Subjective Musical Pitch
W. Dixon Ward · The Journal of the Acoustical Society of America · 1954
The present Acoustical Society of America definition of “pitch” is “that attribute of auditory sensation in terms of which sounds may be ordered on a scale extending from low to high, such as a musical scale.” But since extant musical scales are based upon physical instead of subjective criteria, we are faced with the paradox of a subjective attribute with physical dimensions. Hence, experiments were performed to determine subjective musical scales for nine trained musicians. The assumption was made that, for a given observer, the subjective octave is an invariant relation between pitches, just as the physical octave is an invariant relation between frequencies. The observer adjusted one pure tone so that it appeared to be one octave above another (alternate presentation). Since the “error” (difference between subjective and physical octaves) for a given ear varied systematically with frequency, individual subjective scales of musical pitch could be derived. In agreement with the facts of binaural diplacusis, individual scales are fairly irregular, and scales for the two ears of a single observer are in some cases as different as those from different observers. The average (group) scale shows a gradual “stretching” relative to physical musical scales; i.e., the mean subjective octave corresponds to a frequency ratio of about 2.04:1.