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Mavila: Difference between revisions

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== Modal harmony ==
== Modal harmony ==
{{Main| Mavila temperament modal harmony }}
{{Main| Mavila temperament modal harmony }}
== Scales ==
* [[Mavila-eb]] – 12-tone chromatic scale, equal-beating tuning
=== Mos tree ===
In addition to the 7-note anti-diatonic scale described, Mavila also has a 9 note "superdiatonic" mos, the "super-Ionian" mode of which looks LLLsLLLLs. This is the basis for the [[Armodue theory]].
Mavila generates a 16-tone "chromatic" mos. In a certain sense, much of mavila makes sense if viewed within the lens of a 16-tone chromatic gamut, similarly to how much of meantone is thought of in the setting of a 12-tone chromatic gamut.
After the 16-tone "chromatic" scale is the 23-tone "enharmonic" mos, which can be thought of as an "extended mavila" analogous to the "extended meantone" 19-tone enharmonic scale. If the mavila fifth is flatter than that of 16edo (675 cents), it will instead generate an mos at 25 notes. This is similar to how if the meantone fifth is tuned sharper than 12edo, it will instead generate a 17-tone mos rather than a 19-tone one.


== Tunings ==
== Tunings ==
The fifths of mavila are very flat – 16edo (675.0 cents) and 23edo (678.3 cents) are typical tunings, and the optimal 5-limit tuning is 679.8 cents. As a result, mavila is best played with specialized timbres: either timbres with a lot of rolloff (such as marimba, sine waves, ocarina, etc), or timbres with detuned partials (such as Gamelan or Timbila instruments), etc.
The fifths of mavila are very flat – 16edo (675.0 cents) and 23edo (678.3 cents) are typical tunings, and the optimal 5-limit tuning is 679.8 cents. As a result, mavila is best played with specialized timbres: either timbres with a lot of rolloff (such as marimba, sine waves, ocarina, etc), or timbres with detuned partials (such as Gamelan or Timbila instruments), etc.


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25edo also supports mavila, although the tuning is 672 cents and hence very flat, even flatter than 16edo.
25edo also supports mavila, although the tuning is 672 cents and hence very flat, even flatter than 16edo.


== Scales ==
=== Tuning spectrum ===
* [[Mavila-eb]] – 12-tone chromatic scale, equal-beating tuning
{| class="wikitable center-all left-4"
 
|-
=== Mos tree ===
! Edo<br>Generator
In addition to the 7-note anti-diatonic scale described, Mavila also has a 9 note "superdiatonic" mos, the "super-Ionian" mode of which looks LLLsLLLLs. This is the basis for the [[Armodue theory]].  
! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]<nowiki>*</nowiki>
 
! Generator (¢)
Mavila generates a 16-tone "chromatic" mos. In a certain sense, much of mavila makes sense if viewed within the lens of a 16-tone chromatic gamut, similarly to how much of meantone is thought of in the setting of a 12-tone chromatic gamut.  
! Comments
 
|-
After the 16-tone "chromatic" scale is the 23-tone "enharmonic" mos, which can be thought of as an "extended mavila" analogous to the "extended meantone" 19-tone enharmonic scale. If the mavila fifth is flatter than that of 16edo (675 cents), it will instead generate an mos at 25 notes. This is similar to how if the meantone fifth is tuned sharper than 12edo, it will instead generate a 17-tone mos rather than a 19-tone one.  
| 1\2
|
| 600.000
| Lower bound of 5-odd-limit diamond monotone
|-
|
| 15/8
| 655.866
|
|-
| 5\9
|
| 666.667
|
|-
|
| 5/4
| 671.229
|
|-
| 9\16
|
| 675.000
|
|-
|
| 25/24
| 675.618
|
|-
|
| 9/5
| 683.519
|
|-
| 4\7
|
| 685.714
| Upper bound of 5-odd-limit diamond monotone<br>5-limit 9-odd-limit diamond monotone (singleton)
|-
|
| 5/3
| 678.910
|
|-
|
| 3/2
| 701.995
| Pythagorean tuning
|}
<nowiki>*</nowiki> besides the octave


== Music ==
== Music ==
Retrieved from "https://en.xen.wiki/w/Mavila"