Mavila family: Difference between revisions

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The ''pelogic family'' tempers out [[135/128|135/128]], the pelogic comma, also known as the major chroma or major limma. The [[5-limit|5-limit]] temperament is (5-limit) mavila, so named after the Chopi village where it was discovered. The generator for all of these is a very flat fifth, lying on the spectrum between 7-equal and 9-equal.
The '''pelogic family''' tempers out [[135/128]], the pelogic comma, also known as the major chroma or major limma. The [[5-limit]] temperament is (5-limit) mavila, so named after the Chopi village where it was discovered. The generator for all of these is a very flat fifth, lying on the spectrum between 7-equal and 9-equal.


One of the most salient and characteristic features of pelogic temperament 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|2L 5s)]]
One of the most salient and characteristic features of pelogic temperament 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]]).


Another salient feature of pelogic temperament is the fact that 9 note MOS scales may be produced, thus giving us three different MOS scales to choose from that are not decidedly chromatic in nature; (5, 7, and 9 note scales) This is reflected in the design of the 9 + 7 layout of the Goldsmith keyboard for 16 tone equal temperament. (see[[7L_2s| 7L 2s]])
Another salient feature of pelogic temperament is the fact that 9 note MOS scales may be produced, thus giving us three different MOS scales to choose from that are not decidedly chromatic in nature (5, 7, and 9 note scales). This is reflected in the design of the 9 + 7 layout of the Goldsmith keyboard for 16 tone equal temperament (see [[7L 2s]]).


One of the most common temperaments talked about in the pelogic family is '''mavila''', the 5-limit temperament eliminating 135/128, from which higher-limit extensions are derived.
One of the most common temperaments talked about in the pelogic family is '''mavila''', the 5-limit temperament eliminating 135/128, from which higher-limit extensions are derived.


'Pelogic' (from the Indonesian word ''[https://en.wikipedia.org/wiki/Pelog pelog]'') should probably be pronounced /pɛˈlɒgɪk/ ''pell-LOG-ik''.
'Pelogic' (from the Indonesian word ''[[Wikipedia: Pelog|pelog]]'') should probably be pronounced /pɛˈlɒgɪk/ ''pell-LOG-ik''.


 
= Mavila =
=5-limit parent temperament=
 
==Mavila==
<span style="display: block; text-align: right;">Other languages: [[:de:Mavila|Deutsch]]</span>
<span style="display: block; text-align: right;">Other languages: [[:de:Mavila|Deutsch]]</span>


[[Comma|Comma]]s: 135/128
[[Comma]]: 135/128


[[POTE_tuning|POTE generator]]: 679.806
[[POTE_tuning|POTE generator]]: ~3/2 = 679.806


Map: [&lt;1 0 7|, &lt;0 1 -3|]
Map: [&lt;1 0 7|, &lt;0 1 -3|]


EDOs: [[7edo|7]], [[9edo|9]], [[16edo|16]], [[23edo|23]], [[25edo|25b]], [[30edo|30bc]], [[34edo|34b]], [[41edo|41b]]
EDOs: {{EDOs|7, 9, 16, 23, 30bc}}


= Septimal mavila =
[[Comma|Commas]]: 126/125, 135/128


=7-limit children=
[[POTE_tuning|POTE generator]]: ~3/2 = 677.912
 
==Septimal Mavila==
[[Comma|Comma]]s: 135/128, 126/125
 
[[POTE_tuning|POTE generator]]: 677.912


Map: [&lt;1 0 7 20|, &lt;0 1 -3 -11|]
Map: [&lt;1 0 7 20|, &lt;0 1 -3 -11|]


EDOs: [[7edo|7]], [[16edo|16]], [[23edo|23d]]
EDOs: {{EDOs|7d, 16, 23d}}


Badness: 0.0890
Badness: 0.0890


= Pelogic =
[[Comma|Commas]]: 21/20, 135/128


==Pelogic==
[[POTE_tuning|POTE generator]]: ~3/2 = 672.853
[[Comma|Comma]]s: 135/128, 21/20
 
[[POTE_tuning|POTE generator]]: 672.853


Map: [&lt;1 0 7 9|, &lt;0 1 -3 -4|]
Map: [&lt;1 0 7 9|, &lt;0 1 -3 -4|]


[[wedgie|Wedgie]]: &lt;&lt;1 -3 -4 -7 -9 -1||
[[Wedgie]]: &lt;&lt;1 -3 -4 -7 -9 -1||


EDOs: [[9edo|9]], [[16edo|16d]]
EDOs: {{EDOs|7d, 9, 16d}}


Badness: 0.0387
Badness: 0.0387


===11-limit===
== 11-limit ==
Commas: 21/20, 33/32, 45/44
Commas: 21/20, 33/32, 45/44


Line 59: Line 52:
Map: [&lt;1 0 7 9 5|, &lt;0 1 -3 -4 -1|]
Map: [&lt;1 0 7 9 5|, &lt;0 1 -3 -4 -1|]


EDOs: [[9edo|9]], [[16edo|16d]]
EDOs: {{EDOs|7d, 9, 16d}}


Badness: 0.0228
Badness: 0.0228


= Armodue =
This temperament is also known as '''hexadecimal'''.


==Armodue==
[[Comma|Commas]]: 36/35, 135/128
[[Comma|Comma]]s: 135/128, 36/35


[[POTE_tuning|POTE generator]]: 673.997
[[POTE_tuning|POTE generator]]: ~3/2 = 673.997


Map: [&lt;1 0 7 -5|, &lt;0 1 -3 5|]
Map: [&lt;1 0 7 -5|, &lt;0 1 -3 5|]


[[wedgie|Wedgie]]: &lt;&lt;1 -3 5 -7 5 20||
[[Wedgie]]: &lt;&lt;1 -3 5 -7 5 20||


EDOs: [[9edo|9]], [[16edo|16]], [[23edo|23p]], [[25edo|25b]]
EDOs: {{EDOs|7, 9, 16, 41b, 57bb}}


Badness: 0.0490
Badness: 0.0490


===11-limit===
== 11-limit ==
Commas: 33/32, 36/35, 45/44
Commas: 33/32, 36/35, 45/44


Line 84: Line 78:
Map: [&lt;1 0 7 -5 5|, &lt;0 1 -3 5 -1|]
Map: [&lt;1 0 7 -5 5|, &lt;0 1 -3 5 -1|]


EDOs: [[9edo|9]], [[16edo|16]], [[23edo|23e]], [[25edo|25b]]
EDOs: {{EDOs|7, 9, 16, 25b, 41be, 57bbee}}


Badness: 0.0272
Badness: 0.0272


===13-limit===
== 13-limit ==
Commas: 27/26, 33/32, 36/35, 45/44
Commas: 27/26, 33/32, 36/35, 45/44


Line 95: Line 89:
Map: [&lt;1 0 7 -5 5 -1|, &lt;0 1 -3 5 -1 3|]
Map: [&lt;1 0 7 -5 5 -1|, &lt;0 1 -3 5 -1 3|]


EDOs: 7, 9, 16, 41bef, 57bef
EDOs: {{EDOs|7, 9, 16, 41bef, 57bbeef}}


Badness: 0.0194
Badness: 0.0194


= Hornbostel =
[[Comma|Commas]]: 135/128, 875/864


==Hornbostel==
[[POTE_tuning|POTE generator]]: ~3/2 = 678.947
[[Comma|Comma]]s: 135/128, 875/864
 
[[POTE_tuning|POTE generator]]: 678.947


Map: [&lt;1 0 7 -16|, &lt;0 1 -3 12|]
Map: [&lt;1 0 7 -16|, &lt;0 1 -3 12|]
Line 109: Line 102:
[[wedgie|Wedgie]]: &lt;&lt;1 -3 12 -7 16 36||
[[wedgie|Wedgie]]: &lt;&lt;1 -3 12 -7 16 36||


EDOs: [[7edo|7]], [[16edo|16d]], [[23edo|23d]]
EDOs: {{EDOs|7, 16d, 23d}}


Badness: 0.1213
Badness: 0.1213


= Superpelog =
[[Comma|Commas]]: 49/48, 135/128


==Superpelog==
[[POTE_tuning|POTE generator]]: ~8/7 = 259.952
[[Comma|Comma]]s: 135/128, 49/48
 
[[POTE_tuning|POTE generator]]: 259.952


Map: [&lt;1 0 7 2|, &lt;0 2 -6 1|]
Map: [&lt;1 0 7 2|, &lt;0 2 -6 1|]
Line 123: Line 115:
[[wedgie|Wedgie]]: &lt;&lt;2 -6 1 -14 -4 19||
[[wedgie|Wedgie]]: &lt;&lt;2 -6 1 -14 -4 19||


EDOs: [[9edo|9]], [[14edo|14c]], [[23edo|23d]], [[37edo|37bcd]], [[60edo|60bcd]]
EDOs: {{EDOs|9, 14c, 23d, 37bcd, 60bbccdd}}


Badness: 0.0582
Badness: 0.0582


===11-limit===
== 11-limit ==
Commas: 33/32, 45/44, 49/48
Commas: 33/32, 45/44, 49/48


Line 134: Line 126:
Map: [&lt;1 0 7 2 5|, &lt;0 2 -6 1 -2|]
Map: [&lt;1 0 7 2 5|, &lt;0 2 -6 1 -2|]


EDOs: 9, 14c, 23de, 37bcde
EDOs: {{EDOs|9, 14c, 23de, 37bcde}}


Badness: 0.0285
Badness: 0.0285
Line 140: Line 132:
''[http://micro.soonlabel.com/MOS/20120418-9mos-mindaugas.mp3 Mindaugas Rex Lithuaniae]'' by [http://chrisvaisvil.com/?p=2267 Chris Vaisvil] (in 5\23 tuning)
''[http://micro.soonlabel.com/MOS/20120418-9mos-mindaugas.mp3 Mindaugas Rex Lithuaniae]'' by [http://chrisvaisvil.com/?p=2267 Chris Vaisvil] (in 5\23 tuning)


 
= Bipelog =
==Bipelog==
[[Comma|Commas]]: 50/49, 135/128
[[Comma|Comma]]s: 135/128, 50/49


[[POTE_tuning|POTE generator]]: ~3/2 = 681.195
[[POTE_tuning|POTE generator]]: ~3/2 = 681.195
Line 150: Line 141:
[[wedgie|Wedgie]]: &lt;&lt;2 -6 -6 -14 -15 3||
[[wedgie|Wedgie]]: &lt;&lt;2 -6 -6 -14 -15 3||


EDOs: [[14edo|14c]], [[16edo|16]], [[23edo|23d]], [[37edo|37bcd]]
EDOs: {{EDOs|14c, 16, 30bc, 44bccd}}


Badness: 0.0747
Badness: 0.0747


===11-limit===
== 11-limit ==
Commas: 33/32 45/44 50/49
Commas: 33/32, 45/44, 50/49


POTE generator: ~3/2 = 681.280
POTE generator: ~3/2 = 681.280
Line 161: Line 152:
Map: [&lt;2 0 14 15 10|, &lt;0 1 -3 -3 -1|]
Map: [&lt;2 0 14 15 10|, &lt;0 1 -3 -3 -1|]


EDOs: 14c, 16, 44bcde
EDOs: {{EDOs|14c, 16, 30bce, 44bccdee}}


Badness: 0.0357
Badness: 0.0357


 
= Mohavila =
==Mohavila==
Commas: 135/128, 1323/1250
Commas: 135/128, 1323/1250


Line 175: Line 165:
Wedgie: &lt;&lt;2 -6 -15 -14 -29 -18||
Wedgie: &lt;&lt;2 -6 -15 -14 -29 -18||


EDOs: 32bd, 36
EDOs: {{EDOs|32bd, 36}}


Badness: 0.2224
Badness: 0.2224


===11-limit===
== 11-limit ==
Commas: 33/32, 45/44, 1323/1250
Commas: 33/32, 45/44, 1323/1250


Line 186: Line 176:
Map: [&lt;1 1 4 7 4|, &lt;0 2 -6 -15 -2|]
Map: [&lt;1 1 4 7 4|, &lt;0 2 -6 -15 -2|]


EDOs: 32bde
EDOs: {{EDOs|32bde}}


Badness: 0.0921
Badness: 0.0921


 
= Mavila listening examples =
=Mavila Listening examples=
'''[[Gene Ward Smith]]'''
'''[[Gene_Ward_Smith|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/mushc.ogg Mysterious Mush (spectrally mapped)]
*[http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mush.ogg Mysterious Mush (unmapped)]
*[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
*''[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|Mike Battaglia]]'''
'''[[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-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-16-edo The Mavila Experiments - 16-EDO Version]
Line 203: Line 192:
*[https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-25-edo The Mavila Experiments - 25-EDO Version]
*[https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-25-edo The Mavila Experiments - 25-EDO Version]


'''[[John_Moriarty|John Moriarty]]'''
'''[[John Moriarty]]'''
*''[http://clones.soonlabel.com/public/micro/j_l_moriat/Mavila.mp3 Mavila]''
*''[http://clones.soonlabel.com/public/micro/j_l_moriat/Mavila.mp3 Mavila]''


Line 209: Line 198:
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Pelogic]]
[[Category:Pelogic]]
[[Category:Rank 3]]
[[Category:Rank 2]]
[[Category:Listen]]
[[Category:Listen]]

Revision as of 12:09, 11 November 2020

The pelogic family tempers out 135/128, the pelogic comma, also known as the major chroma or major limma. The 5-limit temperament is (5-limit) mavila, so named after the Chopi village where it was discovered. The generator for all of these is a very flat fifth, lying on the spectrum between 7-equal and 9-equal.

One of the most salient and characteristic features of pelogic temperament 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).

Another salient feature of pelogic temperament is the fact that 9 note MOS scales may be produced, thus giving us three different MOS scales to choose from that are not decidedly chromatic in nature (5, 7, and 9 note scales). This is reflected in the design of the 9 + 7 layout of the Goldsmith keyboard for 16 tone equal temperament (see 7L 2s).

One of the most common temperaments talked about in the pelogic family is mavila, the 5-limit temperament eliminating 135/128, from which higher-limit extensions are derived.

'Pelogic' (from the Indonesian word pelog) should probably be pronounced /pɛˈlɒgɪk/ pell-LOG-ik.

Mavila

Other languages: Deutsch

Comma: 135/128

POTE generator: ~3/2 = 679.806

Map: [<1 0 7|, <0 1 -3|]

EDOs: 7, 9, 16, 23, 30bc

Septimal mavila

Commas: 126/125, 135/128

POTE generator: ~3/2 = 677.912

Map: [<1 0 7 20|, <0 1 -3 -11|]

EDOs: 7d, 16, 23d

Badness: 0.0890

Pelogic

Commas: 21/20, 135/128

POTE generator: ~3/2 = 672.853

Map: [<1 0 7 9|, <0 1 -3 -4|]

Wedgie: <<1 -3 -4 -7 -9 -1||

EDOs: 7d, 9, 16d

Badness: 0.0387

11-limit

Commas: 21/20, 33/32, 45/44

POTE generator: ~3/2 = 672.644

Map: [<1 0 7 9 5|, <0 1 -3 -4 -1|]

EDOs: 7d, 9, 16d

Badness: 0.0228

Armodue

This temperament is also known as hexadecimal.

Commas: 36/35, 135/128

POTE generator: ~3/2 = 673.997

Map: [<1 0 7 -5|, <0 1 -3 5|]

Wedgie: <<1 -3 5 -7 5 20||

EDOs: 7, 9, 16, 41b, 57bb

Badness: 0.0490

11-limit

Commas: 33/32, 36/35, 45/44

POTE generator: ~3/2 = 673.807

Map: [<1 0 7 -5 5|, <0 1 -3 5 -1|]

EDOs: 7, 9, 16, 25b, 41be, 57bbee

Badness: 0.0272

13-limit

Commas: 27/26, 33/32, 36/35, 45/44

POTE generator: ~3/2 = 673.763

Map: [<1 0 7 -5 5 -1|, <0 1 -3 5 -1 3|]

EDOs: 7, 9, 16, 41bef, 57bbeef

Badness: 0.0194

Hornbostel

Commas: 135/128, 875/864

POTE generator: ~3/2 = 678.947

Map: [<1 0 7 -16|, <0 1 -3 12|]

Wedgie: <<1 -3 12 -7 16 36||

EDOs: 7, 16d, 23d

Badness: 0.1213

Superpelog

Commas: 49/48, 135/128

POTE generator: ~8/7 = 259.952

Map: [<1 0 7 2|, <0 2 -6 1|]

Wedgie: <<2 -6 1 -14 -4 19||

EDOs: 9, 14c, 23d, 37bcd, 60bbccdd

Badness: 0.0582

11-limit

Commas: 33/32, 45/44, 49/48

POTE generator: ~8/7 = 259.959

Map: [<1 0 7 2 5|, <0 2 -6 1 -2|]

EDOs: 9, 14c, 23de, 37bcde

Badness: 0.0285

Mindaugas Rex Lithuaniae by Chris Vaisvil (in 5\23 tuning)

Bipelog

Commas: 50/49, 135/128

POTE generator: ~3/2 = 681.195

Map: [<2 0 14 15|, <0 1 -3 -3|]

Wedgie: <<2 -6 -6 -14 -15 3||

EDOs: 14c, 16, 30bc, 44bccd

Badness: 0.0747

11-limit

Commas: 33/32, 45/44, 50/49

POTE generator: ~3/2 = 681.280

Map: [<2 0 14 15 10|, <0 1 -3 -3 -1|]

EDOs: 14c, 16, 30bce, 44bccdee

Badness: 0.0357

Mohavila

Commas: 135/128, 1323/1250

POTE generator: ~25/21 = 337.658

Map: [<1 1 4 7|, <0 2 -6 -15|]

Wedgie: <<2 -6 -15 -14 -29 -18||

EDOs: 32bd, 36

Badness: 0.2224

11-limit

Commas: 33/32, 45/44, 1323/1250

POTE generator: ~25/21 = 337.633

Map: [<1 1 4 7 4|, <0 2 -6 -15 -2|]

EDOs: 32bde

Badness: 0.0921

Mavila listening examples

Gene Ward Smith

Mike Battaglia

John Moriarty

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