Mothra: Difference between revisions

{{Infobox Regtemp

| Odd limit 1 = 7 | Mistuning 1 = ? | Complexity 1 = 31

| Odd limit 2 = (2.3.5.7) 21 | Mistuning 2 = ? | Complexity 2 = 36

 

'''Mothra''' is a temperament in the [[7-limit]] that is a strong extension to [[slendric]], which is defined by splitting the interval of [[3/2]] into three [[8/7]]s and 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 higher limits, one may note that the two-generator interval closely approximates [[17/13]], and that the six-generator interval - the meantone whole tone of [[9/8]][[~]][[10/9]], approximates [[19/17]], so that the 13:17:19 chord is well-approximated; it is worth noting also that this chord is entirely included within the subtemperament obtained from taking every other generator of mothra, which is [[A-team]]. This can be combined with the canonical mapping of 13 for each undecimal extension, which tempers out [[144/143]], to provide a natural route to the [[19-limit]].

As a strong extension of slendric, mothra's intervals can be expressed using the same system of extended diatonic interval naming [[Slendric#Interval categories|used for slendric]]. It is particularly convenient to use diatonic conventions for mothra, because its chain of fifths is meantone, and therefore 5/4 is simply read as a major third.

{| class="wikitable sortable center-all right-3"

! rowspan="3" | &#35; !! rowspan="3" | Extended <br /> diatonic <br /> interval !! rowspan="3" | Cents* !! colspan="3" | Approximate ratios

! rowspan="2" | 7-limit intervals !! colspan="2" | Intervals of undecimal extensions

<nowiki/>* In 7-limit [[CWE tuning]]

== Tuning spectrum ==

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

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

[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]