= Solution
Equal <pitch> need not mean equal <frequency spectrum>. For an ideal periodic <sound wave> of fundamental <frequency> $f$, a <Fourier series> has the form
$$
p(t)=\sum_{n\ge1}A_n\cos(2\pi nft+\phi_n).
$$
Changing relative amplitudes $A_n$ changes the waveform and generally its <timbre> without changing its fundamental period. Attack, decay and the time evolution of the <frequency spectrum> also matter for real musical notes.
The <middle ear> transfers vibration into the <cochlea>. The <basilar membrane> supports a frequency-selective travelling wave: higher-frequency responses occur nearer the base and lower-frequency responses nearer the apex. <Hair cells> in the <organ of Corti> transduce mechanical stimulation into signals transmitted through the <auditory nerve>. Different spectral and temporal patterns therefore produce different sensory-activity patterns.<How Do We Hear? by the National Institute on Deafness and Other Communication Disorders>[Steps 3–6: cochlear travelling wave, hair cells and auditory nerve]{ref}
This supplies a physical basis for <timbre> discrimination. It does not make the <cochlea> a set of independent strings, nor does excitation position alone explain every perceptual distinction: the <cochlear amplifier> and temporal neural coding also contribute.
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