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{{Infobox Regtemp
{{Interwiki
| en = Mothra
| de = Slendrisch #Mothra
}}
{{Infobox regtemp
| Title = Mothra
| Title = Mothra
| Subgroups = 2.3.5.7
| Subgroups = 2.3.5.7
| Comma basis = [[81/80]], [[1029/1024]]
| Comma basis = [[81/80]], [[1029/1024]]
| Edo join 1 = 26 | Edo join 2 = 31
| Edo join 1 = 26 | Edo join 2 = 31
| Generator = 8/7 | Generator tuning = 232.4 | Optimization method = CTE
| MOS scales = [[1L 4s]], [[5L 1s]], [[5L 6s]], ... [[5L 21s]]
| Mapping = 1; 3 12 -1
| Mapping = 1; 3 12 -1
| Generators = 8/7 | Generators tuning = 232.3 | Optimization method = CWE
| MOS scales = [[1L 4s]], [[5L 1s]], [[5L 6s]], …, [[5L 21s]]
| Pergen = (P8, P5/3)
| Pergen = (P8, P5/3)
| Odd limit 1 = 7 | Mistuning 1 = 5.4 | Complexity 1 = 31
| Odd limit 1 = 7 | Mistuning 1 = 5.4 | Complexity 1 = 31
| Odd limit 2 = (2.3.5.7) 21 | Mistuning 2 = 10.8 | Complexity 2 = 36
| Odd limit 2 = (2.3.5.7) 21 | Mistuning 2 = 10.8 | Complexity 2 = 36
}}
}}
 
'''Mothra''', also known as '''cynder''', is a temperament of the [[7-limit]] that is a strong extension to [[slendric]], which is defined by splitting a perfect fifth representing [[3/2]] into three intervals of [[8/7]], tempering out [[1029/1024]]. The fifth of mothra is flattened to a [[meantone]] fifth, so that it reaches [[5/4]] when stacked four times and [[81/80]] is tempered out, unlike that of the other slendric extension [[rodan]], which is sharpened from just. This has the effect of bringing the generator 8/7 considerably closer to just, and also allowing [[MOS scale]]s of mothra to be more melodically usable than those of other forms of slendric, as the structurally-pervasive small step known as the [[quark]] (the residue between the octave and 5 generators, representing [[49/48]], [[64/63]], and in mothra also [[36/35]]) is larger here. [[EDOs]] that support mothra include [[26edo]], [[31edo]], and [[36edo]], and 31 is a particularly good tuning.
'''Mothra''' is a temperament in the [[7-limit]] that is a strong extension to [[slendric]], which is defined by splitting a perfect fifth representing [[3/2]] into three intervals of [[8/7]], tempering out [[1029/1024]]. The fifth of mothra is flattened to a [[meantone]] fifth, so that it reaches [[5/4]] when stacked four times and [[81/80]] is tempered out, unlike that of the other slendric extension [[rodan]], which is sharpened from just. This has the effect of bringing the generator 8/7 considerably closer to just, and also allowing [[MOS scale]]s of mothra to be more melodically usable than those of other forms of slendric, as the structurally-pervasive small step known as the [[quark]] (the residue between the octave and 5 generators, representing [[49/48]], [[64/63]], and in mothra also [[36/35]]) is larger here. [[EDOs]] that support mothra include [[26edo]], [[31edo]], and [[36edo]], and 31 is a particularly good tuning.


In the [[11-limit]], two extensions are of note: undecimal mothra (26 & 31), which tempers out [[99/98]], [[385/384]] and [[441/440]] to find the 11th harmonic at 8 generators down, and mosura (31 & 36), which tempers out [[176/175]] to find the 11th harmonic at 23 generators up. These two mappings merge at 31edo, which is therefore a uniquely suitable tuning for 11-limit mothra.
In the [[11-limit]], two extensions are of note: undecimal mothra (26 & 31), which tempers out [[99/98]], [[385/384]] and [[441/440]] to find the 11th harmonic at 8 generators down, and mosura (31 & 36), which tempers out [[176/175]] to find the 11th harmonic at 23 generators up. These two mappings merge at 31edo, which is therefore a uniquely suitable tuning for 11-limit mothra.
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<nowiki/>* In 7-limit [[CWE tuning]], octave reduced
<nowiki/>* In 7-limit [[CWE tuning]], octave reduced


== Tuning spectrum ==
== Tunings ==
{{see also|Slendric #Tuning spectrum}}
=== Norm-based tunings ===
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~8/7 = 232.3996{{c}}
| CWE: ~8/7 = 232.2514{{c}}
| POTE: ~8/7 = 232.1933{{c}}
|}
 
=== Tuning spectrum ===
{{See also| Slendric #Tuning spectrum }}


Vals refer to the appropriate undecimal extension in the EDO's range.
Vals refer to the appropriate undecimal extension in the edo's range.


{| class="wikitable center-all left-4 left-5"
{| class="wikitable center-all left-4 left-5"
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|  
|  
|  
|  
|-
| [[165edo|32\165]]
|
| 232.727
|
| 165bc val
|-
|-
| [[67edo|13\67]]
| [[67edo|13\67]]
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== Music ==
== Music ==
[http://micro.soonlabel.com/16-ET/mothra/20141028_mothra16br4.mp3 Prelude for solo piano in mothra16, brat 4 tuning] by [http://chrisvaisvil.com/prelude-for-solo-piano-in-mothra16-brat-4-tuning/ Chris Vaisvil]
; [[Chris Vaisvil]]
* ''Prelude for solo piano'' (2014) by [[Chris Vaisvil]] – [https://web.archive.org/web/20201127013310/http://micro.soonlabel.com/16-ET/mothra/20141028_mothra16br4.mp3 play] | [https://www.chrisvaisvil.com/prelude-for-solo-piano-in-mothra16-brat-4-tuning/ blog] – in Mothra[16], brat 4 tuning


[[Category:Mothra| ]] <!-- main article -->
[[Category:Mothra| ]] <!-- main article -->
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