Topic: Some Mothra scales

4 scales

Thread (2 messages)

From: genewardsmith (2010-05-09)
Subject: Some Mothra scales

! mothra11br4.scl
Mothra[11] with a brat of 4
11
!
194.55680981190403133
232.42613496865067188
426.98294478055470324
464.85226993730134382
659.40907974920537509
697.27840490595201564
891.83521471785604685
929.70453987460268758
1124.2613496865067188
1162.1306748432533594
1200.0000000000000000
! x^12 + 2x^3 - 8

! mothra16br4.scl
Mothra[16] with a brat of 4
16
!
156.68748465515739066
194.55680981190403133
232.42613496865067188
389.11361962380806258
426.98294478055470324
464.85226993730134382
621.53975459245873435
659.40907974920537509
697.27840490595201564
853.96588956110940631
891.83521471785604685
929.70453987460268758
1086.3920245297600782
1124.2613496865067188
1162.1306748432533594
1200.0000000000000000
! x^12 + 2x^3 - 8

From: genewardsmith (2010-05-09)
Subject: Re: Some Mothra scales

--- In [email protected], "genewardsmith" <genewardsmith@...> wrote:
>
> ! mothra11br4.scl
> Mothra[11] with a brat of 4
> 11

It occurs to me that triads are complex in Mothra and Mothra[11] doesn't have any major triads. As a rule, you shouldn't have a polynomial of degree greater than the number of notes in your rank two scale if the genrators are all contiguous. Below I give degree one and degree seven versions of Mothra[11].

! mothra11rat.scl
Mothra[11] with exact 8/7 as generator
11
!
16807/16384
8/7
2401/2048
64/49
343/256
512/343
49/32
4096/2401
7/4
32768/16807
2

! mothra11sub.scl
Mothra[11] with subminor third beats
11
!
39.857902275036850177
232.02841954499262996
271.88632182002948016
464.05683908998525998
503.91474136502211010
696.08525863497788988
735.94316091001474006
928.11367817997051984
967.97158045500737002
1160.1420977249631499
1200.0000000000000000
! 4x^7 - 13x^4 + 12