Abstract

Consider a stimulus consisting of three sine tones with the same frequency spacing. For some listeners such a stimulus elicits a residual tone. Obviously, their hearing system interprets the three sine tones as three adjacent partials of a complex tone with a fundamental frequency equal to the frequency spacing. On the other hand, some subjects easily hear out some or even all single sine tones.

One can therefore distinguish between two hearing modes: the case of the residue pitch is referred to as fundamental hearing, whereas the ability to resolve single partials is called spectral hearing or overtone hearing.
Subjects may differ considerably in their capability for fundamental or spectral hearing. Depending on factors as the frequency region of the stimuli or the frequency of the residue pitch (missing fundamental) or depending on psychological factors as attention or individual hearing dispositions, subjects may even change between both modes of hearing.

The present study demonstrates that possessors of absolute pitch show significant differences in spectral versus fundamental hearing compared to possessors of relative pitch. In some frequency regions, possessors and non-possessors of absolute pitch prefer either fundamental hearing or spectral hearing quite individually and often may change between both modes of hearing. However, statistically, possessors of absolute pitch show a significantly higher preference for perceiving a residue tone than possessors of relative pitch do.

A mathematical model is presented here to explain the sensation of consonance and dissonance on the basis of neuronal coding and the properties of a neuronal periodicity detection mechanism. This mathematical model makes use of physiological data from a neuronal model of periodicity analysis in the midbrain, whose operation can be described mathematically by autocorrelation functions with regard to time windows. Musical intervals produce regular firing patterns in the auditory nerve that depend on the vibration ratio of the two tones. The mathematical model makes it possible to define a measure for the degree of these regularities for each vibration ratio. It turns out that this measure value is in line with the degree of tonal fusion as described by Stumpf Tonpsychologie Psychology of Tones Knuf, Hilversum, reprinted 1965. This finding makes it probable that tonal fusion is a consequence of certain properties of the neuronal periodicity detection mechanism. Together with strong roughness resulting from interval tones with fundamentals close together or close to the octave, this neuronal mechanism may be regarded as the basis of consonance and dissonance.

© 2008 Acoustical Society of America. DOI: 10.1121/1.2968688
PACS numbers: 43.75.Cd, 43.60.Ek, 43.64.Bt, 43.66.Ba DD Pages: 2320–2329