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absoute-pitch realization of George's Rational Well Temperament @ a'=445Hz?

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  • Andreas Sparschuh
    ... Hi George, Tom & all others, ... starting in chromatically order from: http://en.wikipedia.org/wiki/Middle_C ... I.m.h.o. any tuning for a conrete
    Message 1 of 63 , Apr 24 7:45 AM
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      --- In tuning@yahoogroups.com, "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)
      > > 12
      > > !
      > > 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
      > > 2/1
      > > >
      Actually i realized that on my on piano in the absoute-pitches:
      > >
      starting in chromatically order from:
      http://en.wikipedia.org/wiki/Middle_C
      Tenor-C:
      > C: 531 := 59*9
      > C# 560 280 140 70 35 = 7*5
      > D: 594.675 := 264.3*9/4
      > Eb 630 315 = 7*5*9
      > E: 666 333 = 37*9
      > F: 708 354 177 = 59*3
      > F# 747.625 = 1329*9/16
      > G: 794.7 = 88.3*9
      > G# 840 = 240*3
      > A: 890 445Hz ? probably yours intend A4=445 cps ?
      > Bb 945 = 105*9
      > B: 997.875 = 887*9/8
      >
      > I didn't intend any particular absolute pitches when giving these
      > ratios.
      I.m.h.o. any tuning for a conrete instrument
      appears to me as yet incomplete,
      if the start pitch is lacking,
      when intervals are given barely in relative ratios alone,
      without definition of any concrete reference-tone intension,
      that can be deduced from an absoute fixed standard normal-pitch:
      alike:
      http://en.wikipedia.org/wiki/A440
      (in german:)
      http://de.wikipedia.org/wiki/Kammerton

      > I expected that you would use whatever pitch reference you
      > like.
      Hence for your's tuning i do prefer the correspoding above:
      http://upload.wikimedia.org/wikipedia/commons/d/d7/445.ogg

      That beats againt the normal with
      5Hz := 445Hz - 440Hz sharper
      or with
      300 Metronome beats = 5Hz *60 beats/min
      synchrone to an
      http://en.wikipedia.org/wiki/Metronome

      445HZ was broadly used by my friend:
      the late
      http://en.wikipedia.org/wiki/Herbert_von_Karajan
      critziesed by
      http://en.wikipedia.org/wiki/Andr%C3%A1s_Schiff
      in
      http://www.schillerinstitute.org/fid_02-06/021-2schiff.html
      "For example, his fight against the absurdly high "Karajan-tuning,"
      which he broadened with a new battle on the sidelines of the last
      Salzburg Festival. Because of his invitation, members of the Berlin
      and Vienna Philaharmonics (both of which orchestras play at extremely
      high pitch, even above A=445 Hz) ,as well as opera singers, and even
      conductors,...."

      On which conrete pitch for a'=44?Hz
      do you would realize yours above temperament
      on yours own personal piano?

      Sincerely
      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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