Human hearing can in principle distinguish astronomically many timbres.

Evidence

The number of possible timbres is enormous. Theoretically, since the frequency resolution of hearing is 1 ERB and the entire auditory frequency range consists of 42 bands, and since the level resolution is 1 dB for a dynamic range of about 100 dB, there are about 10042 possible timbres. However, when the masking effect is taken into account, this number is smaller. Nevertheless, even for a dynamic range of only 6 dB, the number of timbres is 642 > 4 · 1032, which is still a colossal number. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1182

Categorization

• CANDY: The 10042 figure — some 10^84 timbres from band and level resolution alone — is a striking party fact about the theoretical capacity of hearing.
• QUESTION: Does the masking-effect reduction bring this down to a number that’s meaningful for musical composition or synthesis design? Worth chasing.