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getting rid of the broade dog-5th defect by bug fixing, wasRe:Rational Well Temp

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  • Andreas Sparschuh
    ... Dear George, as cycle of 5ths: C 149 g: (447 ) 446 G=223 d: (669 ) 668 334 D=167 a: (501 ) 500 A=250 125 e: (375 ) 374 E=187 b: (561 ) 560 B=280 140 70 35
    Message 1 of 63 , Apr 25 12:16 PM
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      --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:

      > I found a WT with simpler brats (with one 5th tempered 4.62c narrow):
      >
      > ! SecorSWT149
      > George Secor's 149-based synchronous WT
      > 12
      > !
      > 315/298
      > 167/149 ! D
      > 177/149
      > 187/149 ! E
      > 199/149 ! F
      > 210/149
      > 223/149 ! G
      > 236/149
      > 250/149 ! A
      > 265/149 ! Bb or proposal 531/298 in order to avoid here an dog-5th?
      > 280/149 ! B
      > 2/1
      >
      > I originally found this one with 167 as a common denominator, with
      > the best major triad on Bb, so I transposed the ratios to put it on >C.
      Dear George,

      as cycle of 5ths:
      C 149
      g: (447>) 446 G=223
      d: (669>) 668 334 D=167
      a: (501>) 500 A=250 125
      e: (375>) 374 E=187
      b: (561>) 560 B=280 140 70 35
      f# 210 105
      c# 315
      g# (945>) 944 472 G#236 118 59
      Eb 177
      ???????????????????????????????????????????????????????????????????
      bb (531>) 530 Bb=265 ??????????????????????????????????????????????
      F: (795<) 796 398 F=199 did you really intend here an broade dog-5th?
      ???????????????????????????????????????????????????????????????????
      c: (597>) 596 298 149

      In order to get rid of the buggy wide dog-5th inbetween Bb and F,
      there i do reccomend to arise Bb a little bit, so that Brad
      Lehman's overtempering defect vanishes, simply in replacing
      the formerly old Bb 265 by
      the new more apt higher value: 265.5 := 531/2
      ....
      Eb 177
      bb 531 Bb=265.5
      F: (1593>) 1592 796 398 F=199
      c: (597>) 596 298 C=149

      Do you agree with that improving suggestion?
      http://launch.groups.yahoo.com/group/tuning/message/71930

      Yours 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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