Spectrum magnitude, not phase, drives the perceived timbre of a sound

Evidence

However, the complex exponential form of the Fourier series automatically gives us a single, complex value for the coefficients, and by finding their absolute values, or modulus, we get the magnitude of the spectrum, which is usually more perceptually relevant to the listener’s appreciation of timbre. On the other hand, the phase of the signal f(t) at each harmonic frequency is given by the argument of each of the complex coefficients Cn. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2756

However, the complex exponential form of the Fourier series automatically gives us a single, complex value for the coefficients, and by finding their absolute values, or modulus, we get the magnitude of the spectrum, which is usually more perceptually relevant to the listener’s appreciation of timbre. On the other hand, the phase of the signal f(t) at each harmonic frequency is given by the argument of each of the complex coefficients Cn. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2756

Categorization

• XREF: Connects to the perceptual research showing our ears are largely phase-deaf; magnitude-dominant timbre perception echoes findings in auditory scene analysis.
• QUESTION: To what degree does phase matter for transient/percussive sounds, where it clearly does? Worth chasing the caveats to this general rule.
• DEFINE: Introduces modulus/argument as the two readings of a complex Fourier coefficient, with a perceptual weighting attached to each.
• corroborated: 2 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2756