theorem Th66:
  @Octave(MS,frequency) /
    @(spiral_of_fifths(MS,frequency,frequency).3)
    = ((32 qua Real) / 27)
  proof
    now
      thus spiral_of_fifths(MS,frequency,frequency).3
        = (27 qua Real) / 16 * @frequency by Th60;
      ex fr be positive Real st frequency = fr &
        Octave(MS,frequency) = 2 * fr by Def15;
      hence @Octave(MS,frequency) = 2 * @frequency;
    end;
    then @Octave(MS,frequency) /
      @(spiral_of_fifths(MS,frequency,frequency).3)
        = ((4 qua Real) / 2)/((27 qua Real) / 16) by XCMPLX_1:91
       .= ((32 qua Real) / 27);
    hence thesis;
end;
