Auditory filter bandwidth determines which harmonics of a note get resolved

Evidence

Confirm the result illustrated in Table 3.5 that the sixth harmonic will be resolved but the seventh harmonic will not be resolved for an f0 of 110 Hz Using Equation A1.2 in Appendix 1: … Find the center frequency (fc) for which the critical bandwidth (ERB) equals 110.0 Hz by substituting 110 Hz for ERB. (Bear in mind that the center frequency is in kHz in this equation.) … The center frequency of the filter whose critical bandwidth is 110.0 Hz is 790 Hz. All filters above 790 Hz will have bandwidths that are greater than its bandwidth of 110 Hz, because we know that the critical bandwidth increases with center frequency (see Figure 3.8). As it lies below the center frequency of the filter midway between the seventh (770 Hz) and eighth (880 Hz) harmonics, those harmonics will not be resolved, since the filter that does lie between them will have a bandwidth that is greater than 110 Hz. Therefore, harmonics up to the sixth will be resolved, and harmonics from the seventh upward will not be resolved. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 879

Categorization

• DEFINE: Demonstrates how critical bandwidth/ERB works as a working quantity by solving a concrete example.
• XREF: connects to: A filter resolves a harmonic it is centered on even when bandwidth exceeds spacing — David Howard, Jamie Angus, coustics and Psychoacoustics, 884; Harmonics above the seventh exceed auditory filter bandwidth and cease to be resolved — David Howard, Jamie Angus, coustics and Psychoacoustics, 1528