There would be no differences in timbre for notes that are the same amplitude and frequency. In practice though, notes are never the same frequency, notes (and indeed all naturally occurring sounds) are combinations of different frequencies, a fundamental frequency plus a number of harmonics (mathematically related frequencies) and it's the number and balance (relative amplitude) of all those frequencies that account for differences in timbre. The exception is if we generate an (artificial) note which is just a single sine wave, in which case there are no other frequencies (harmonics) but then of course there would be no differences in timbre either.
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