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Re: Inbetween K. Wegscheider 416Hz (June 2003) and T. Dent 419Hz (September 200

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  • Paul Poletti
    ... I don t know abot others, here, Andreas, but I am not even gonna try to unravel what you might trying to say until you stop doing several rediculous
    Message 1 of 5 , Jun 26, 2008
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      --- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
      wrote:
      >
      > --- In tuning@yahoogroups.com, Brad Lehman <bpl@> wrote:
      >
      I don't know abot others, here, Andreas, but I am not even gonna try
      to unravel what you might trying to say until you stop doing several
      rediculous things:

      (1) Peppering you posts with endless wiki links for really stupid
      things, like middle C or piano keyboard frequencies.

      (2) Start using just ONE clear and easy to understand method for
      indicating temperaments. All that scala mismash and wierd stuff like
      multiplying frequencies by 3 instead of 1,5 just makes it all not
      worth the time.

      Try being simple and clear for just once. Maybe you've really got
      something to say, who knows? At the moment it just looks like the
      ravings of a madman.

      Ciao,

      P
    • Andreas Sparschuh
      ... Hi Paul, ... Simply consider all given values there as frequencies in Hz of absolute pitches, that are subjects of 3 possible sequential operations:
      Message 2 of 5 , Jun 27, 2008
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        --- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:

        Hi Paul,
        > Start using just ONE clear and easy to understand method for
        > indicating temperaments.
        Simply consider all given values there
        as frequencies in Hz of absolute pitches,
        that are subjects of 3 possible sequential operations:

        Algorithm for synchroneous well-temperaments:
        1. Step 19-times an octaves down, by halfing the pitch-frequency
        2. Go 12 times to partial 3:1, by multipying with facor 3.
        occasional
        3. Decrement frequncy by -1Hz down, when intend tempering flattend.

        but only if you insist in "wide-5ths" then allow also too:
        (4. Increment by +1Hz upwards, for an sharper "French"-5th.)

        Comeback condition:
        Choose the chain of flow in the operation sequence
        so that the circle of a dozen 5ths returns back to the initial
        start after 12times 3:1 and 19times 1:2 while fitting the
        decrements so, that they yield an distribution of the PC=3^12:2^19
        into
        http://en.wikipedia.org/wiki/Superparticular_ratio
        s.



        > All that scala mismash and wierd stuff like
        > multiplying frequencies by 3 instead of 1,5 just makes it all not
        > worth the time.

        That ratio of 3/2 = 1.5 arises operationally from taking the
        quotient of the 3rd partial (3:1) over an octve (2:1),
        when realting that both overtones #2 and #3 to theirs fundamental
        (1:1) base.

        http://en.wikipedia.org/wiki/Harmonic_series_(music)
        "...allowed wavelengths are 1/2, 1/3, 1/4, 1/5, 1/6, etc. times of the
        fundamental."

        but on strings there never appear 2/3 = 1:(3/2) due to the lack of
        http://en.wikipedia.org/wiki/Subharmonics
        in pianos:
        http://www.sfu.ca/sonic-studio/handbook/Subharmonic.html
        "Subharmonics do not normally occur in natural sounds, although the
        subharmonic f/2 may be generated by the cone of a LOUDSPEAKER."

        That makes an 5th (3:2 = 1.5) less fundamental than the ratio
        inbetween the overtones 3:1 and 2:1 within the harmonic series.

        Hence an 5th is composed by an
        division of an 12th (3:1) as nominator
        over an octave (2:1) as denominator by the calculation

        (3:2) := (3:1):(2:1)

        In other words:
        any 5th (3:2) consists terms of
        http://en.wikipedia.org/wiki/Harmonic
        as composed of the difference of an '12th'-'8th'.
        "3 just perfect fifth P8 + P5 1902.0 702.0"
        when both do refer to the same (1:1) base or
        http://en.wikipedia.org/wiki/Fundamental_frequency

        hope that helps,
        why i do prefer the multiplication by the "harmoic" factor 3
        in order to stay wihin the partial-series.


        Even Brad understood that in his:
        http://www-personal.umich.edu/~bpl/larips/bachtemps.html
        "...in the line of fifths A-E-B-F#-C#-G#-D#-Bb-F-C-G-D-A to reduce the
        next note by 1 Hz, i.e. introducing a beat rate of 1 per second
        against the preceding fifth. The fifths F#-C#-G#-D# and D-A are kept
        pure. The other eight are adjusted by different geometric amounts,
        based on the superparticular ratios described in his algorithm.
        (Arithmetically, it amounts to subtracting 1 Hz from the top of most
        of the columns, in his chart, wherever there are values in
        parentheses.)"...

        Brad contiues or the experts:
        "Sparschuh's mathematical algorithm resembles the classic unproven
        "Collatz Conjecture" from 1937, except that Sparschuh's iterated
        function uses (3n-1) rather than (3n+1). [And see Eric Roosendaal's
        3x+1 web site, along with this page by Frits Beukers demonstrating and
        comparing the numerical sequences....]"


        Yours Sincerely
        A.S.

        Yours Sincerely
        A.S.
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