Observations on Inharmonic Signals
Egbert de Boer · The Journal of the Acoustical Society of America · 1957
Schouten's “residue” can be readily observed when a group of closely spaced Fourier components is presented. Such a sound often exhibits a basic pitch, especially when the complex stimulus is harmonic. The pitch level is then judged to be the fundamental frequency (which in this case equals the difference frequency). In the present study signals consisting of a restricted number of equally spaced components were investigated. The sound observed is steady in both pitch and timbre even when the stimulus is inharmonic. The pitch level however corresponds not necessarily to the difference frequency as can be demonstrated when all components are displaced by the same amount in frequency. For small departures from harmonicity, the pitch appears to follow the direction of this frequency shift of the complex. More specifically, the relative pitch change is approximately equal to the relative frequency change of the central component, the timbre not being affected much. The timbre depends strongly upon the relative phases of the components, so that it seems closely tied to the shape of the envelope of the signal's wave form. [This work was supported in part by the U. S. Army (Signal Corps), U. S. Air Force (Office of Scientific Research, Air Research, and Development Command), and the U. S. Navy (Office of Naval Research).]