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Mavila family: Difference between revisions

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{{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


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


[[Tuning ranges]]:  
[[Tuning ranges]]:  
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{{Optimal ET sequence|legend=1| 7, 9, 16, 23, 30bc }}
{{Optimal ET sequence|legend=1| 7, 9, 16, 23, 30bc }}


[[Badness]]: 0.039556
[[Badness]] (Sintel): 0.928


=== Overview to extensions ===
=== Overview to extensions ===
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* ''[[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.
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=== 2.3.5.11 subgroup ===
=== 2.3.5.11 subgroup ===
[[Subgroup]]: 2.3.5.11
Subgroup: 2.3.5.11


[[Comma list]]: 33/32, 45/44
Comma list: 33/32, 45/44


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


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


: [[gencom]]: [2 3; 33/32, 45/44]
Optimal tunings:  
 
* WE: ~2 = 1208.454{{c}}, ~3/2 = 684.577{{c}}
[[Optimal tuning]]s:  
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 678.978{{c}}
* [[CTE]]: ~2 = 1200.000, ~3/2 = 676.039
* [[POTE]]: ~2 = 1200.000, ~3/2 = 679.788


{{Optimal ET sequence|legend=1| 7, 16, 23e, 30bce }}
{{Optimal ET sequence|legend=0| 7, 16, 23e, 30bce }}


[[Tp tuning #T2 tuning|RMS error]]: 4.705 cents
Badness (Sintel): 0.424


== Armodue ==
== Armodue ==
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{{Mapping|legend=1| 1 0 7 -5 | 0 1 -3 5 }}
{{Mapping|legend=1| 1 0 7 -5 | 0 1 -3 5 }}
: mapping generators: ~2, ~3
{{Multival|legend=1| 1 -3 5 -7 5 20 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 675.099
* [[WE]]: ~2 = 1204.996{{c}}, ~3/2 = 676.803{{c}}
: [[error map]]: {{val| 0.000 -26.856 -11.610 +6.668 }}
: [[error map]]: {{val| +4.996 -20.157 +3.261 +15.187 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 673.997
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 674.220{{c}}
: error map: {{val| 0.000 -27.958 -8.304 +1.158 }}
: error map: {{val| 0.000 -27.735 -8.974 +2.275 }}


[[Tuning ranges]]:  
[[Tuning ranges]]:  
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{{Optimal ET sequence|legend=1| 7, 9, 16 }}
{{Optimal ET sequence|legend=1| 7, 9, 16 }}


[[Badness]]: 0.049038
[[Badness]] (Sintel): 1.24


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 0 7 -5 5 | 0 1 -3 5 -1 }}
Mapping: {{mapping| 1 0 7 -5 5 | 0 1 -3 5 -1 }}
: mapping generators: ~2, ~3


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


{{Optimal ET sequence|legend=0| 7, 9, 16 }}
{{Optimal ET sequence|legend=0| 7, 9, 16 }}


Badness: 0.027211
Badness (Sintel): 0.900


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 0 7 -5 5 -1 | 0 1 -3 5 -1 3 }}
Mapping: {{mapping| 1 0 7 -5 5 -1 | 0 1 -3 5 -1 3 }}
: mapping generators: ~2, ~3


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


{{Optimal ET sequence|legend=0| 7, 9, 16 }}
{{Optimal ET sequence|legend=0| 7, 9, 16 }}


Badness: 0.019351
Badness (Sintel): 0.800


==== Armodog ====
==== Armodog ====
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Comma list: 27/26, 33/32, 36/35, 39/38, 45/44
Comma list: 27/26, 33/32, 36/35, 39/38, 45/44


Mapping: {{mapping| 1 0 7 -5 5 -1 -2 | 0 1 -3 5 -1 3 4 }}
Subgroup-val mapping: {{mapping| 1 0 7 -5 5 -1 -2 | 0 1 -3 5 -1 3 4 }}
 
: mapping generators: ~2, ~3


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


{{Optimal ET sequence|legend=0| 7, 9, 16, 25bf }}
{{Optimal ET sequence|legend=0| 7, 9, 16, 25bf }}


Badness: 0.0160
Badness (Sintel): 0.830


== Mavling ==
== Mavling ==
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{{Mapping|legend=1| 1 0 7 20 | 0 1 -3 -11 }}
{{Mapping|legend=1| 1 0 7 20 | 0 1 -3 -11 }}


{{Multival|legend=1| 1 -3 -11 -7 -20 -17 }}
[[Optimal tuning]]s:
 
* [[WE]]: ~2 = 1208.187{{c}}, ~3/2 = 682.538{{c}}
: mapping generators: ~2, ~3
: [[error map]]: {{val| +8.187 -11.230 -1.178 -3.057 }}
 
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 677.350{{c}}
[[Optimal tuning]]s
: error map: {{val| 0.000 -24.605 -18.363 -19.672 }}
* [[CTE]]: ~2 = 1200.000, ~3/2 = 675.749
: [[error map]]: {{val| 0.000 -26.206 -13.561 -2.067 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 677.913
: error map: {{val| 0.000 -24.042 -20.052 -25.866 }}


[[Tuning ranges]]:  
[[Tuning ranges]]:  
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{{Optimal ET sequence|legend=1| 7d, 16, 23d }}
{{Optimal ET sequence|legend=1| 7d, 16, 23d }}


[[Badness]]: 0.089013
[[Badness]] (Sintel): 2.25


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 0 7 20 5 | 0 1 -3 -11 -1 }}
Mapping: {{mapping| 1 0 7 20 5 | 0 1 -3 -11 -1 }}
: mapping generators: ~2, ~3


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


{{Optimal ET sequence|legend=0| 7d, 16, 23de }}
{{Optimal ET sequence|legend=0| 7d, 16, 23de }}


Badness: 0.042049
Badness (Sintel): 1.39


== Pelogic ==
== Pelogic ==
''Pelogic'' (from the Indonesian word ''[[Wikipedia: Pelog|pelog]]'') should probably be pronounced /pɛˈlɒgɪk/ ''pell-LOG-ik''. This name dates back to as early as 2004<ref name="big temp list"/><ref name="pelogic & hex"/> and has been approved of by [[Mike Battaglia]] in 2011, reasoning that Pelog is supposed to be flatter than [[16edo|16-]] or [[23edo]], and this temperament, tempering out 21/20 and described as the {{nowrap| 7d & 9 }} temperament, tends towards such a tuning<ref name="mike's cleanup"/>.  
''Pelogic'' (from the Indonesian word ''[[pelog]]'') should probably be pronounced /pɛˈlɒgɪk/ ''pell-LOG-ik''. This name dates back to as early as 2004<ref name="big temp list"/><ref name="pelogic & hex"/> and has been approved of by [[Mike Battaglia]] in 2011, reasoning that Pelog is supposed to be flatter than [[16edo|16-]] or [[23edo]], and this temperament, tempering out 21/20 and described as the {{nowrap| 7d & 9 }} temperament, tends towards such a tuning<ref name="mike's cleanup"/>.  


The 7/4 is mapped to the major sixth of the antidiatonic scale.  
The 7/4 is mapped to the major sixth of the antidiatonic scale.  
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{{Mapping|legend=1| 1 0 7 9 | 0 1 -3 -4 }}
{{Mapping|legend=1| 1 0 7 9 | 0 1 -3 -4 }}
: mapping generators: ~2, ~3
{{Multival|legend=1| 1 -3 -4 -7 -9 -1 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 667.557
* [[WE]]: ~2 = 1210.184{{c}}, ~3/2 = 678.563{{c}}
: [[error map]]: {{val| 0.000 -34.398 +11.014 -39.055 }}
: [[error map]]: {{val| +10.184 -13.208 +18.732 -32.160 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 672.853
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 671.548{{c}}
: error map: {{val| 0.000 -29.102 -4.873 -60.239 }}
: error map: {{val| 0.000 -30.407 -0.957 -55.017 }}


[[Tuning ranges]]:  
[[Tuning ranges]]:  
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{{Optimal ET sequence|legend=1| 7d, 9, 16d }}
{{Optimal ET sequence|legend=1| 7d, 9, 16d }}


[[Badness]]: 0.038661
[[Badness]] (Sintel): 0.978


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 0 7 9 5 | 0 1 -3 -4 -1 }}
Mapping: {{mapping| 1 0 7 9 5 | 0 1 -3 -4 -1 }}


: mapping generators: ~2, ~3
Optimal tunings:  
 
* WE: ~2 = 1209.379{{c}}, ~3/2 = 677.901{{c}}
Optimal tunings:
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 671.507{{c}}
* CTE: ~2 = 1200.000, ~3/2 = 667.180
* POTE: ~2 = 1200.000, ~3/2 = 672.644


{{Optimal ET sequence|legend=0| 7d, 9, 16d }}
{{Optimal ET sequence|legend=0| 7d, 9, 16d }}


Badness: 0.022753
Badness (Sintel): 0.752


== Hornbostel ==
== Hornbostel ==
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{{Mapping|legend=1| 1 0 7 -16 | 0 1 -3 12 }}
{{Mapping|legend=1| 1 0 7 -16 | 0 1 -3 12 }}
: mapping generators: ~2, ~3
{{Multival|legend=1| 1 -3 12 -7 16 36 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 680.371
* [[WE]]: ~2 = 1207.970{{c}}, ~3/2 = 683.457{{c}}
: [[error map]]: {{val| 0.000 -21.584 -27.425 -4.380 }}
: [[error map]]: {{val| +7.970 -10.529 -4.805 +0.775 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 678.947
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 679.270{{c}}
: error map: {{val| 0.000 -23.008 -23.156 -21.456 }}
: error map: {{val| 0.000 -22.685 -24.124 -17.583 }}


{{Optimal ET sequence|legend=1| 7, 16d, 23d, 53bbccd }}
{{Optimal ET sequence|legend=1| 7, 16d, 23d, 53bbccd }}


[[Badness]]: 0.121294
[[Badness]] (Sintel): 3.07


=== 11-limit ===
=== 11-limit ===
Line 267: Line 238:


Mapping: {{mapping| 1 0 7 -16 5 | 0 1 -3 12 -1 }}
Mapping: {{mapping| 1 0 7 -16 5 | 0 1 -3 12 -1 }}
: mapping generators: ~2, ~3


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


{{Optimal ET sequence|legend=0| 7, 16d, 23de, 53bbccdee }}
{{Optimal ET sequence|legend=0| 7, 16d, 23de, 53bbccdee }}


Badness: 0.055036
Badness (Sintel): 1.82


== Bipelog ==
== Bipelog ==
Line 286: Line 255:


: mapping generators: ~7/5, ~3
: mapping generators: ~7/5, ~3
{{Multival|legend=1| 2 -6 -6 -14 -15 3 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 600.000, ~3/2 = 677.114
* [[WE]]: ~7/5 = 603.757{{c}}, ~3/2 = 685.461{{c}}
: [[error map]]: {{val| 0.000 -24.841 -17.656 -0.168 }}
: [[error map]]: {{val| +7.514 -8.980 -12.641 +8.604 }}
* [[POTE]]: ~7/5 = 600.000, ~3/2 = 681.195
* [[CWE]]: ~7/5 = 600.000{{c}}, ~3/2 = 680.206{{c}}
: error map: {{val| 0.000 -20.760 -29.900 -12.412 }}
: error map: {{val| 0.000 -21.749 -26.932 -9.444 }}


{{Optimal ET sequence|legend=1| 14c, 30bc, 44bccd }}
{{Optimal ET sequence|legend=1| 14c, 30bc, 44bccd }}


[[Badness]]: 0.074703
[[Badness]] (Sintel): 1.89


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 2 0 14 15 10 | 0 1 -3 -3 -1 }}
Mapping: {{mapping| 2 0 14 15 10 | 0 1 -3 -3 -1 }}


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


{{Optimal ET sequence|legend=0| 14c, 30bce, 44bccdee }}
{{Optimal ET sequence|legend=0| 14c, 30bce, 44bccdee }}


Badness: 0.035694
Badness (Sintel): 1.18


== Mohavila ==
== Mohavila ==
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: mapping generators: ~2, ~25/21
: mapping generators: ~2, ~25/21
{{Multival|legend=1| 2 -6 -15 -14 -29 -18 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~25/21 = 336.122
* [[WE]]: ~2 = 1208.410{{c}}, ~25/21 = 340.025{{c}}
: [[error map]]: {{val| 0.000 -29.712 -3.043 -10.649 }}
: [[error map]]: {{val| +8.410 -13.496 +7.177 -10.327 }}
* [[POTE]]: ~2 = 1200.000, ~25/21 = 337.658
* [[CWE]]: ~2 = 1200.000{{c}}, ~25/21 = 337.260{{c}}
: error map: {{val| 0.000 -26.638 -12.264 -33.701 }}
: error map: {{val| 0.000 -27.435 -9.872 -27.722 }}


{{Optimal ET sequence|legend=1| 7d, 25b, 32bd }}
{{Optimal ET sequence|legend=1| 7d, 25b, 32bd }}


[[Badness]]: 0.222377
[[Badness]] (Sintel): 5.63


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 1 4 7 4 | 0 2 -6 -15 -2 }}
Mapping: {{mapping| 1 1 4 7 4 | 0 2 -6 -15 -2 }}
: mapping generators: ~2, ~25/21


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


{{Optimal ET sequence|legend=0| 7d, 25b, 32bde }}
{{Optimal ET sequence|legend=0| 7d, 25b, 32bde }}


Badness: 0.092074
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:Mavila family| ]] <!-- main article -->
[[Category:Catalogs of rank-2 temperaments]]
[[Category:Mavila| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Listen]]
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