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discerning narrow-well-5ths against an corrresponding wide-French one 5th

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  • Andreas Sparschuh
    ... Dear Paul, nothing of all that presupmtions, except of tuning for example on my own acoustic-piano -as precisely as i can do that- in the following circle
    Message 1 of 31 , Jun 25, 2008
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      --- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote/asked:

      > Andreas, my dear fellow, I am most interested in knowing what truly
      > exceptional super-human auditory capability you posses which allows
      > you, upon hearing them, to tell a 704 cent fifth from a 700 cent
      > fifth. They both beat extremely slowly by exactly the same amount.
      > Have you got some sort of advanced technology in your ears, perhaps a
      > harmonic Babelfish or some such?
      >
      Dear Paul,

      nothing of all that presupmtions,
      except of tuning for example on my own acoustic-piano
      -as precisely as i can do that-
      in the following circle of tempered 5ths:

      A2 = 221 A442Hz, that's 120Metronome-Beats/min sharper above 440Hz
      E4 = E331 e662 (<663 := 3*A2)
      B0 = 31 62 124 248 B496 b992 (<993:=3*E4)
      rem:
      B0=31Hz is the lowest pitch on 5string doublebass
      or the second whithe key on a modern piano, without inharmonicity
      F#2 = 93 := 3*B0
      C#4 = C#279 := 3*F#2
      G#5 = 837 := 3*C#4
      Eb3 = 158 Eb314 eb628 1256 2512 (>2151 := 3*G#5) ~+0.7Cents wide 5th
      Bb4 = B471 := 3*Eb3
      F4 = F353 f706 1412 (<1413 := 3*Bb4)
      C5 = (33 66 132 264 528 <) 529 1058 (<1059 := 3*F4)
      G2 = 99 := 3*33
      D2 = 37 74 148 D296 (<297 := 3*G2)
      A3 = 221 (<222 111 := 3*D2)

      that's in acending order over the usual 2 tuning octaves in
      http://www.xs4all.nl/~huygensf/scala/scl_format.html

      !Sparschuh442wideFrench5th.scl
      !
      ! relative deviations in the circle of 5ths, beginning from:
      ! 442Hz=A 662:663 E 992:993 B F# C# G#
      inbetween the "french"5th G#-Eb 2512:2511 =~0.7Cents widend sharper
      ! Eb Bb 1412:1413 F 1058:1059 C 528:529 G 296:297 D 221:222 A=442Hz
      ! and with all other 5ths JI-pure or narrow flattend.
      12
      !
      ! that yields the concrete absolute pitches on the keys, starting from
      ! 264.5Hz C4 http://en.wikipedia.org/wiki/Middle_C
      ! 279 C#
      ! 314 Eb
      ! 331 E
      ! 353 F
      ! 372 F#
      ! 396 G
      ! 416.5 G#
      ! 442 A that's exactly 2Hz above: http://en.wikipedia.org/wiki/A440
      ! 471 Bb
      ! 496 B
      ! 523Hz c5 http://en.wikipedia.org/wiki/Tenor_C
      558/523 ! c#
      592/523 ! d
      628/523 ! eb
      662/523 ! e (5:4)*(2652:2645) ~4.6 Cents sharper above 5/4 JI 3rd
      706/523 ! f (4:3)*(1059:1058) ~1.6 Cents sharper above 4/3 JI 4th
      744/523 ! f#
      792/523 ! g (3:2)*(528:529) ~3.3Cents flattend up than 3/2 JI 5th
      884/523 ! a
      942/523 ! bb
      992/523 ! b
      2/1 ! 1058Hz c6 http://en.wikipedia.org/wiki/Soprano_C
      !
      !

      After a while in retuning and playing in that again and again:
      Sooner or later,
      most professional tuners become aware about the
      different quality of the wide-"french"5th against
      all others narrow-well ones.

      Question:
      How does that sound on yours piano?

      Next step:
      Once if you have mastered the above one and:
      if you do also prefer A4=416Hz
      -the modern pseudo-historically "Cammer-thone"-
      then you should try out:
      http://www.wegscheider-orgel.de/html/artikel.php?filename=artikel.php&tabname=Artikel&sz=22&Unterpunkt=H.C.%A0Snerha%A0und%A0die%A0Bachstimmung
      with an even even about 3 times
      smaller wide 5th inbetween G#-Eb
      of the merely tiny deviation:

      702,2276...Cent -701,9550...Cent = ~+0,2726..Cents wider than 3/2 JI.

      that's even
      about less than 7-times smaller
      against Brad's alleged PC^(1/12) of ~+2Cents

      Jsut try it out!
      A.S.
    • Afmmjr@aol.com
      Kraig mused: On the performance of 17th-18th century music couldn t we say what Feldman said about a rehearsal of his piece..... It s too damn fast and it
      Message 31 of 31 , Jun 26, 2008
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        Kraig mused:  On the performance of 17th-18th century music couldn't we say what
        Feldman said about a rehearsal of his piece.....
        'It 's too damn fast and it too damn loud!'

        Johnny amused:  there is tuning sense here.  When he key is different in tuning, slower tempo makes sense.  When each key is identical, other than obvious pitch height, one might as well play faster because there is nothing lese to contrast.
         
        Different intervals benefit from an increased time for appreciation.
         
        Margo, loved your post.  Brava!!
         
        Johnny




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