Perceptual significance of inharmonicity and spectral envelope in the piano bass range

Professionals consider the differences in the timbre of bass tones between large grand pianos and  small  uprights  as  significant.  By  tradition  this  difference  has  been  attributed  mainly  to  lower inharmonicity in grand pianos, due to longer bass strings. In this study, the importance of the spectral envelope, representing the dynamic balance between high-frequency and low-frequency  energy  in  the  spectrum,  is  contrasted  against  the  importance  of  the  level  of  inharmonicity.  Results  from  two  listening  tests  indicate  that  the  inharmonicity  is  less  important than the spectrum bandwidth in determining the timbre of piano bass tones.