Yes, in a dark room we can recognise a sound produced by a piano or a violine very easily on the basis of 'quality of timber'. The quality of sound depends upon:
(i) The number and frequency of the overtones present
in the given sound.
(ii) Relative intensity of the overtones.
The two sources, even though having the same intensity and fundamental frequency will be associated with different number of overtones of different relative intensities. These overtones will combine to produce different sounds which enable us to distinguish them.