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The '''mavila family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] [[135/128]], the mavila comma, also known as the major chroma or major limma. The [[5-limit]] temperament is [[mavila]], so named after the Chopi village where it was discovered, and is the base from which higher limit temperaments are derived. The generator for all of these is a very flat fifth, lying on the spectrum between [[7edo|7-equal]] and [[9edo|9-equal]].
{{Technical data page}}
The '''mavila family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] [[135/128]], the mavila comma, also known as the major chroma or major limma. The [[5-limit]] temperament is [[mavila]], so named after the Chopi village where it was discovered, and is the base from which higher limit temperaments are derived. The generator for all of these is a very flat fifth, lying on the spectrum between [[7edo]] and [[9edo]].


One of the most salient and characteristic features of mavila temperaments is that when you stack 4 of the tempered fifths you get to a minor third instead of the usual major third that you would get if the fifths were pure. This also means that the arrangement of small and large steps in a 7-note mavila scale is the inverse of a diatonic scale of 2 small steps and 5 large steps; mavila has 2 large steps and 5 small steps (see [[2L 5s]]).  
One of the most salient and characteristic features of mavila temperaments is that when you stack 4 of the tempered fifths you get to a minor third instead of the usual major third that you would get if the fifths were pure. This also means that the arrangement of small and large steps in a 7-note mavila scale is the inverse of a diatonic scale of 2 small steps and 5 large steps; mavila has 2 large steps and 5 small steps (see [[2L 5s]]).  
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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 = 1\1, ~3/2 = 677.145
* [[WE]]: ~2 = 1208.287{{c}}, ~3/2 = 684.501{{c}}
* [[POTE]]: ~2 = 1\1, ~3/2 = 679.806
: [[error map]]: {{val| +8.287 -9.167 -6.667 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 679.111{{c}}
: error map: {{val| 0.000 -22.844 -23.648 }}


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* 5-odd-limit [[diamond monotone]]: ~3/2 = [600.000, 685.714] (1\2 to 4\7)
* [[5-odd-limit]] [[diamond monotone]]: ~3/2 = [600.000, 685.714] (1\2 to 4\7)
* 5-odd-limit [[diamond tradeoff]]: ~3/2 = [671.229, 701.955] (1/3-comma to Pyth.)
* 5-odd-limit [[diamond tradeoff]]: ~3/2 = [671.229, 701.955] (1/3-comma to Pyth.)


{{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 ===
The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. That means [[126/125]] for septimal mavila, [[21/20]] for pelogic, [[36/35]] for armodue, [[875/864]] for hornbostel, [[49/48]] for superpelog, and [[50/49]] for bipelog.
==== 7-limit extensions ====
The second comma of the [[normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. That means [[36/35]] for armodue, [[126/125]] for mavling, [[21/20]] for pelogic, [[875/864]] for hornbostel, [[49/48]] for superpelog, [[50/49]] for bipelog, and [[1323/1250]] for mohavila.


Temperaments discussed elsewhere include
Temperaments discussed elsewhere include
* ''[[Wallaby]]'' (+28/27) → [[Trienstonic clan #Wallaby|Trienstonic clan]]
* ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa|Very low accuracy temperaments]]
* ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa|Very low accuracy temperaments]]
* ''[[Superpelog]]'' (+49/48) → [[Slendro clan #Superpelog|Slendro clan]]
* ''[[Wallaby]]'' (+28/27) → [[Very low accuracy temperaments #Wallaby|Very low accuracy temperaments]]
* ''[[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]]


== Septimal mavila ==
Considered below are mavling, pelogic, armodue, hornbostel, bipelog, and mohavila.
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 126/125, 135/128
==== Subgroup extensions ====
Mavila naturally extends to the 2.3.5.11 subgroup, with the generator standing in for ~16/11 and ~22/15, as is given right below.


{{Mapping|legend=1| 1 0 7 20 | 0 1 -3 -11 }}
=== 2.3.5.11 subgroup ===
Subgroup: 2.3.5.11


{{Multival|legend=1| 1 -3 -11 -7 -20 -17 }}
Comma list: 33/32, 45/44


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


[[Optimal tuning]]s
Gencom mapping: {{mapping| 1 0 7 0 5 | 0 1 -3 0 -1 }}
* [[CTE]]: ~2 = 1\1, ~3/2 = 675.7492
* [[POTE]]: ~2 = 1\1, ~3/2 = 677.913


[[Tuning ranges]]:  
Optimal tunings:  
* 7-odd-limit [[diamond monotone]]: ~3/2 = [675.000, 678.261] (9\16 to 13\23)
* WE: ~2 = 1208.454{{c}}, ~3/2 = 684.577{{c}}
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [671.229, 701.955]
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 678.978{{c}}


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


[[Badness]]: 0.089013
Badness (Sintel): 0.424


=== Undecimal mavila ===
== Armodue ==
Subgroup: 2.3.5.7.11
Armodue, also known as '''hexadecimal''', is the main 7-limit extension of mavila, and also the main temperament of [[Armodue theory]]. It tempers out 36/35, and can be described as the {{nowrap| 7 & 9 }} temperament. 7/4 is mapped to the minor seventh of the antidiatonic scale, where we will find 9/5 in the 5-limit. [[16edo]] shows us an obvious tuning.  


Comma list: 33/32, 45/44, 126/125
The name ''armodue'' has been established in 2011 thanks to [[Mike Battaglia]]<ref name="mike's cleanup">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101194.html Yahoo! Tuning Group | ''Higher-limit mavila extension spring cleaning'']</ref>. The alternative name ''hexadecimal'' was attested as early as 2004<ref name="big temp list">[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_8809.html Yahoo! Tuning Group | ''114 7-limit temperaments'']</ref><ref name="pelogic & hex">[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_9670.html Yahoo! Tuning Group | ''Pelogic and "hexidecimal"'']</ref>.


Mapping: {{mapping| 1 0 7 20 5 | 0 1 -3 -11 -1 }}
[[Subgroup]]: 2.3.5.7


: mapping generators: ~2, ~3
[[Comma list]]: 36/35, 135/128


Optimal tunings:
{{Mapping|legend=1| 1 0 7 -5 | 0 1 -3 5 }}
* CTE: ~2 = 1\1, ~3/2 = 675.6200
* POTE: ~2 = 1\1, ~3/2 = 677.924


Optimal ET sequence: {{Optimal ET sequence| 7d, 16, 23de }}
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1204.996{{c}}, ~3/2 = 676.803{{c}}
: [[error map]]: {{val| +4.996 -20.157 +3.261 +15.187 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 674.220{{c}}
: error map: {{val| 0.000 -27.735 -8.974 +2.275 }}


Badness: 0.042049
[[Tuning ranges]]:  
* [[7-odd-limit]] [[diamond monotone]]: ~3/2 = [666.667, 675.000] (5\9 to 9\16)
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [666.718, 701.955]


==== 2.3.5.11 subgroup ====
{{Optimal ET sequence|legend=1| 7, 9, 16 }}
Subgroup: 2.3.5.11


[[Comma list]]: 33/32, 45/44
[[Badness]] (Sintel): 1.24


[[Gencom]]: [2 4/3; 33/32, 45/44]
=== 11-limit ===
Subgroup: 2.3.5.7.11


[[Gencom|Gencom mapping]]: [{{val|1 2 1 0 3}}, {{val|0 -1 3 0 1}}]
Comma list: 33/32, 36/35, 45/44


[[Mapping|Sval mapping]]: [{{val|1 2 1 3}}, {{val|0 -1 3 1}}]
Mapping: {{mapping| 1 0 7 -5 5 | 0 1 -3 5 -1 }}


[[Tp tuning|POL2 generator]]: ~4/3 = 520.212
Optimal tunings:  
* WE: ~2 = 1205.460{{c}}, ~3/2 = 676.873{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 673.952{{c}}


{{Optimal ET sequence|legend=1| 7, 16, 23e, 30bce }}
{{Optimal ET sequence|legend=0| 7, 9, 16 }}


[[Tp tuning #T2 tuning|RMS error]]: 4.705 cents
Badness (Sintel): 0.900


== Pelogic ==
=== 13-limit ===
'Pelogic' (from the Indonesian word ''[[Wikipedia: Pelog|pelog]]'') should probably be pronounced /pɛˈlɒgɪk/ ''pell-LOG-ik''.
Subgroup: 2.3.5.7.11.13


[[Subgroup]]: 2.3.5.7
Comma list: 27/26, 33/32, 36/35, 45/44


[[Comma list]]: 21/20, 135/128
Mapping: {{mapping| 1 0 7 -5 5 -1 | 0 1 -3 5 -1 3 }}


{{Mapping|legend=1| 1 0 7 9 | 0 1 -3 -4}}
Optimal tunings:
* WE: ~2 = 1205.396{{c}}, ~3/2 = 676.792{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 673.988{{c}}


: mapping generators: ~2, ~3
{{Optimal ET sequence|legend=0| 7, 9, 16 }}


{{Multival|legend=1| 1 -3 -4 -7 -9 -1 }}
Badness (Sintel): 0.800


[[Optimal tuning]]s:
==== Armodog ====
* [[CTE]]: ~2 = 1\1, ~3/2 = 667.5573
Subgroup: 2.3.5.7.11.13.19
* [[POTE]]: ~2 = 1\1, ~3/2 = 672.853


[[Tuning ranges]]:  
Comma list: 27/26, 33/32, 36/35, 39/38, 45/44
* 7-odd-limit [[diamond monotone]]: ~3/2 = 666.667 (5\9)
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [617.488, 701.955]


{{Optimal ET sequence|legend=1| 7d, 9, 16d }}
Subgroup-val mapping: {{mapping| 1 0 7 -5 5 -1 -2 | 0 1 -3 5 -1 3 4 }}


[[Badness]]: 0.038661
Optimal tunings:  
 
* WE: ~2 = 1204.838{{c}}, ~3/2 = 675.997{{c}}
=== 11-limit ===
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 673.540{{c}}
Subgroup: 2.3.5.7.11
 
Comma list: 21/20, 33/32, 45/44
 
Mapping: {{mapping| 1 0 7 9 5 | 0 1 -3 -4 -1 }}


: mapping generators: ~2, ~3
{{Optimal ET sequence|legend=0| 7, 9, 16, 25bf }}


Optimal tunings:
Badness (Sintel): 0.830
* CTE: ~2 = 1\1, ~3/2 = 667.1801
* POTE: ~2 = 1\1, ~3/2 = 672.644


Optimal ET sequence: {{Optimal ET sequence| 7d, 9, 16d }}
== Mavling ==
Mavling tempers out 126/125 and may be described as the {{nowrap| 7d & 16 }} temperament. The 7/4 is mapped to the augmented sixth of the antidiatonic scale.


Badness: 0.022753
This temperament was formerly known as ''septimal mavila'', but decanonicalized in 2025 per community consensus.
 
== Armodue ==
This temperament is also known as '''hexadecimal'''.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 36/35, 135/128
[[Comma list]]: 126/125, 135/128


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


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 675.0988
* [[WE]]: ~2 = 1208.187{{c}}, ~3/2 = 682.538{{c}}
* [[POTE]]: ~2 = 1\1, ~3/2 = 673.997
: [[error map]]: {{val| +8.187 -11.230 -1.178 -3.057 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 677.350{{c}}
: error map: {{val| 0.000 -24.605 -18.363 -19.672 }}


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* 7-odd-limit [[diamond monotone]]: ~3/2 = [666.667, 675.000] (5\9 to 9\16)
* [[7-odd-limit]] [[diamond monotone]]: ~3/2 = [675.000, 678.261] (9\16 to 13\23)
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [666.718, 701.955]
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [671.229, 701.955]


{{Optimal ET sequence|legend=1| 7, 9, 16 }}
{{Optimal ET sequence|legend=1| 7d, 16, 23d }}


[[Badness]]: 0.049038
[[Badness]] (Sintel): 2.25


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 33/32, 36/35, 45/44
Comma list: 33/32, 45/44, 126/125


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


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 674.6841
* WE: ~2 = 1208.243{{c}}, ~3/2 = 682.582{{c}}
* POTE: ~2 = 1\1, ~3/2 = 673.807
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 677.434{{c}}


Optimal ET sequence: {{Optimal ET sequence| 7, 9, 16 }}
{{Optimal ET sequence|legend=0| 7d, 16, 23de }}


Badness: 0.027211
Badness (Sintel): 1.39


=== 13-limit ===
== Pelogic ==
Subgroup: 2.3.5.7.11.13
''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"/>.  


Comma list: 27/26, 33/32, 36/35, 45/44
The 7/4 is mapped to the major sixth of the antidiatonic scale.


Mapping: {{mapping| 1 0 7 -5 5 -1 | 0 1 -3 5 -1 3 }}
[[Subgroup]]: 2.3.5.7


: mapping generators: ~2, ~3
[[Comma list]]: 21/20, 135/128


Optimal tunings:
{{Mapping|legend=1| 1 0 7 9 | 0 1 -3 -4 }}
* CTE: ~2 = 1\1, ~3/2 = 675.2877
* POTE: ~2 = 1\1, ~3/2 = 673.763


Optimal ET sequence: {{Optimal ET sequence| 7, 9, 16 }}
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1210.184{{c}}, ~3/2 = 678.563{{c}}
: [[error map]]: {{val| +10.184 -13.208 +18.732 -32.160 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 671.548{{c}}
: error map: {{val| 0.000 -30.407 -0.957 -55.017 }}


Badness: 0.019351
[[Tuning ranges]]:  
* [[7-odd-limit]] [[diamond monotone]]: ~3/2 = 666.667 (5\9)
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [617.488, 701.955]


==== Armodog ====
{{Optimal ET sequence|legend=1| 7d, 9, 16d }}
Subgroup: 2.3.5.7.11.13.19
 
[[Badness]] (Sintel): 0.978


Comma list: 27/26, 33/32, 36/35, 39/38, 45/44
=== 11-limit ===
Subgroup: 2.3.5.7.11


Mapping: {{mapping| 1 0 7 -5 5 -1 -2 | 0 1 -3 5 -1 3 4 }}
Comma list: 21/20, 33/32, 45/44


: mapping generators: ~2, ~3
Mapping: {{mapping| 1 0 7 9 5 | 0 1 -3 -4 -1 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~3/2 = 675.1703
* WE: ~2 = 1209.379{{c}}, ~3/2 = 677.901{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 671.507{{c}}


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


Badness: 0.0160
Badness (Sintel): 0.752


== Hornbostel ==
== Hornbostel ==
Hornbostel tempers out 729/700 and may be described as the {{nowrap| 7 & 23d }} temperament. The 7/4 is mapped to the diminished seventh of the antidiatonic scale.
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 218: Line 221:


{{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 = 1\1, ~3/2 = 680.3705
* [[WE]]: ~2 = 1207.970{{c}}, ~3/2 = 683.457{{c}}
* [[POTE]]: ~2 = 1\1, ~3/2 = 678.947
: [[error map]]: {{val| +7.970 -10.529 -4.805 +0.775 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 679.270{{c}}
: 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 237: 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 = 1\1, ~3/2 = 680.2409
* WE: ~2 = 1208.145{{c}}, ~3/2 = 683.517{{c}}
* POTE: ~2 = 1\1, ~3/2 = 678.909
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 679.150{{c}}


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


Badness: 0.055036
Badness (Sintel): 1.82


== Bipelog ==
== Bipelog ==
Line 256: 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 = 1\2, ~3/2 = 677.114
* [[WE]]: ~7/5 = 603.757{{c}}, ~3/2 = 685.461{{c}}
* [[POTE]]: ~7/5 = 1\2, ~3/2 = 681.195
: [[error map]]: {{val| +7.514 -8.980 -12.641 +8.604 }}
* [[CWE]]: ~7/5 = 600.000{{c}}, ~3/2 = 680.206{{c}}
: 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 ===
Line 274: Line 273:
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}}
* CWE: ~7/5 = 600.000{{c}}, ~3/2 = 680.267{{c}}


Optimal tunings:
{{Optimal ET sequence|legend=0| 14c, 30bce, 44bccdee }}
* CTE: ~7/5 = 1\2, ~3/2 = 676.3926
* POTE: ~7/5 = 1\2, ~3/2 = 681.280


Optimal ET sequence: {{Optimal ET sequence| 14c, 30bce, 44bccdee }}
Badness (Sintel): 1.18


Badness: 0.035694
== Mohavila ==
Named by Mike Battaglia in 2012<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104134.html Yahoo! Tuning Group | ''Mohavila temperament'']</ref>, mohavila splits the mavila fifth in two. Unlike [[mohaha]], this generator is not used as an ~11/9. In fact, the prime 11 is the same as in mavila, so the ~11/9 is the major third, tempered together with ~5/4. The fifth is only split to derive septimal intervals.  


== Mohavila ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 292: Line 291:


: 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 = 1\1, ~25/21 = 336.1216
* [[WE]]: ~2 = 1208.410{{c}}, ~25/21 = 340.025{{c}}
* [[POTE]]: ~2 = 1\1, ~25/21 = 337.658
: [[error map]]: {{val| +8.410 -13.496 +7.177 -10.327 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~25/21 = 337.260{{c}}
: 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 ===
Line 309: Line 308:


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 = 1\1, ~25/21 = 336.0156
* WE: ~2 = 1208.211{{c}}, ~25/21 = 339.943{{c}}
* POTE: ~2 = 1\1, ~25/21 = 337.633
* CWE: ~2 = 1200.000{{c}}, ~25/21 = 337.286{{c}}


Optimal ET sequence: {{Optimal ET sequence| 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]''


[[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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