--- In tuning@yahoogroups.com, Kurt Bigler <kkb@...> wrote:
multiply all ratios by factor 264=11*3*2*2 in order to
obtain integral absolute pitch-frequencies
> > ! bihexany.scl
> > Hole around [0, 1/2, 1/2, 1/2]
> > 12
> > !
C4 264 from 1/1 middle C=264Hz
C# 280 > 35/33
(D4 297 > 9/8) inserted instead Cb=B# for smoothening the 5ths
Eb 308 > 7/6
E4 330 > 5/4
F4 336 > 14/11
F# 360 > 15/11
G4 396 > 3/2
G# 420 > 35/22
A4 440 > 5/3 !normal pitch 440Hz
Bb 462 > 7/4
B4 480 > 20/11
(Cb=B# 504 > 21/11)
C5 528 > 2
or arranged in a cycle of a dozen partial tempered 5ths
C 33,..,264 begin, starting @ middle-C
G 99:=33*3,198,396
D (37,74,148,296)297:=99*3
A 55,110(111:=37*3),220,440 ! (111:110)*(297:296)=81:80 the SC
E (41,82,164)165:=55*3,330
B 15,30,60,,(123:=41*3)120,240,480 ! (165:164)*(41:40)=33:32
F# 45:=15*3,..,360
C# 35,70,(135:=45*3)140,280 ! 140:135=28:27
G# (13,26,52,104)105:=35*3,210,420
Eb (39:=13*3,78)77,154,308
!(105:104)*(77:78)=2695:2704=299.4444.../300.4444...
Bb (7,...,228)231:=77*3,462 ! 231:228=77:76
F (11,22)21:=7*3,42,84,168,336
C 33:=11*3 cycle closed, ready done.
i.m.o: heavy harsh tempering, but it works.
A.S.