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Mavila family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus
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Line 14: Line 14:


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


Line 20: Line 19:
* [[WE]]: ~2 = 1208.287{{c}}, ~3/2 = 684.501{{c}}
* [[WE]]: ~2 = 1208.287{{c}}, ~3/2 = 684.501{{c}}
: [[error map]]: {{val| +8.287 -9.167 -6.667 }}
: [[error map]]: {{val| +8.287 -9.167 -6.667 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 679.806{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 679.111{{c}}
: error map: {{val| 0.000 -22.844 -23.648 }}
: error map: {{val| 0.000 -22.844 -23.648 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 677.145{{c}}
: error map: {{val| 0.000 -24.810 -17.749 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 679.806{{c}}
: error map: {{val| 0.000 -22.149 -25.732 }} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 44: Line 39:
* ''[[Superpelog]]'' (+49/48) → [[Semaphoresmic clan #Superpelog|Semaphoresmic clan]]
* ''[[Superpelog]]'' (+49/48) → [[Semaphoresmic clan #Superpelog|Semaphoresmic clan]]
* ''[[Clyndro]]'' (+360/343) → [[Gamelismic clan #Clyndro|Gamelismic clan]]
* ''[[Clyndro]]'' (+360/343) → [[Gamelismic clan #Clyndro|Gamelismic clan]]
* ''[[Jamesbond]]'' (+25/24) → [[7th-octave temperaments #Jamesbond|7th-octave temperaments]]
* ''[[Jamesbond]]'' (+25/24) → [[Whitewood family #Jamesbond|Whitewood family]]


Considered below are mavling, pelogic, armodue, hornbostel, bipelog, and mohavila.
Considered below are mavling, pelogic, armodue, hornbostel, bipelog, and mohavila.
Line 56: Line 51:
Comma list: 33/32, 45/44
Comma list: 33/32, 45/44


Subgoup-val mapping: {{mapping| 1 0 7 5 | 0 1 -3 -1 }}
{{Mapping|legend=2| 1 0 7 5 | 0 1 -3 -1 }}


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


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1208.454{{c}}, ~3/2 = 684.577{{c}}
* WE: ~2 = 1208.454{{c}}, ~3/2 = 684.577{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 678.978{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 678.978{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 676.039{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 679.788{{c}} -->


{{Optimal ET sequence|legend=0| 7, 16, 23e, 30bce }}
{{Optimal ET sequence|legend=0| 7, 16, 23e, 30bce }}
Line 86: Line 79:
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 674.220{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 674.220{{c}}
: error map: {{val| 0.000 -27.735 -8.974 +2.275 }}
: error map: {{val| 0.000 -27.735 -8.974 +2.275 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 675.099{{c}}
: [[error map]]: {{val| 0.000 -26.856 -11.610 +6.668 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 673.997{{c}}
: error map: {{val| 0.000 -27.958 -8.304 +1.158 }} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 104: Line 93:
Comma list: 33/32, 36/35, 45/44
Comma list: 33/32, 36/35, 45/44


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


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1205.460{{c}}, ~3/2 = 676.873{{c}}
* WE: ~2 = 1205.460{{c}}, ~3/2 = 676.873{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 673.952{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 673.952{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 674.684{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 673.807{{c}} -->


{{Optimal ET sequence|legend=0| 7, 9, 16 }}
{{Optimal ET sequence|legend=0| 7, 9, 16 }}
Line 121: Line 108:
Comma list: 27/26, 33/32, 36/35, 45/44
Comma list: 27/26, 33/32, 36/35, 45/44


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


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1205.396{{c}}, ~3/2 = 676.792{{c}}
* WE: ~2 = 1205.396{{c}}, ~3/2 = 676.792{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 673.988{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 673.988{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 675.288{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 673.763{{c}} -->


{{Optimal ET sequence|legend=0| 7, 9, 16 }}
{{Optimal ET sequence|legend=0| 7, 9, 16 }}
Line 138: Line 123:
Comma list: 27/26, 33/32, 36/35, 39/38, 45/44
Comma list: 27/26, 33/32, 36/35, 39/38, 45/44


Subgroup-val mapping: {{mapping| 1 0 7 -5 5 -1 -2 | 0 1 -3 5 -1 3 4 }}
{{Mapping|legend=2| 1 0 7 -5 5 -1 -2 | 0 1 -3 5 -1 3 4 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1204.838{{c}}, ~3/2 = 675.997{{c}}
* WE: ~2 = 1204.838{{c}}, ~3/2 = 675.997{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 673.540{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 673.540{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 675.170{{c}} -->


{{Optimal ET sequence|legend=0| 7, 9, 16, 25bf }}
{{Optimal ET sequence|legend=0| 7, 9, 16, 25bf }}
Line 165: Line 149:
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 677.350{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 677.350{{c}}
: error map: {{val| 0.000 -24.605 -18.363 -19.672 }}
: error map: {{val| 0.000 -24.605 -18.363 -19.672 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 675.749{{c}}
: [[error map]]: {{val| 0.000 -26.206 -13.561 -2.067 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 677.913{{c}}
: error map: {{val| 0.000 -24.042 -20.052 -25.866 }} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 183: Line 163:
Comma list: 33/32, 45/44, 126/125
Comma list: 33/32, 45/44, 126/125


Mapping: {{mapping| 1 0 7 20 5 | 0 1 -3 -11 -1 }}
{{Mapping|legend=0| 1 0 7 20 5 | 0 1 -3 -11 -1 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1208.243{{c}}, ~3/2 = 682.582{{c}}
* WE: ~2 = 1208.243{{c}}, ~3/2 = 682.582{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 677.434{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 677.434{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 675.620{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 677.924{{c}} -->


{{Optimal ET sequence|legend=0| 7d, 16, 23de }}
{{Optimal ET sequence|legend=0| 7d, 16, 23de }}
Line 211: Line 189:
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 671.548{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 671.548{{c}}
: error map: {{val| 0.000 -30.407 -0.957 -55.017 }}
: error map: {{val| 0.000 -30.407 -0.957 -55.017 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 667.557{{c}}
: [[error map]]: {{val| 0.000 -34.398 +11.014 -39.055 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 672.853{{c}}
: error map: {{val| 0.000 -29.102 -4.873 -60.239 }} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 229: Line 203:
Comma list: 21/20, 33/32, 45/44
Comma list: 21/20, 33/32, 45/44


Mapping: {{mapping| 1 0 7 9 5 | 0 1 -3 -4 -1 }}
{{Mapping|legend=0| 1 0 7 9 5 | 0 1 -3 -4 -1 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1209.379{{c}}, ~3/2 = 677.901{{c}}
* WE: ~2 = 1209.379{{c}}, ~3/2 = 677.901{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 671.507{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 671.507{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 667.180{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 672.644{{c}} -->


{{Optimal ET sequence|legend=0| 7d, 9, 16d }}
{{Optimal ET sequence|legend=0| 7d, 9, 16d }}
Line 255: Line 227:
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 679.270{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 679.270{{c}}
: error map: {{val| 0.000 -22.685 -24.124 -17.583 }}
: error map: {{val| 0.000 -22.685 -24.124 -17.583 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 680.371{{c}}
: [[error map]]: {{val| 0.000 -21.584 -27.425 -4.380 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 678.947{{c}}
: error map: {{val| 0.000 -23.008 -23.156 -21.456 }} -->


{{Optimal ET sequence|legend=1| 7, 16d, 23d, 53bbccd }}
{{Optimal ET sequence|legend=1| 7, 16d, 23d, 53bbccd }}
Line 269: Line 237:
Comma list: 33/32, 45/44, 729/700
Comma list: 33/32, 45/44, 729/700


Mapping: {{mapping| 1 0 7 -16 5 | 0 1 -3 12 -1 }}
{{Mapping|legend=0| 1 0 7 -16 5 | 0 1 -3 12 -1 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1208.145{{c}}, ~3/2 = 683.517{{c}}
* WE: ~2 = 1208.145{{c}}, ~3/2 = 683.517{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 679.150{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 679.150{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 680.241{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 678.909{{c}} -->


{{Optimal ET sequence|legend=0| 7, 16d, 23de, 53bbccdee }}
{{Optimal ET sequence|legend=0| 7, 16d, 23de, 53bbccdee }}
Line 295: Line 261:
* [[CWE]]: ~7/5 = 600.000{{c}}, ~3/2 = 680.206{{c}}
* [[CWE]]: ~7/5 = 600.000{{c}}, ~3/2 = 680.206{{c}}
: error map: {{val| 0.000 -21.749 -26.932 -9.444 }}
: error map: {{val| 0.000 -21.749 -26.932 -9.444 }}
<!-- * [[CTE]]: ~7/5 = 600.000{{c}}, ~3/2 = 677.114{{c}}
: [[error map]]: {{val| 0.000 -24.841 -17.656 -0.168 }}
* [[POTE]]: ~7/5 = 600.000{{c}}, ~3/2 = 681.195{{c}}
: error map: {{val| 0.000 -20.760 -29.900 -12.412 }} -->


{{Optimal ET sequence|legend=1| 14c, 30bc, 44bccd }}
{{Optimal ET sequence|legend=1| 14c, 30bc, 44bccd }}
Line 309: Line 271:
Comma list: 33/32, 45/44, 50/49
Comma list: 33/32, 45/44, 50/49


Mapping: {{mapping| 2 0 14 15 10 | 0 1 -3 -3 -1 }}
{{Mapping|legend=0| 2 0 14 15 10 | 0 1 -3 -3 -1 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~7/5 = 603.958{{c}}, ~3/2 = 685.773{{c}}
* WE: ~7/5 = 603.958{{c}}, ~3/2 = 685.773{{c}}
* CWE: ~7/5 = 600.000{{c}}, ~3/2 = 680.267{{c}}
* CWE: ~7/5 = 600.000{{c}}, ~3/2 = 680.267{{c}}
<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 676.393{{c}}
* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 681.280{{c}} -->


{{Optimal ET sequence|legend=0| 14c, 30bce, 44bccdee }}
{{Optimal ET sequence|legend=0| 14c, 30bce, 44bccdee }}
Line 337: Line 297:
* [[CWE]]: ~2 = 1200.000{{c}}, ~25/21 = 337.260{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~25/21 = 337.260{{c}}
: error map: {{val| 0.000 -27.435 -9.872 -27.722 }}
: error map: {{val| 0.000 -27.435 -9.872 -27.722 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~25/21 = 336.122{{c}}
: [[error map]]: {{val| 0.000 -29.712 -3.043 -10.649 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~25/21 = 337.658{{c}}
: error map: {{val| 0.000 -26.638 -12.264 -33.701 }} -->


{{Optimal ET sequence|legend=1| 7d, 25b, 32bd }}
{{Optimal ET sequence|legend=1| 7d, 25b, 32bd }}
Line 351: Line 307:
Comma list: 33/32, 45/44, 1323/1250
Comma list: 33/32, 45/44, 1323/1250


Mapping: {{mapping| 1 1 4 7 4 | 0 2 -6 -15 -2 }}
{{Mapping|legend=0| 1 1 4 7 4 | 0 2 -6 -15 -2 }}


Optimal tunings:
Optimal tunings:
* WE: ~2 = 1208.211{{c}}, ~25/21 = 339.943{{c}}
* WE: ~2 = 1208.211{{c}}, ~25/21 = 339.943{{c}}
* CWE: ~2 = 1200.000{{c}}, ~25/21 = 337.286{{c}}
* CWE: ~2 = 1200.000{{c}}, ~25/21 = 337.286{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~25/21 = 336.016{{c}}
* POTE: ~2 = 1200.000{{c}}, ~25/21 = 337.633{{c}} -->


{{Optimal ET sequence|legend=0| 7d, 25b, 32bde }}
{{Optimal ET sequence|legend=0| 7d, 25b, 32bde }}
Line 363: Line 317:
Badness (Sintel): 3.04
Badness (Sintel): 3.04


== Listening examples ==
== References ==
; [[Gene Ward Smith]]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mushc.ogg Mysterious Mush (spectrally mapped)]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mush.ogg Mysterious Mush (unmapped)]
* ''[http://micro.soonlabel.com/gene_ward_smith/transformers/hopper.mp3 Hopper]'' by Singer-Medora-White-Smith; in f^4-10f+10=0 equal-beating mavila
 
; [[Mike Battaglia]]
* [https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo The Mavila Experiments - 9-EDO Version]
* [https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-16-edo The Mavila Experiments - 16-EDO Version]
* [https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments The Mavila Experiments - 23-EDO Version]
* [https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-25-edo The Mavila Experiments - 25-EDO Version]
 
; [[John Moriarty]]
* ''[http://clones.soonlabel.com/public/micro/j_l_moriat/Mavila.mp3 Mavila]''
 
== Notes ==


[[Category:Mavila family| ]] <!-- main article -->
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Catalogs of rank-2 temperaments]]
[[Category:Mavila family| ]] <!-- main article -->
[[Category:Mavila| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Listen]]
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