Octave-reduce

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Octave-reducing a fraction r means to make it fit into the range from 1 (the unison) to (excluding) 2 (the octave):

1 <= r < 2

If r does not satisfy this inequality, it has to be

  • multiplied by 2 while less than 1 or
  • divided by 2 while greater than or equal to 2

Examples

  • 3/4 is less than 1, so multiply by 2 to get 3/2
  • 7/2 is greater than 2, so divide by 2 to get 7/4
  • 4/2 is greater than 2, so divide by 2 to get 2, which is equal to 2, so divide by 2 to get 1

See also