Two to the one twelth power

[David Nereson]

  -----Original Message-----
  From: pianotech-bounces at ptg.org
[mailto:pianotech-bounces at ptg.org]On Behalf Of KeyKat88 at aol.com
  Sent: Saturday, September 30, 2006 2:43 AM
  To: pianotech at ptg.org
  Subject: Two to the one twelth power


  Greetings,

         Punching 2 to the 1/12 power into my calculator, it
gives me 1.05946285.  How far does this number go on? Is it a
number like Pi that goes on and on? What sort of software will
let me see how far it can go?  If I am doing harmony
calculations, how far is it practical to go? What is the norm?

  Julia
  Reading, PA

  My calculator gives 1.059463094.  I've always used 1.0594631,
but when reversing the operation with the first number, the
result is 1.999999992, and with the second, 2.000000128, so the
mantissa is longer, but how much, I don't know.  I doubt it goes
on forever -- my intuitive feeling, not being a mathematician,
is that the 12th root of 2 is of a different nature from pi,
i.e. I think it's finite whereas pi may be infinite.  (?)
      --David Nereson, RPT
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