Harmonics are unresolved when critical bandwidth exceeds harmonic spacing.
Evidence
Consider a sound consisting of all harmonics (f0, 2 f0, 3 f0, 4 f0, 5 f0, etc.) whose f0 is 110 Hz.The frequencies of the first 10 harmonics are given in the left-hand column of the table. The next column shows the critical bandwidth of a filter centered on each of these harmonics by calculation using Equation 2.6. The critical bandwidth increases with filter center fre quency (see Figure 3.8), and the frequency analysis action of the basilar membrane is equivalent to a bank of filters. Harmonics will cease to be resolved by the place mechanism when the critical bandwidth exceeds the frequency spacing between adjacent harmonics, which is f0 when all adja cent harmonics are present. — David Howard, Jamie Angus, coustics and Psychoacoustics, 883
Categorization
- DEFINE: Explains when the cochlea stops resolving individual harmonics — the resolution criterion.
- corroborated: 2 independent passages support this claim — David Howard, Jamie Angus, coustics and Psychoacoustics, 883
- XREF: connects to: Roughness from harmonics requires fundamental frequencies below 100 Hz; Unresolved harmonics smear together as frequency rises; Harmonics resolve only while their spacing exceeds the ear’s ERB (+8 more)
Broader Connections
- Only harmonics separated by more than the ear’s critical bandwidth are resolved
#corroborates(0.98) - Harmonics resolve only while their spacing exceeds the ear’s ERB
#corroborates(0.95) - Critical band bandwidths grow from 100 Hz to over 2 kHz with frequency
#expands(0.85) - Loudness stays constant below critical bandwidth then grows beyond it
#corroborates(0.80) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1034 - Perceived dissonance arises when nearby harmonics fall within critical bandwidth
#expands(0.80) - Place coding of fundamental pitch fails at high frequencies when harmonics smear together
#expands(0.80) - Masking acts within critical bandwidths, leaving distant-frequency sounds unaffected
#expands(0.75) — Eric J. Heller, Why You Hear What You Hear- An…, 2009