## preferred Re: absoute-pitch... @ a'=445Hz? on the violin & piano

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• ... at the moment i do prefer from Werckmeister s septenarian comma versus the SC 81/80 = (99/98)*(441/440) divided into 3 epimoric subparts: 99/98 =
Message 1 of 63 , Apr 25, 2008
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--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:
>
> A=440 is my preference. (I see no reason why the frequencies of all
> of the pitches should be exact integers.) With most well-
> temperaments C will be higher in pitch than in 12-equal with A=440;
> for the rationalized Dent-Young-Neidhardt C will be ~262.5 Hz.
>
at the moment i do prefer
from Werckmeister's septenarian comma versus the SC

81/80 = (99/98)*(441/440)

divided into 3 epimoric subparts:

99/98 = (297/296)*(296/295)*(295/294)

tempering the 5ths G-D-A-E flattend by the corresponding amounts:

G 296/297 D 295/296 A 294/295 E

yielding on the violin empty stings the absolute pitches:

g3: 198 cps = 99*2 := 220*(9/10) a minor-tone below a3=440Hz/2
d4: 296
a4: 442.5 := 885/2
e5: 631.5 := 1323/2

as subset of the tuning procedere in 5ths on my piano:

C: 523Hz (>522 264 132 66 33) 'tenoor-C'
G: 99 (((> 98 49=7*7 overtaken from Werckmeister's "septenarius")))
D: (297>) 296 (>295 (>294 147=49*3)
A: 885 (>882 441=49*9)
E: 1323 = 49*27
B: (49*81 = 3969>) 3968 ... 496...31 through all 7 'B's on the keys
F# 93
C# 279 a semitone above 'middle-C'
G# 837
Eb 2511
Bb (7533>) 7532 3716 1883
F: (5649>) 5648 2824 1412 706 353
C: (1059>) 1058 529 = 23^2 cycle returend back to the above 'tenor-C'

!sparschuhPiano.scl
!
from Andreas Sparschuh's violin strings G 296/297 D 295/296 A 294/295
12
!
558/523 ! C#
598/523 ! D
628/523 ! Eb
1323/1058 ! E = 661.5/523
706/523 ! F
724/523 ! F#
792/523 ! G
837/523 ! G#
885/523 ! A absolute 442.5Hz
1883/1058 ! Bb = 941.5/523
992/523 ! B
2/1
!

have a lot of fun with that
A.S
• ... Hi George, ... in deed, even that *.scl-file contained some unfixed bug. ... Many thanks again for that repair. ... when considering more evaluated digits,
Message 63 of 63 , May 8, 2008
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--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:

Hi George,
> > 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,
>
> >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:

> F~ -1.636 ~C
(1 200 * ln(1 058 / 1 059)) / ln(2) = ~-1.63555425...

> ~C~ -3.276 ~G
(1 200 * ln(528 / 529)) / ln(2) = ~-3.27575131...

>~G~ -5.839 ~D
(1 200 * ln(296 / 297)) / ln(2) = ~-5.83890621...
arises that deviation here due to your's rounding procedere?

~D~ -5.784 ~A
1 200 * ln(295 / 296)) / ln(2) = ~-5.85866566...
arises that deviation here due to your's rounding procedere?

~A~ -5.953 ~E
(1 200 * ln(294 / 295)) / ln(2) = ~-5.8785593...

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?

~E~ -0.436 ~B
(1 200 * ln(3 968 / 3 969)) / ln(2) = ~-0.436243936...

> B F# C# G# all just pure 5ths

Eb~ -0.2298 ~Bb
(1 200 * ln(7 532 / 7 533)) / ln(2) = ~-0.229835254...

Bb~ -0.306 ~F
(1 200 * ln(5 648 / 5 649)) / ln(2) = ~-0.306494477...

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)

?

Yours Sincerely
Andreas
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