Spheres octaves and pitch

  1. Dose anyone know the relationship of cube root numbers and the fraction of 1/8

    "Assuming a body of a size represented by X has a pitch of 1024 per second, then a pitch of 2048 (double 1024) per second will be produced by a body having a volume of some mean between 1/8 of X and the cube root of X"

    I understand why a pitch double the original will be produced by a sphere 1/8 the volume because if you double the diameter of a sphere you increase its volume by eightfold.

    I don't however understand the relationship between 1/8 and cube root numbers, any ideas?
     
    Last edited: Feb 10, 2008
  2. jcsd
  3. The pitch depends on the radius of the sphere. Doubling the radius multiplies the volume by
    2^3=8.
     
  4. Is it as simple as that...haha lol, I knew 2^3 was 8 but I had assumed I was looking for something more complex, funny when you look for the complex you miss the simple.

    Would this only work for spheres then?
     
  5. clem

    clem 1,276
    Science Advisor

    It would also work for the frequencies of a 3D object. For a drumhead, the pitch would go like 2^2.
     
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