Tree spacing and viewing angle mathematically reproduce the octave-up echo.
Evidence
Suppose the high pitch the woman needed to sing was near A4, 440 Hz. Her voice would carry 440, 880,1320,1760,… Hz partials. Assuming trees spaced by 4 m, they would have been standing about 6 degrees off the normal from a line connecting the first two trees in the front row. This would cause the required 1.1 ms repetition delay, removing the 440, 1320, 2200,… components, leaving a resonantly enhanced 880, 1760, 2640,… harmonic series—that is, an octave higher. However, other angles will also work, since a time delay of three times the minimum, or 3.3 ms, creates a notch at 147, 440, 733, 1027, 1320, … , which includes the series 440, 1320, 2200, and other frequencies that do not matter to a 440 Hz tone. Thus 17 and 29 degrees also work. The formula is that the delay has to be τn = (n + 1/2)/f, n = 0, 1, 2,… , where f is the fundamental frequency to be filtered out. — Eric J. Heller, Why You Hear What You Hear- An…, 2654
Categorization
Category: Factual Claims
- SEED: The notch-filter math with concrete numbers (4 m spacing, 6/17/29 degrees, Ď„%3D(n%2B1/2)/f) is a ready-made worked example for an essay on how periodic structures reshape pitch in the wild.
Related
- A row of trees can filter a voice to sound an octave higher (similarity 0.82)
- Equally spaced trees yield near-equal repetitive echoes ideal for notch suppression (similarity 0.80)
Broader Connections
- Repetition pitch equals the reciprocal of the echo delay time
#expands(0.85) — Eric J. Heller, Why You Hear What You Hear- An…, 2146 - Room echoes sculpt sharp resonant peaks into a sound’s spectrum
#qualifies(0.78) — Eric J. Heller, Why You Hear What You Hear- An…, 1111 - A returning echo creates power-spectrum peaks spaced by its inverse time
#expands(0.75) — Eric J. Heller, Why You Hear What You Hear- An…, 1096 - Moving sources make reflected-sound comb-filtering audible as pitch rather than mere colouration
#qualifies(0.75) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1112 - Spectral line structure predicts pitch strength magnitude.
#expands(0.75) — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 797