63, 2430/2401
Comma list: 55/54, 64/63, 2430/2401


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


Optimal tunings:  
Optimal tunings:  
Line 290: Line 251:
: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Ultrapyth (5-limit)]].''
: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Ultrapyth (5-limit)]].''


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


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 313: Line 274:
Comma list: 55/54, 64/63, 2401/2376
Comma list: 55/54, 64/63, 2401/2376


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


Optimal tunings:  
Optimal tunings:  
Line 328: Line 289:
Comma list: 55/54, 64/63, 91/90, 1573/1568
Comma list: 55/54, 64/63, 91/90, 1573/1568


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


Optimal tunings:  
Optimal tunings:  
Line 343: Line 304:
Comma list: 64/63, 100/99, 3773/3645
Comma list: 64/63, 100/99, 3773/3645


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


Optimal tunings:  
Optimal tunings:  
Line 358: Line 319:
Comma list: 64/63, 91/90, 100/99, 847/845
Comma list: 64/63, 91/90, 100/99, 847/845


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


Optimal tunings:  
Optimal tunings:  
Line 413: Line 374:
Comma list: 45/44, 64/63, 99/98
Comma list: 45/44, 64/63, 99/98


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


Optimal tunings:  
Optimal tunings:  
Line 454: Line 415:
Comma list: 64/63, 100/99, 686/675
Comma list: 64/63, 100/99, 686/675


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


Optimal tunings:  
Optimal tunings:  
Line 469: Line 430:
Comma list: 64/63, 91/90, 100/99, 169/168
Comma list: 64/63, 91/90, 100/99, 169/168


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


Optimal tunings:  
Optimal tunings:  
Line 484: Line 445:
Comma list: 56/55, 64/63, 540/539
Comma list: 56/55, 64/63, 540/539


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


Optimal tunings:  
Optimal tunings:  
Line 499: Line 460:
Comma list: 56/55, 64/63, 78/77, 91/90
Comma list: 56/55, 64/63, 78/77, 91/90


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


Optimal tunings:  
Optimal tunings:  
Line 514: Line 475:
Comma list: 55/54, 64/63, 686/675
Comma list: 55/54, 64/63, 686/675


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


Optimal tunings:  
Optimal tunings:  
Line 529: Line 490:
Comma list: 55/54, 64/63, 91/90, 169/168
Comma list: 55/54, 64/63, 91/90, 169/168


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


Optimal tunings:  
Optimal tunings:  
Line 543: Line 504:
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Progress]].''
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Progress]].''


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.  
Progress tempers out [[392/375]] and may be described as {{nowrap| 15 & 17c }}. It splits the [[3/1|perfect twelfth]] into three generators of [[~]][[10/7]]; its [[ploidacot]] is alpha-tricot. The 11-limit extension simply equates the generator to [[16/11]], and the 13-limit extension further equates it to [[13/9]]. [[32edo|32c-edo]] gives an obvious tuning.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 550: Line 511:


{{Mapping|legend=1| 1 0 5 6 | 0 3 -5 -6 }}
{{Mapping|legend=1| 1 0 5 6 | 0 3 -5 -6 }}
: mapping generators: ~2, ~10/7
: mapping generators: ~2, ~10/7


Line 568: Line 528:
Comma list: 56/55, 64/63, 77/75
Comma list: 56/55, 64/63, 77/75


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


Optimal tunings:  
Optimal tunings:  
Line 583: Line 543:
Comma list: 56/55, 64/63, 66/65, 77/75
Comma list: 56/55, 64/63, 66/65, 77/75


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


Optimal tunings:  
Optimal tunings:  
Line 598: Line 558:
Comma list: 26/25, 56/55, 64/63, 77/75
Comma list: 26/25, 56/55, 64/63, 77/75


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


Optimal tunings:  
Optimal tunings:  
Line 607: Line 567:


Badness (Sintel): 1.35
Badness (Sintel): 1.35
== Kangaroo ==
: ''For 5-limit version, see [[Miscellaneous 5-limit temperaments #Kangaroo]].''
Kangaroo splits the [[3/1|perfect twelfth]] into three [[35/24]][[~]][[40/27]] generators; its [[ploidacot]] is alpha-tricot. The 11-limit extension simply equates the generator to [[16/11]]. This favors a particularly sharp diatonic fifth (around 710–720 cents) because otherwise the ~[[5/4]] will be too flat.
Originally the canonical extension of 5-limit kangaroo was [[trienstonic clan #Parakangaroo|parakangaroo]], but it was decanonized in 2024 in favor of this extension because parakangaroo is an [[exotemperament]] that only supports the [[patent val]] of [[15edo]], while this extension is a bit more practical since it is at least low-medium accuracy and supports the [[patent val]]s of 15edo, [[17edo]] and [[32edo]].
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 64/63, 6125/5832
{{Mapping|legend=1| 1 0 -3 6 | 0 3 10 -6 }}
: mapping generators: ~2, ~35/24
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1198.1767{{c}}, ~35/24 = 637.2914{{c}}
: [[error map]]: {{val| -1.823 +9.919 -7.930 -3.514 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~35/24 = 638.1977{{c}}
: error map: {{val| 0.000 +12.638 -4.336 +1.988 }}
{{Optimal ET sequence|legend=1| 15, 32, 47b }}
[[Badness]] (Sintel): 2.91
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 55/54, 64/63, 245/242
{{Mapping|legend=0| 1 0 -3 6 4 | 0 3 10 -6 -1 }}
Optimal tunings:
* WE: ~2 = 1197.8893{{c}}, ~16/11 = 637.1922{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/11 = 638.2605{{c}}
{{Optimal ET sequence|legend=0| 15, 32, 47b }}
Badness (Sintel): 1.65


== Fervor ==
== Fervor ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Fervor]].''
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Fervor]].''


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.  
Fervor tempers out [[9604/9375]] and may be described as {{nowrap| 25 & 27 }}. It splits the [[6/1|6th harmonic]] into five generators of [[~]][[10/7]]; its ploidacot is beta-pentacot. The 11-limit extension simply equates the generator to [[16/11]]. [[27edo]] is about as accurate as it can be tuned.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 618: Line 617:


{{Mapping|legend=1| 1 -1 7 8 | 0 5 -9 -10 }}
{{Mapping|legend=1| 1 -1 7 8 | 0 5 -9 -10 }}
: mapping generators: ~2, ~10/7
: mapping generators: ~2, ~10/7


Line 636: Line 634:
Comma list: 56/55, 64/63, 1350/1331
Comma list: 56/55, 64/63, 1350/1331


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


Optimal tunings:  
Optimal tunings:  
Line 651: Line 649:
Comma list: 56/55, 64/63, 78/77, 507/500
Comma list: 56/55, 64/63, 78/77, 507/500


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


Optimal tunings:  
Optimal tunings:  
Line 665: Line 663:
{{See also| Dual-fifth temperaments #Dual-3 Sixix }}
{{See also| Dual-fifth temperaments #Dual-3 Sixix }}


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.  
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. An important val not in the [[optimal ET sequence]] is 39c, that is, [[39edo]] using the second-best approximation of [[5/4]] (the 369-cent one inherited from [[13edo]]). It is also supported by [[57edo|57b-edo]], which uses the sharper of [[57edo]]'s two diatonic fifths.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 688: Line 686:
Comma list: 55/54, 64/63, 125/121
Comma list: 55/54, 64/63, 125/121


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


Optimal tunings:  
Optimal tunings:  
Line 703: Line 701:
Comma list: 40/39, 55/54, 64/63, 125/121
Comma list: 40/39, 55/54, 64/63, 125/121


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


Optimal tunings:  
Optimal tunings:  
Line 718: Line 716:
Comma list: 40/39, 55/54, 64/63, 85/84, 125/121
Comma list: 40/39, 55/54, 64/63, 85/84, 125/121


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


Optimal tunings:  
Optimal tunings:  
Line 727: Line 725:


Badness (Sintel): 2.00
Badness (Sintel): 2.00
== Subgroup extensions ==
=== Supra (2.3.7.11) ===
Subgroup: 2.3.7.11
Comma list: 64/63, 99/98
{{Mapping|legend=2| 1 0 6 13 | 0 1 -2 -6 }}
{{Mapping|legend=4| 1 0 0 6 13 | 0 1 0 -2 -6 }}
Optimal tunings:
* WE: ~2 = 1197.2650{{c}}, ~3/2 = 705.5803{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 707.4981{{c}}
{{Optimal ET sequence|legend=0| 5, 12, 17, 39d, 56d }}
Badness (Sintel): 0.352
Scales: [[supra7]], [[supra12]]
==== Supraphon ====
This extension maps [[13/11]] to the minor third (C–E♭), [[12/11]][[~]][[14/13]] to the augmented unison (C–C♯), and [[13/12]] to the diminished third (C–E𝄫).
Subgroup: 2.3.7.11.13
Comma list: 64/63, 78/77, 99/98
{{Mapping|legend=2| 1 0 6 13 18 | 0 1 -2 -6 -9 }}
{{Mapping|legend=4| 1 0 0 6 13 18 | 0 1 0 -2 -6 -9 }}
Optimal tunings:
* WE: ~2 = 1197.1909{{c}}, ~3/2 = 704.4836{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 706.4289{{c}}
{{Optimal ET sequence|legend=0| 12f, 17 }}
Badness (Sintel): 0.498
Scales: [[supra7]], [[supra12]]
=== Oceanfront (2.3.7.13/5) ===
This is the [[restriction]] of [[#Ultrapyth|ultrapyth]] to the 2.3.7.13/5 subgroup, mapping [[13/10]] to the major third.
[[Subgroup]]: 2.3.7.13/5
[[Comma list]]: 64/63 ({{monzo| 6 -2 -1 0 }}), 91/90 ({{monzo| -1 -2 1 1 }})
{{Mapping|legend=3| 1 0 6 -5 | 0 1 -2 4 }}
[[Optimal tuning]]s:
* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1197.2656{{c}}, ~3/2 = 710.1993{{c}}
* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 711.7413{{c}}
{{Optimal ET sequence|legend=1| 5, 17, 22, 27, 32, 59 }}
[[Tp tuning #T2 tuning|RMS error]]: 2.063 cents
Scales: [[Oceanfront scales]]


[[Category:Archytas clan| ]] <!-- main article -->
[[Category:Archytas clan| ]] <!-- main article -->
[[Category:Archytas| ]] <!-- key article -->
[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Rank 2]]
[[Category:Catalogs of rank-2 temperaments]]
Retrieved from "https://en.xen.wiki/w/Archytas_clan"