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Ah, the power of a least-squares fit. :)

There doesn't seem be any fitting involved. I think he just took the speech spectrogram and used it as a piano score. Thus the acoustic output of the piano is not meant to approximate the acoustics of talking. We hear speech nonetheless because there's enough of a speech-like signal for our auditory functions to hold on to.

The human auditory system does a remarkable job of filling in missing data. Sometimes it's amazing.

For example we can:

Hear a song we recognize, playing softly in the background, in a crowded noisy room

Talk and understand conversations over the telephone even with it's amazingly small bandwidth

Understand speech with something like 70% signal loss

Hear the cry of a baby in the middle of a battlefield over the sound of guns

and on and on and on

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