Shifting all spectral components uniformly changes perceived virtual pitch in a sawtooth pattern

Evidence

If the five frequency components of the filtered harmonic complex tone are shifted by a constant amount, say 100 Hz, towards lower frequencies, then the lowest component will have a frequency of 1400 Hz, the next component will be located at 1700 Hz, the following at 2000 Hz and so forth. In this case, the frequencies of the components are no longer integer multiples of the fundamental frequency of 300 Hz, and the whole complex is called an incomplete inharmonic complex tone, with a pitch corresponding to 270 Hz. Hence, a shift of all spectral components by 100 Hz towards lower frequencies yields a decrease of 20 Hz in the matching frequency. As displayed in Fig. 5.11, a shift of all spectral components by 100 Hz towards higher frequencies leads to a matching frequency of 310 Hz. For an upward shift of 150 Hz, the lowest component has a frequency of 1650 Hz. As indicated by the dashed lines in Fig. 5.11, the pitch of the inharmonic complex tone in this case becomes faint and ambiguous, and pitch matches are possible both at 260 and 320 Hz. If the spectral lines of the filtered harmonic complex tone are shifted further towards higher frequencies, the pitch again becomes more prominent and less ambiguous. Figure 5.11 indicates that the pitch of such inharmonic complex tones shows a sawtooth like shape: starting from a situation in which the frequency of the lowest component is, say, 1400 Hz, the pitch first increases with increasing shift of the spectral components, then becomes ambiguous and, near where the frequency of the lowest component is 1650 Hz, jumps down to a lower value only to increase again for the further increasing shift of the spectral components. — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 720

Categorization

• QUESTION: Why does the virtual pitch become ambiguous specifically near a component shift of 150 Hz, then snap to a lower pitch? The mechanism behind this sawtooth discontinuity is worth chasing.
• DEFINE: Defines an ‘incomplete inharmonic complex tone’ — a harmonic complex whose components are uniformly shifted so they are no longer integer multiples of the fundamental.