Mavila: Difference between revisions

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I think it's still useful to mention this (as Wad Wizard said it's a great "pitch" for mavila) but it should be in the context of the antidiatonic scale rather than mavila as a temperament
Tuning spectrum: Added 11edo
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: ''This page is about the regular temperament. For the scale structures sometimes associated with it, see [[7L 2s]] and [[2L 5s]].''  
: ''This page is about the regular temperament. For the scale structures sometimes associated with it, see [[7L 2s]] and [[2L 5s]].''  


{{Infobox regtemp
| Title = Mavila
| Subgroups = 2.3.5, 2.3.5.11
| Comma basis = [[135/128]] (2.3.5)<br>[[33/32]], [[45/44]] (2.3.5.11)
| Mapping = 1; 1 -3 -1
| Edo join 1 = 7 | Edo join 2 = 9
| Generators = 3/2
| Generators tuning = 679.0
| Optimization method = CWE
| Pergen = (P8, P5)
| Color name = Layobiti
| MOS scales = [[2L&nbsp;3s]], [[2L&nbsp;5s]], [[7L&nbsp;2s]]
| Odd limit 1 = 5 | Mistuning 1 = 23.0 | Complexity 1 = 5
| Odd limit 2 = 2.3.5.11 11 | Mistuning 2 = 36.9 | Complexity 2 = 7
}}
'''Mavila''' is a [[regular temperament|temperament]] where the major chroma, [[135/128]], is [[tempering out|tempered out]]. Like [[meantone]], mavila is based on the [[chain of fifths]], but as a result of tempering out 135/128 rather than [[81/80]], the fifths are supposedly very flat ({{nowrap|~{{dash|670, 680}}}}{{c}} or so), flatter than even that of [[7edo]] (4\7). Consequently, stacking 7 of these fifths gives you an [[2L 5s|antidiatonic]] [[mos scale]], where in a certain sense, major and minor intervals get reversed. For example, stacking four fifths and octave-reducing now gets you a [[6/5]] ''minor'' third, whereas stacking three fourths and octave-reducing now gets you a [[5/4]] ''major'' third. Note that since we have a heptatonic scale, terms like ''fifths'', ''thirds'', etc. make perfect sense and really are the fifth, third, etc. steps in the antidiatonic scale.
'''Mavila''' is a [[regular temperament|temperament]] where the major chroma, [[135/128]], is [[tempering out|tempered out]]. Like [[meantone]], mavila is based on the [[chain of fifths]], but as a result of tempering out 135/128 rather than [[81/80]], the fifths are supposedly very flat ({{nowrap|~{{dash|670, 680}}}}{{c}} or so), flatter than even that of [[7edo]] (4\7). Consequently, stacking 7 of these fifths gives you an [[2L 5s|antidiatonic]] [[mos scale]], where in a certain sense, major and minor intervals get reversed. For example, stacking four fifths and octave-reducing now gets you a [[6/5]] ''minor'' third, whereas stacking three fourths and octave-reducing now gets you a [[5/4]] ''major'' third. Note that since we have a heptatonic scale, terms like ''fifths'', ''thirds'', etc. make perfect sense and really are the fifth, third, etc. steps in the antidiatonic scale.


This has some very strange implications for music. The mavila antidiatonic scale is similar to the normal [[5L 2s|diatonic]] scale, except interval classes are flipped. Wherever there was a major third, you will find a minor third, and vice versa. Half steps become whole steps and whole steps become half steps (closer to neutral second range, however). When you sharpen the leading tone in minor, you end up sharpening it down instead, meaning you flatten it. Also, minor is now major – instead of a diminished triad in the major scale, there is now an augmented triad.
Mavila tunings range from [[9edo]] to 7edo, with [[16edo]], [[23edo]], and [[25edo]] being typical. These tunings detune 5/4 and 3/2 by significant amounts; it is thus reasonable to call mavila an [[exotemperament]], though it is certainly more accurate than the archetypal exotemperaments such as [[father]].


As an example, the anti-Ionian scale has steps of ssLsssL, which looks like the regular Ionian scale except the "L" intervals are now "s" and vice versa.
Mavila's antidiatonic scale is similar to [[Pelog]] scales used in Indonesian gamelan music. While Pelog's exact tuning is subject to significant regional variation and usually has unequal intervals throughout the scale (as opposed to having exactly two interval sizes), it can be well approximated by the antidiatonic scales of 9edo and 16edo.
 
Because of the structure of this unique tuning, every existing piece of common practice music has, effectively, a shadow version in antidiatonic. That is, with {{w|Ludwig van Beethoven|Beethoven}}'s {{w|Für Elise}}, there are actually two compositions – the one that you know, and the antidiatonic equivalent that has never been heard before until now. Examples of this are provided in the [[#Music]] section.
 
Mavila's antidiatonic scale is similar to [[Pelog]] scales used in Indonesian gamelan music. While Pelog's exact tuning is subject to significant regional variation and usually has unequal intervals throughout the scale (as opposed to having exactly two interval sizes), it can be well approximated by the antidiatonic scales of [[9edo]] and [[16edo]].


Mavila was first discovered by [[Erv Wilson]], possibly in 1989<ref>A ''Linear Tuning of 4-"5"-"6" Artihmetic Mean (−3=5)'' paper from 1989 was referenced in Erv Wilson's ''Meta Meantone & Meta Mavila'' paper.</ref>, after studying the tuning of the timbila music of the Chopi tribe in Mozambique.  
Mavila was first discovered by [[Erv Wilson]], possibly in 1989<ref>A ''Linear Tuning of 4-"5"-"6" Artihmetic Mean (−3=5)'' paper from 1989 was referenced in Erv Wilson's ''Meta Meantone & Meta Mavila'' paper.</ref>, after studying the tuning of the timbila music of the Chopi tribe in Mozambique.  


See [[Mavila family #Mavila]] for more technical data.
See [[Mavila family #Mavila]] for more technical data.
== Notation ==
{{Mavila}}


== Interval chain ==
== Interval chain ==
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<nowiki/>* In 2.3.5.11-subgroup CWE tuning, octave reduced
<nowiki/>* In 2.3.5.11-subgroup CWE tuning, octave reduced


== Modal harmony ==
== Chords and harmony ==
{{Main| Mavila temperament modal harmony }}
{{See also| Mavila temperament modal harmony }}
 
Mavila's tuning has some very strange implications for music. The mavila antidiatonic scale is similar to the normal [[5L 2s|diatonic]] scale, except interval classes are flipped. Wherever there was a major third, you will find a minor third, and vice versa. Half steps become whole steps and whole steps become half steps (closer to neutral second range, however). When you sharpen the leading tone in minor, you end up sharpening it down instead, meaning you flatten it. Also, minor is now major – instead of a diminished triad in the major scale, there is now an augmented triad.
 
As an example, the anti-Ionian scale has steps of ssLsssL, which looks like the regular Ionian scale except the "L" intervals are now "s" and vice versa.
 
Because of the structure of this unique tuning, every existing piece of common practice music has, effectively, a shadow version in antidiatonic. That is, with {{w|Ludwig van Beethoven|Beethoven}}'s {{w|Für Elise}}, there are actually two compositions – the one that you know, and the antidiatonic equivalent that has never been heard before until now. Examples of this are provided in the [[#Music]] section.


== Scales ==
== Scales ==
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25edo also supports mavila. The tuning is 672{{c}} and hence very flat, even flatter than 16edo, but not as flat as 9edo. This is 25edo's second-best 3/2; the alternate fifth generates 5edo.
25edo also supports mavila. The tuning is 672{{c}} and hence very flat, even flatter than 16edo, but not as flat as 9edo. This is 25edo's second-best 3/2; the alternate fifth generates 5edo.


=== Norm-based tunings ===
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 5-limit prime-optimized tunings
|+ style="font-size: 105%; white-space: nowrap;" | 5-limit norm-based tunings
|-
|-
! rowspan="2" |  
! rowspan="2" |  
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{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 2.3.5.11-subgroup prime-optimized tunings
|+ style="font-size: 105%; white-space: nowrap;" | 2.3.5.11-subgroup norm-based tunings
|-
|-
! rowspan="2" |  
! rowspan="2" |  
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| POTE: ~3/2 = 679.788{{c}}
| POTE: ~3/2 = 679.788{{c}}
|}
|}
=== Other tunings ===
* [[DKW theory|DKW]] (2.3.5): ~2 = 1200.000{{c}}, ~3/2 = 675.456{{c}}


=== Tuning spectrum ===
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
! Edo<br />Generator
! Edo<br>generator
! [[Eigenmonzo|Eigenmonzo<br />(Unchanged interval)]]*
! [[Eigenmonzo|Eigenmonzo<br>(unchanged interval)]]*
! Generator (¢)
! Generator (¢)
! Comments
! Comments
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| 600.000
| 600.000
| Lower bound of 5-odd-limit diamond monotone
| Lower bound of 5-odd-limit diamond monotone
|-
|
| 11/8
| 648.682
|
|-
| 6\11
|
| 654.545
|
|-
|-
|  
|  
| 15/8
| 15/8
| 655.866
| 655.866
| 1/2 comma
|-
|
| 15/11
| 663.049
|  
|  
|-
|-
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| 5/4
| 5/4
| 671.229
| 671.229
|  
| 1/3 comma
|-
|-
| 9\16
| 9\16
|  
|  
| 675.000
| 675.000
|
|-
|
| 11/6
| 675.319
|  
|  
|-
|-
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| 25/24
| 25/24
| 675.618
| 675.618
|  
| 2/7 comma
|-
|-
|  
|  
|  
| ''f''<sup>4</sup> + ''f''<sup>3</sup> - 8 = 0
| 676.337
| 676.337
| octave mirror to Wilson's 523.662 meta-mavila
| 1–3–5 equal-beating tuning, Erv Wilson's meta-mavila
|-
|-
| 13\23
| 13\23
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| 5/3
| 5/3
| 678.910
| 678.910
| 5-odd-limit minimax
| 1/4 comma, 5-odd-limit minimax
|-
|
| 11/10
| 682.502
|
|-
|-
|  
|  
| 9/5
| 9/5
| 683.519
| 683.519
| 5-limit 9-odd-limit minimax
| 1/5 comma, 5-limit 9-odd-limit minimax
|-
|
| 11/9
| 684.197
|
|-
|-
| 4\7
| 4\7
|  
|  
| 685.714
| 685.714
| Upper bound of 5-odd-limit diamond monotone<br />5-limit 9-odd-limit diamond monotone (singleton)
| Upper bound of 5-odd-limit diamond monotone<br>5-limit 9-odd-limit and 2.3.5.11-subgroup 11-odd-limit diamond monotone (singleton)
|-
|-
|  
|  
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| Pythagorean tuning
| Pythagorean tuning
|}
|}
<nowiki />* Besides the octave
<nowiki/>* Besides the octave
 
=== Other tunings ===
* [[DKW theory|DKW]] (2.3.5): ~2 = 1200.000{{c}}, ~3/2 = 675.456{{c}}


== Music ==
== Music ==
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; [[Herman Miller]]
; [[Herman Miller]]
* [https://soundcloud.com/morphosyntax-1/kosma-jumis-lul Kôsma jumiś lul] (2017)
* [https://soundcloud.com/morphosyntax-1/kosma-jumis-lul ''Kôsma jumiś lul''] (2017)


; [[John Moriarty]]
; [[John Moriarty]]
* [https://web.archive.org/web/20201127014303/http://clones.soonlabel.com/public/micro/j_l_moriat/Mavila.mp3 ''Mavila'']
* [https://www.youtube.com/watch?v=QzZw-KCn2ig ''Netbeans''] (2019)
* [https://www.youtube.com/watch?v=QzZw-KCn2ig ''Netbeans''] (2019)


; [[Sevish]]
; [[Sevish]]
* from ''Sean but not Heard'' (2012)
* from ''Sean but not Heard'' (2012)
** "Sea Poem" – [https://sevish.bandcamp.com/track/sea-poem Bandcamp] | [https://www.youtube.com/watch?v=2p3z9YEpW1k YouTube] – mavila[9] in an unknown non-edo tuning
** "Sea Poem" – [https://sevish.bandcamp.com/track/sea-poem Bandcamp] | [https://www.youtube.com/watch?v=2p3z9YEpW1k YouTube] – in Mavila[9], an unknown non-edo tuning
** "Marooned at Home" – [https://sevish.bandcamp.com/track/marooned-at-home Bandcamp] | [https://www.youtube.com/watch?v=1tdHPqKPOWc YouTube]
** "Marooned at Home" – [https://sevish.bandcamp.com/track/marooned-at-home Bandcamp] | [https://www.youtube.com/watch?v=1tdHPqKPOWc YouTube]
; [[Gene Ward Smith]]
* ''Mysterious Mush'' – [https://web.archive.org/web/20201127014704/http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mush.ogg unmapped version] · [https://web.archive.org/web/20201127013337/http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mushc.ogg spectrally mapped version]{{clarify}}
* [https://web.archive.org/web/20201127015551/http://micro.soonlabel.com/gene_ward_smith/transformers/hopper.mp3 ''Hopper''] by Singer-Medora-White-Smith{{clarify}}; in {{nowrap|''f''<sup>4</sup> − 10''f'' + 10}} =&nbsp;0 equal-beating mavila


; [[Starshine]]
; [[Starshine]]
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=== Experiments ===
=== Experiments ===
Mike Battaglia has "translated" several common practice pieces into mavila by using Graham Breed's Lilypond code to tune the generators flat. Musical examples are provided in 9edo, 16edo, 23edo, and 25edo, for comparison. Note that the melodic and/or intonational properties differ slightly for each tuning.
Mike Battaglia has translated several common practice pieces into mavila by using Graham Breed's Lilypond code to tune the generators flat. Musical examples are provided in 9edo, 16edo, 23edo, and 25edo, for comparison. Note that the melodic and/or intonational properties differ slightly for each tuning.


* 9edo: <soundcloud>https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo</soundcloud>
* [https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo 9edo version] · [https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-16-edo 16edo version] · [https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments 23edo version] · [https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-25-edo 25edo version]
* 16edo: <soundcloud>https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-16-edo</soundcloud>
* 23edo: <soundcloud>https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments</soundcloud>
* 25edo: <soundcloud>https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-25-edo</soundcloud>


== See also ==
== See also ==
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[[Category:Exotemperaments]]
[[Category:Exotemperaments]]
[[Category:Mavila family]]
[[Category:Mavila family]]
[[Category:Starling temperaments]]