Volume and Energy Estimation

Erich Zimmerman, Dean Berg, Prof. John Sahr

Volume is a parameter which is usually passed in a MIDI message to describe a musical note. This parameter is determined by measuring the energy of a string at one point. The total energy of a string is a function of both time and location on the string Kinetic energy = 1/2 mass * (particle velocity)^2. The second term is a function of time and location as mentioned. The guitar uses a magnetic pick-up which indicates string velocity at a point. Since the displacement of the string is only known at one point and a number of initial conditions need to be known to determine the velocity of the string at all points along the entire string, the magnetic signal squared is used to represent energy (volume) of the signal. The following graph represents the positive part of the test signal, which is an actual guitar signal, and two curves labelled volume1 and volume2.
Volume1 is the guitar signal squared and averaged over a time period to smooth the results. When the signal is not available (noise only), a short window of six samples (shortest pitch possible) is used to average the volume measurement. When a valid signal occurs, the volume measurement is averaged over one period of time or the amount of pitch measured. Volume2 is the absolute value of the guitar signal averaged over the time periods mentioned. The STATE description page describes how the time periods are obtained to make the volume calculations. Conclusions: Volume1 follows the shape of the guitar signal better than volume2. The guitar signal is a direct indication of the relative measure of the energy of the string.