Humans can hear the sign (180-degree overall phase) of a waveform

Evidence

Figure 24.6 shows some detail in a 1-second trace of the waveform sin(2π · 200t) + sin(2π · 301t); the shape changes in the waveform are clear. In spite of near-coincidences, the exact function (as opposed to its overall shape) does not repeat in less than 1 second. The two red traces differ in time by 1/2 second and have the same shape, although they are not quite identical in detail. The red and black traces at the bottom are the same shape except they are each other’s negative (one is upside-down compared to the other). They are only a quarter-second apart. If they sounded the same, the beating would be 4 Hz, but instead it is 2 Hz. Thus a waveform and its negative generally do not sound exactly the same, even though they differ only by an overall sign. The relative phases of the partials are the same whether or not the signal is inverted; so now we know that even an overall phase (of π or 180 degrees) of the whole waveform can change the timbre. Apparently, we can hear the sign of a waveform, which is easy enough to check, assuming one’s sound reproduction equipment is responding linearly. The author finds noticeable differences between the sound of waveforms 1 and 2 of figure 24.7. — Eric J. Heller, Why You Hear What You Hear- An…, 2231

Categorization

• DEFINE: Establishes that overall sign/phase of a waveform alters perceived timbre, not just relative partial phases.