theorem Th64:
  @(spiral_of_fifths(MS,frequency,frequency).1) /
  @(spiral_of_fifths(MS,frequency,frequency).4)
    = ((32 qua Real) / 27)
  proof
    spiral_of_fifths(MS,frequency,frequency).4
      = (81 qua Real) / 64 * @frequency &
      spiral_of_fifths(MS,frequency,frequency).1
      = (3 qua Real) / 2 * @frequency
      by Th58,Th61;
    then @(spiral_of_fifths(MS,frequency,frequency).1) /
      @(spiral_of_fifths(MS,frequency,frequency).4)
      = ((3 qua Real) / 2)/((81 qua Real) / 64) by XCMPLX_1:91
     .= ((32 qua Real) / 27);
    hence thesis;
  end;
