Loading ...
Sorry, an error occurred while loading the content.

RE: [Nature Recordists] RE: Marty's Magic Number

Expand Messages
  • Barb Beck
    Think I can figure out your question (but realize that my students drug me to the bar after class ended tonight and I am not really responsible for being
    Message 1 of 7 , Nov 1, 2001
    View Source
    • 0 Attachment
      Think I can figure out your question (but realize that my students drug me
      to the bar after class ended tonight and I am not really responsible for
      being logical and old grannies are not supposed to be bothering their
      fragile brains with logs and exponents and such but......)

      Marty's Magic number we will call A (could have been X but I liked A
      tonight)

      You know that to get from Note 1 to a note a half tone higher you multiply
      the frequency by A. We will use F1 to stand for the initial frequency.

      to raise it an octave you must raise it 12 half tones or

      F1*A*A*A*A*A*A*A*A*A*A*A In old FORTRAN notation A**12 indicating A to the
      power 12... sorry I work in plain text and do not have exponents.

      We know that the frequency of a note an octave higher is twice that of the
      original note SO.... 2*F1 is equal to the note one octave higher

      OR....

      F1*A**12 = 2F1 (or F1 multiplied by A 12 times is equal to twice the
      original frequency)


      Dividing both sides of the equation by F1 you get rid of them and are left
      with

      A**12 = 2

      To get Martys magic number, A, we have to handle that messy exponent and
      that calls for the magic of logs.

      Take the logarithm of each side..

      ln(A**12) = ln(2)

      12*lnA = ln(2)

      ln(A) = ln(2)/12

      taking the exponential of each side of the equation

      exp(lnA) = exp(ln(2)/12)

      But the left side of the equation is merely A

      So you get A = exp(ln(2)/12) or
      A = 1.059463094 or at least that is what I got when I typed
      =exp(ln(2)/12) into an excel worksheet (couldn't find my slide rule)

      Is that close enough to your number?

      Note it does not matter what base you are working, base2, natural logs or
      base10 etc just as long as your base is consistent throughout

      Happy Halloween - I am headed for another chocolate bar then to get some
      sleep - a three hour class of bird and butterfly identification has done me
      in. Hope I managed to explain this clearly

      Barb




      -----Original Message-----
      From: Marty Michener [mailto:marty@...]
      Sent: October 31, 2001 1:18 PM
      To: naturerecordists@yahoogroups.com
      Subject: Re: [Nature Recordists] RE: Log base 2 and Halloween Sounds



      >HI Barb: I love discussions of sound and music and numbers, esp.
      >logs. All the sensory systems seem to do log input tricks.

      Here is a question that is seldom asked or even wondered,
      that I asked myself in high school:

      What is the numerical music interval, the number by
      which you multiply any music note by to get the
      next (halftone) above it. Hint twelve of this operation
      makes exactly an octave.

      I use this number off the top of my head to at least
      get music teachers attention and wonder some about math.

      Ans: ca. 1.0595 - But how do you get it? - it is almost as
      handy to know as pi, since you can always figure out the pitch
      of any note starting with A=440 and then multiplying a lot. ;^)


      my very best,

      Marty Michener
      MIST Software Associates
      75 Hannah Drive, Hollis, NH 03049

      coming soon : EnjoyBirds bird identification software.




      To unsubscribe from this group, send an email to:
      naturerecordists-unsubscribe@egroups.com



      Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
    • Marty Michener
      Barb & recordists: Barb is exactly correct. In my own words, any number A that you use as the geometric series constant, must, when raised to the twelfth
      Message 2 of 7 , Nov 1, 2001
      View Source
      • 0 Attachment
        Barb & recordists:

        Barb is exactly correct. In my own words, any number
        "A" that you use as the geometric series constant, must,
        when raised to the twelfth power, be exactly 2.00.

        Or: A = 12th root of 2.00, and of course I rounded to 1.0595.

        I also have a son who is both mathemagical and musical,
        now taking Honors Music Compositon, 11th grade. His
        favorite subject. He is way over my head in both subjects.
        If A=440, then B is 440 x A^2, C is 440 x A^3, etc.

        best to all,

        Marty Michener
        MIST Software Associates
        75 Hannah Drive, Hollis, NH 03049

        coming soon : EnjoyBirds bird identification software.
      • Stuart Fairbairn
        Barb how nice to have such a clear and logical explanation. A rare thing these days. I bet your students all get high marks! Best wishes from down under.
        Message 3 of 7 , Nov 1, 2001
        View Source
        • 0 Attachment
          Barb how nice to have such a clear and logical explanation. A rare thing
          these days. I bet your students all get high marks!

          Best wishes from down under.

          Stuart Fairbairn
          fbairn@...
          Sydney Australia
        Your message has been successfully submitted and would be delivered to recipients shortly.