Rotating siren holes changes partial phase but also alters shared partial amplitude.

Evidence

Ever the resourceful experimentalist, Rudolf Koenig set out to test sensitivity to the phase of the partials in periodic tones. It might seem sufficient just to rotate different sets of holes in a siren relative to each other to change the phase, but this also affects the amplitude, not just the phase, of any partials shared by the two tones. For example, a circle of 20 holes and a circle of 30 holes create a 200 Hz and a 300 Hz tone if the disk rotates at 10 revolutions per second. The two tones, which are a perfect fifth apart, both have amplitude in a 600 Hz partial. If both partials had the same amplitude and phase, the amplitude of the sum would be twice that of each of its components. But a 180-degree phase change of one of them would change the sign, canceling the amplitude of the 600 Hz partial. Since a change of phase of one of the notes changes the amplitude of the 600 Hz partial, the timbre will change, since it depends on the relative intensity of the partials. — Eric J. Heller, Why You Hear What You Hear- An…, 2247

Categorization

• XREF: Connects to how timbre depends on relative partial intensity — ties to the broader timbre/phase question the whole chapter addresses.