... Hi George, Tom & all others, ... Did you mean by that following corresponding absolute pitches, or which other frequncies had you concrete in mind when
Message 1 of 63
, Apr 23, 2008
--- In firstname.lastname@example.org, "George D. Secor" <gdsecor@...> wrote:
Hi George, Tom & all others,
> ! Dent-YN-RWT.scl
> Tom Dent's Young-Neidhardt well-temperament (rationalized by G. Secor)
> 560/531 ! C#
> 2643/2360 ! D
> 70/59 ! Eb
> 74/59 ! E
> 315/236 ! F
> 1329/944 ! F#
> 883/590 ! G
> 280/177 ! G#
> 890/531 ! A
> 105/59 ! A#
> 887/472 ! B
Did you mean by that following corresponding absolute pitches,
or which other frequncies had you concrete in mind when
creating that particular one by the factor 59?
Hence i do agree with your's observation:
> The brats aren't nearly as simple as with the harmonic temperaments
> we've been looking at lately, but OTOH the fifths are much more
> consistent in size (all tempered <4 cents).
... Hi George, ... in deed, even that *.scl-file contained some unfixed bug. ... Many thanks again for that repair. ... when considering more evaluated digits,
> > epimoric decomposition
> > F 1058:1059 C 528:529 G 296/297 D 295/296 A 294/295 E 3968:3969 B
> > B F# C# G# Eb 7532:7533 Bb 5648:5649 F
> >Cents approximation,
> > about the amounts:
> >F~ -1.635 ~C~ -3.275 ~G~ -5.839 ~D~ -5.859 ~A~ -5.879 ~E~ -0.436 ~B
> > B F# C# G# Eb~ -0.2298 ~Bb~ -0.306 ~F
> I believe there are still a few mistakes.
in deed, even that *.scl-file contained some unfixed bug.
> From the sizes of the
> fifths you give, I think that perhaps you meant this:
Now -as far as i can see- those ratios appearto be correct:
> 558/529 ! C#
> 592/529 ! D
> 2511/2116 ! Eb = 627.75/529
> 1323/1058 ! E = 661.5/529
> 706/529 ! F
> 744/529 ! F#
> 792/529 ! G
> 837/529 ! G#
> 875/523 ! A = 442.5Hz*2 absolute a4
> 1883/1058 ! Bb = 941.5/529
> 992/529 ! B
Many thanks again for that repair.
> This will result in:
when considering more evaluated digits,
as calculated by "Google"s arithmetics, which yields:
same question as for D~A?
Or what else could be the reason for the tiny
discrepancy amounting about tiny 1/10 Cents
inbetween ours calculations of the relative deviations
in the tempered 5ths flatnesses?
at least we both do agree now in all others 5ths except D~A~E.
What do you think about that well-temperement,
with an almost JI the C-major chord:
C:E:G = 4 : 5*(2646/2645) : 6*(529/528)
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