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

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  • Andreas Sparschuh
    ... 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 12:54 PM
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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
    • Andreas Sparschuh
      ... 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,
        > > 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:


        > 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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