But on the other hand, first, we think of the mathematical [element] which enables us to pronounce on the proportion between these oscillations in music and thus to judge of them; and by analogy with which we easily may judge of the distinctions between colours. Secondly, we recall instances (although they are rare) of men who with the best sight in the world cannot distinguish colours, and with the sharpest hearing cannot distinguish tones; whilst for those who can do this the perception of an altered quality (not merely of the degree of sensation) in the different intensities in the scale of colours and tones is definite; and further, the very number of these is fixed by intelligible differences. Thus we may be compelled to see that both kinds of sensations are to be regarded not as mere sensible impressions,