A combined waveform can produce a perceived pitch absent from its actual frequency components

Evidence

In figure 3.11, the smaller fork is vibrating faster than the larger fork by factor of exactly 3/2. Using f1 = 200 and f2 = 300, the displacement of the smaller tines reads … Notice that it is perfectly periodic. Its frequency is 100 Hz, lower than either the 200 Hz or the 300 Hz component. The two waves return to their starting phase at the same time after three periods of the 300 Hz wave and two periods of the 200 Hz wave; this time is 0.01 second, corresponding to a frequency of 100 Hz. Here is the first hint of a crucial issue, one that extends to theories of music and hearing. If any single pitch can be associated with this combination, it is certainly 100 Hz, but there is no 100 Hz frequency present at all. One can also easily “hear out,” as it is called, the 200 and 300 Hz “atomic” components as individual sinusoidal pure tones embedded in the “molecular” whole. There is much more evidence to present regarding pitch perception, and we leave this subject for a full discussion in chapter 23. — Eric J. Heller, Why You Hear What You Hear- An…, 323

Categorization

• DEFINE: Introduces ‘hearing out’ atomic components and the ‘missing fundamental’ paradox, a core pitch-perception concept.
• QUESTION: The missing-fundamental phenomenon is telegraphed here and promised in chapter 23 — worth chasing that full discussion.
• XREF: Connects to the reader’s larger auditory-processing cluster and to figure/ground signal-separation ideas from the soundscape books. — connects to: A short pop can still carry a recognizable resonant pitch; Pitch can be perceived even when no partial exists at that frequency — Eric J. Heller, Why You Hear What You Hear- An…, 2031; The siren showed sinusoid partials arise without any sinusoidally vibrating source (+22 more)
• corroborated: 2 independent passages support this claim — Eric J. Heller, Why You Hear What You Hear- An…, 323

Broader Connections

• Listeners reconstruct a perceived pitch that is not physically present #expands (0.95)
• Combination tones fill in missing harmonics of a perceived fundamental #expands (0.90) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1620
• Mixing noise with its own delayed copy can create a sense of pitch #exemplifies (0.85) — David Howard, Jamie Angus, coustics and Psychoacoustics, 939
• Echoed sounds spaced 1-10 ms generate a perceived pitch of 100-1000 Hz #exemplifies (0.80)
• Pitch perception corresponds to peaks in the autocorrelation function #complicates (0.80) — Eric J. Heller, Why You Hear What You Hear- An…, 2033