if __name__ == '__main__':
  print('1.000')
  for i in range(1,13):
    print('2^({0:d}/12) = {1:.3f}'.format(i,round(2**(i/12),3)))

def ratio(target):

  loop = 100
  frac, denom = 3,2
  error = 0.0095

  while loop:
    diff = abs(target*denom/frac -1)
    if diff < error:
      just = frac/denom;
      print('{0:d}/{1:d}={2:.3f}'.format(frac,denom,just))
      return
    else:
      frac +=1
      if (frac/denom)>=2.0:
        denom +=1
        frac = denom + 1
    loop -= 1

  print('{0:d}/{1:d}'.format(frac,denom))

if __name__ == '__main__':
  print('1.000')
  for i in range(1,12):
    hz = round(2**(i/12),3)
    print('{0:.3f} '.format(hz),end="")
    ratio(hz)

import matplotlib.pyplot as plt
import math

if __name__ == '__main__':
  lcm       = 16
  sampling  = 64
  amplitude = [0]*sampling*lcm
  cycle     = [0]*sampling*lcm
  for i in range(0,sampling*lcm):
    amplitude4 = math.sin(2*math.pi*i/sampling)
    amplitude5 = math.sin(2*math.pi*(5/4)*i/sampling)
    amplitude6 = math.sin(2*math.pi*(3/2)*i/sampling)
    amplitude[i] = amplitude4 + amplitude5 + amplitude6
    cycle[i] = i/sampling

  plt.plot(cycle, amplitude)
  plt.show()
  plt.close()