Half-period delay of a tone cancels odd partials and raises pitch an octave
Evidence
If a complex periodic tone of frequency f and period T = 1/f is time delayed by half of its period—a time T/2—and added to its original self, the pitch of the tone will go up by an octave. The lowest partial, and in fact every odd (the 3rd, the 5th, and so on) partial above it, is nullified if it is added to itself half a period later: these partials are always the negative of themselves half a period of the fundamental earlier. For a 100 Hz tone, this is a delay of 0.005 s. If all the odd partials in a 100 Hz tone with 100, 200, 300, 400,… Hz partials are killed, leaving 200, 400, 600, … Hz, a 200 Hz pitch results (an octave higher). — Eric J. Heller, Why You Hear What You Hear- An…, 2137
Categorization
Category: Causal Relationships
- DEFINE: Explains the mechanism of repetition pitch via delay-and-add cancellation of odd harmonics.
- XREF: Explains Rayleigh’s harmonic echo and connects echo physics to the reader’s silence/soundscape interests.
Related
- Adding higher partials can drop the perceived pitch of a tone (similarity 0.85)
- Repetition pitch equals the reciprocal of the echo delay time (similarity 0.82)
- Time-delayed repetition of sound produces a matching repetition pitch (similarity 0.80)
- Echoed sounds spaced 1-10 ms generate a perceived pitch of 100-1000 Hz (similarity 0.79)
- A single delayed sound repetition creates a perceived pitch even from white noise (similarity 0.79)
- Mixing noise with its own delayed copy can create a sense of pitch (similarity 0.79)
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 - Delays too short for echoes still audibly alter timbre through spectral combs
#corroborates(0.80) — Eric J. Heller, Why You Hear What You Hear- An…, 2551 - Mixing noise with its own delayed copy can create a sense of pitch
#expands(0.75) — David Howard, Jamie Angus, coustics and Psychoacoustics, 939