The power spectrum is blind to the relative phase of a sound’s components

Evidence

However, although the time domain waveform is radically different the fre­ quency domain is very similar, as the amplitudes are identical—only the phase of some of the harmonics has changed. … Interestingly, in many cases, the resulting wave is perceived as sounding the same, even though the waveform is different. This is because the ear, as we will see later, appears to be less sensitive to the phase of the individual fre­ quency compared with the relative amplitudes. However, if the phase changes are extreme enough we can hear a difference (see Schroeder, 1975). — David Howard, Jamie Angus, coustics and Psychoacoustics, 451 (#corroborates, via linked claim)

In anechoic listening to buzzy signals, minimal changes in group delays may be audible. This has already been demonstrated with a sawtooth wave, modified by a group delay smooth with frequency, but containing local abrupt change. In the top-left and top-right cases in Figure 11.11, the amplitude spectra are otherwise equal, but the phase of one harmonic has been reversed. This corresponds to applying a group delay of only 0.32 ms at 3100 Hz and none at other frequencies, making that frequency much louder. Such frequency-dependent variations in an otherwise smooth group delay can thus have a large effect during anechoic or headphone listening. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1282 (#complicates, via linked claim)

Categorization

• XREF: connects to: Echo interference creates sinusoidal power fluctuations that average to zero; Wind-instrument harmonic phases are set by resonant pulse enhancement, not chance.; The ear is far less sensitive to phase than to amplitude of frequency components (+10 more)

Broader Connections

• The human ear is largely insensitive to signal phase #corroborates (0.85) — David Howard, Jamie Angus, coustics and Psychoacoustics, 451
• The ear is far less sensitive to phase than to amplitude of frequency components #corroborates (0.80)
• Reversing the phase of a single harmonic can drastically change its perceived loudness #complicates (0.75) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1282