The basilar membrane’s fixed-spread frequency resolution shrinks relative bandwidth as frequency rises

Evidence

Georg von Bèkèsy’s basilar membrane studies around 1960 established a physical basis for Harvey Fletcher’s 1940s concept of a critical bandwidth. Von Bèkèsy found that a pure tone excites the basilar membrane into vibration in a zone on average about 1 mm wide. The zone slides up or down the basilar membrane according to frequency, giving us rough tonotopic frequency resolution. One mm represents the limits of resolution by the physical membrane. (Other neural and hair cell feedback processes refine frequency detection well beyond that of a 1 mm uncertainty.) One millimeter corresponds to a finite frequency bandwidth, which gets larger at higher frequencies (figure 26.3). The critical bandwidth is about 100 Hz wide at 100 Hz, 150 Hz wide at 1000 Hz, and 1000 Hz wide at 10,000 Hz. For frequencies greater than 1000 Hz, the critical bandwidth is approximately a fixed fraction (about 15%) of the center frequency of the band. Thus, a 2000 Hz center frequency has a critical bandwidth spanning 150 Hz on either side. A 300 Hz and 380 Hz pair of partials sound quite good together, but a 1300 Hz and 1380 Hz pair do not, even though both pairs are separated by the same 80 Hz. The critical bandwidth at 300 Hz is plus or minus 50 Hz, so 300 Hz and 380 Hz fall outside each other’s critical band. The critical bandwidth at 1000 Hz is roughly 150 Hz, so 1300 Hz and 1380 Hz fall inside the same critical bandwidth. — Eric J. Heller, Why You Hear What You Hear- An…, 2328

The effect of each narrowband component of the input signal spreads in frequency in a manner similar to the effect of the narrowband masker in Figure 9.6. This spread can be characterized by a spreading function B(z), which depends both on frequency and level, like the masking curves. For average levels of speech (about 60 dB SPL), a single-peak function has an approximate peak (at −3 dB) of about 1 ERB (or Bark), and the slopes are about 8 dB/ERB (10 dB/Bark) towards high frequencies, and about 20 dB/ERB (25 dB/Bark) towards low frequencies. The closest physiological correlate of the spreading function is the envelope of the vibration on the basilar membrane when excited by a single sinusoid. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1151

Categorization

• DEFINE: Establishes the critical bandwidth concept with concrete numbers: 100 Hz at 100 Hz center, ~15% above 1000 Hz.
• XREF: Directly builds on basilar membrane mechanics from earlier chapters; also explains why equal frequency separations sound different at different pitches — relevant to piano tuning.
• SHARE: Sharable with someone into auditory models: pitch spreading slopes 8dB/ERB up vs 20dB/ERB down — concrete numbers useful for filter design.
• corroborated: 2 independent passages support this claim — Eric J. Heller, Why You Hear What You Hear- An…, 2328; Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1151