Factors Contributing to the Multiple Decrement of Piano Tone Envelope
T. Chase Hundley, Daniel W. Martin, Hugo Benioff · The Journal of the Acoustical Society of America · 1956
The decrease in decrement of piano tone envelope with tone duration has been reported previously. Possible causes of the rate change have now been investigated, including the following: different rates for different groups of vibration modes; nonlinearity of transformation of mechanical energy to acoustical energy; storage of mechanical energy for subsequent acoustical radiation; transfer of energy between string modes perpendicular and parallel to the bridge; interference between strings which are almost exactly in tune; and change in rate of energy transfer from the multiple-string source, before and after transition from an initial in-phase condition to a later out-of-phase condition. The suggestion of the last factor and its theoretical basis was the specific contribution of Dr. Benioff. The last two factors, which are closely related, were found to control the rate change in most cases.