Mavila family: Difference between revisions

The '''pelogic family''' tempers out [[135/128]], the pelogic 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]].

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 scale]]s 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]]).

 

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

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 677.145

* 5-odd-limit [[diamond monotone]]: ~3/2 = [600.000, 685.714] (1\2 to 4\7)

[[Badness]]: 0.039556

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.

* ''[[Superpelog]]'' (+49/48) → [[Slendro clan #Superpelog|Slendro clan]]

* ''[[Jamesbond]]'' (+25/24) → [[7th-octave temperaments #Jamesbond|7th-octave temperaments]]

== Septimal mavila ==

[[Subgroup]]: 2.3.5.7

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

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

{{Multival|legend=1| 1 -3 -11 -7 -20 -17 }}

: mapping generators: ~2, ~3

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 675.7492

* 7-odd-limit [[diamond monotone]]: ~3/2 = [675.000, 678.261] (9\16 to 13\23)

* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [671.229, 701.955]

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

[[Badness]]: 0.089013

Subgroup: 2.3.5.7.11

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

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

: mapping generators: ~2, ~3

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 675.6200

Optimal ET sequence: {{Optimal ET sequence| 7d, 16, 23de }}

Badness: 0.042049

== Pelogic ==

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 21/20, 135/128

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

: mapping generators: ~2, ~3

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 667.5573

[[Tuning ranges]]:  

* 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 }}

[[Badness]]: 0.038661

=== 11-limit ===

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 tuning (CTE): ~2 = 1\1, ~3/2 = 667.1801

Optimal ET sequence: {{Optimal ET sequence| 7d, 9, 16d }}

Badness: 0.022753

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

[[Subgroup]]: 2.3.5.7

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

{{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]] ([[CTE]]): ~2 = 1\1, ~3/2 = 675.0988

* 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]

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

[[Badness]]: 0.049038

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

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

: mapping generators: ~2, ~3

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 674.6841

Optimal ET sequence: {{Optimal ET sequence| 7, 9, 16 }}

Badness: 0.027211

Subgroup: 2.3.5.7.11.13

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 generators: ~2, ~3

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 675.2877

Optimal ET sequence: {{Optimal ET sequence| 7, 9, 16 }}

Subgroup: 2.3.5.7.11.13.19

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 }}

: mapping generators: ~2, ~3

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 675.1703

Optimal ET sequence: {{Optimal ET sequence| 7, 9, 16, 25bf }}

Badness: 0.0160

: mapping generators: ~2, ~3

 

{{Multival|legend=1| 1 -3 12 -7 16 36 }}

 

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 680.3705

[[Badness]]: 0.121294

: mapping generators: ~2, ~3

 

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 680.2409

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

Badness: 0.055036

{{Multival|legend=1| 2 -6 -6 -14 -15 3 }}

 

[[Optimal tuning]] ([[CTE]]): ~7/5 = 1\2, ~3/2 = 677.114

[[Badness]]: 0.074703

: mapping generators: ~7/5, ~3

 

Optimal tuning (CTE): ~7/5 = 1\2, ~3/2 = 676.3926

Optimal ET sequence: {{Optimal ET sequence| 14c, 30bce, 44bccdee }}

Badness: 0.035694

{{Multival|legend=1| 2 -6 -15 -14 -29 -18 }}

 

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~25/21 = 336.1216

[[Badness]]: 0.222377

: mapping generators: ~2, ~11/9

 

Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 336.0156

 

Optimal ET sequence: {{Optimal ET sequence| 7d, 25b, 32bde }}

 

* ''[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

* [https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo The Mavila Experiments - 9-EDO Version]

[[Category:Pelogic family| ]] <!-- main article -->

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