Mavila: Difference between revisions

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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]].''

{{Infobox regtemp

| Title = Mavila

| Subgroups = 2.3.5, 2.3.5.11

| Comma basis = [[135/128]] (2.3.5) [[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 3s]], [[2L 5s]], [[7L 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.

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.

~~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.

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]].

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See [[Mavila family #Mavila]] for more technical data.

== Notation ==

== Interval chain ==

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

== ~~Modal~~ harmony ==

== Chords and 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 ==

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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.

=== Norm-based tunings ===

{| 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" |

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{| 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" |

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| 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 ===

{| class="wikitable center-all left-4"

|-

! Edo ~~Generator~~

! Edo generator

! [[Eigenmonzo|Eigenmonzo (~~Unchanged~~ interval)]]*

! [[Eigenmonzo|Eigenmonzo (unchanged interval)]]*

! Generator (¢)

! Comments

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| 600.000

| Lower bound of 5-odd-limit diamond monotone

|-

|

| 11/8

| 648.682

|

|-

| 6\11

|

| 654.545

|

|-

|

| 15/8

| 655.866

| 1/2 comma

|-

|

| 15/11

| 663.049

|

|-

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| 5/4

| 671.229

|

| 1/3 comma

|-

| 9\16

|

| 675.000

|

|-

|

| 11/6

| 675.319

|

|-

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| 25/24

| 675.618

|

| 2/7 comma

|-

|

| ''f''4 + ''f''3 - 8 = 0

| 676.337

| ~~octave mirror to~~ Wilson's ~~523.662~~ meta-mavila

| 1–3–5 equal-beating tuning, Erv Wilson's meta-mavila

|-

| 13\23

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| 5/3

| 678.910

| 5-odd-limit minimax

| 1/4 comma, 5-odd-limit minimax

|-

|

| 11/10

| 682.502

|

|-

|

| 9/5

| 683.519

| 5-limit 9-odd-limit minimax

| 1/5 comma, 5-limit 9-odd-limit minimax

|-

|

| 11/9

| 684.197

|

|-

| 4\7

|

| 685.714

| Upper bound of 5-odd-limit diamond monotone 5-limit 9-odd-limit diamond monotone (singleton)

| Upper bound of 5-odd-limit diamond monotone 5-limit 9-odd-limit and 2.3.5.11-subgroup 11-odd-limit diamond monotone (singleton)

|-

|

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| 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 ==

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; [[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]]

* [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)

; [[Sevish]]

* 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]

; [[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''4 − 10''f'' + 10}} = 0 equal-beating mavila

; [[Starshine]]

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=== 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 ==

@@ Line 1: / Line 1: @@
 : ''This page is about the regular temperament. For the scale structures sometimes associated with it, see [[7L&nbsp;2s]] and [[2L&nbsp;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.
-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.
-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.
 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]].
@@ Line 16: / Line 25: @@
 See [[Mavila family #Mavila]] for more technical data.
+== Notation ==
+{{Mavila}}
 == Interval chain ==
@@ Line 59: / Line 71: @@
 <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 ==
@@ Line 89: / Line 107: @@
 edo 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"
-|+ 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" |
@@ Line 106: / Line 125: @@
 {| 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" |
@@ Line 120: / Line 139: @@
 | 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 ===
 {| class="wikitable center-all left-4"
 |-
-! Edo<br />Generator
+! Edo<br>generator
-! [[Eigenmonzo|Eigenmonzo<br />(Unchanged interval)]]*
+! [[Eigenmonzo|Eigenmonzo<br>(unchanged interval)]]*
 ! Generator (¢)
 ! Comments
@@ Line 133: / Line 155: @@
 | 600.000
 | Lower bound of 5-odd-limit diamond monotone
+|-
+|
+| 11/8
+| 648.682
+|
+|-
+| 6\11
+|
+| 654.545
+|
 |-
 |
 | 15/8
 | 655.866
+| 1/2 comma
+|-
+|
+| 15/11
+| 663.049
 |
 |-
@@ Line 147: / Line 184: @@
 | 5/4
 | 671.229
-|
+| 1/3 comma
 |-
 | 9\16
 |
 | 675.000
+|
+|-
+|
+| 11/6
+| 675.319
 |
 |-
@@ Line 157: / Line 199: @@
 | 25/24
 | 675.618
-|
+| 2/7 comma
 |-
 |
-|
+| ''f''<sup>4</sup> + ''f''<sup>3</sup> - 8 = 0
 | 676.337
-| octave mirror to Wilson's 523.662 meta-mavila
+| 1–3–5 equal-beating tuning, Erv Wilson's meta-mavila
 |-
 | 13\23
@@ Line 172: / Line 214: @@
 | 5/3
 | 678.910
-| 5-odd-limit minimax
+| 1/4 comma, 5-odd-limit minimax
+|-
+|
+| 11/10
+| 682.502
+|
 |-
 |
 | 9/5
 | 683.519
-| 5-limit 9-odd-limit minimax
+| 1/5 comma, 5-limit 9-odd-limit minimax
+|-
+|
+| 11/9
+| 684.197
+|
 |-
 | 4\7
 |
 | 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)
 |-
 |
@@ Line 189: / Line 241: @@
 | 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 ==
@@ Line 211: / Line 260: @@
 ; [[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]]
+* [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)
 ; [[Sevish]]
 * 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]
+; [[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]]
@@ Line 225: / Line 279: @@
 === 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 ==