Pitch, Timbre and uncertainty principle: Sound synthesis helps to delimit domain of appicability for some laws of physics, Prof. Piotr Zieliski (Inst. of Nuclear Physics, Polish Academy of Sciences, Cracow)

26.05.2015 von 17:00 bis 18:00

Gastgeber: Dr. B. Murphy

The ear is a detector of frequency. A periodic acoustic signal of frequency f produces, namely, a sensation of pitch H (the tone height), that in the MIDI (Musical Instrument Digital Interface) system is given by the logarithmic formula H = 69 + 12log(f/440Hz). Sounds of the same fundamental frequencies but different power spectra show different timbres (tone colours). The timbre is independent of the harmonics’ phases to an astonishing extent, as was found by H. von Helmholtz. The famous theorem fails, however, once the spectrum varies too fast. The effect will be illustrated with ordinary, but appropriately treated musical instruments. Its origin resides, in fact, in the time-frequency uncertainty relation (Gabor uncertainty relations equivalent to Heisenberg’s time-energy uncertainty relation). It will be demonstrated how short should the signal be to loose its pitch. A side effect of this demonstration is that very short signals produce a sensation of a pseudo pitch extremely sensitive to the signal’s duration time. This property, obeying in fact the Weber-Fechner law, allows one to distinguish duration times of pulses beyond the reach of any direct method.

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