Transcribing Piano Rolls, the Pythonic Way (opens in new tab)

    def fourier_transform(signal, period, tt):
        """ See http://en.wikipedia.org/wiki/Fourier_transform
        How come Numpy and Scipy don't implement this ??? """
        f = lambda func : (signal*func(2*pi*tt/period)).sum()
        return f(cos)+ 1j*f(sin)

What you want is the power spectral density in the discrete case, called the power spectrum. It can be calculated by multiplying the discrete Fourier transform (FFT) with its conjugate, and shifting. NumPy can do it. Here is an example: http://stackoverflow.com/questions/15382076/plotting-power-s...

If was a fun place to see in the 70's after watching my father rebuild our player piano.

Relevant: Zenph makes "re-performances" of old piano recordings. They take a recording, do music transcription magic to get the exact timings and velocities of each note event, and then feed that into a player piano. So it's as if you are listening to the ghost of Rachmaninov sitting at the piano, as shown here: https://www.youtube.com/watch?v=eevzbV6Hkkk&t=28 (music starts at 0:28)

(I just visited http://zenph.com for the first time in about a year, and it appears that they've pivoted into a music education company.)