a ratio due to 'use.' Again, with sounds from most sources there is a fundamental tone which is strong and a mathematical series of overtones rapidly but proportionally decreasing in strength upwards. There is also a set of 'difference tones' decreasing in strength mathematically downward. The specific organs of all the various tones get exercise in proportion to the strength of the tones they emit. Consequently we have here another ratio, due to use, between the various tones. And it will be observed that these two ratios fall on and supplement each other. The maximum for frequency of exercise falls precisely on that for strength of exercise, and the ratios run together mathematically throughout. We could work out a 'permutation and combination' formula expressing, for the specific organ of each tone of which the ear is capable, its total developmental stimulation, based upon the relationships of frequency and strength of occurrence between usual fundamental tones and the octaves, fifths, fourths, thirds, and so on of their overtones. And it will be observed that the ratios of these would correspond inversely to the disagreeableness of these intervals. But this is precisely what we should expect according to the doctrine of specific nerves. Let us recall here our discussion of pain nerves as warners, and of their distribution with reference to usual functions and working equilibrium. We should not expect to find pain nerves among the cells and fibres mediating the most ordinary sounds. They would be in the way there, and soon crowded out. We should expect to find them crowded in everywhere close up to a margin line, determined as for our above formula by the common uses and experiences of the ear.
Let us seek an illustration that may, perhaps, elucidate all this. Under this doctrine aesthetic modifications would be likely to occur under any marked changes of auditory experience. It is well known that musical 'thirds' was the limit of agreeableness to the Greeks. Handel accepted 'fourths'; Beethoven 'fifths'; while Wagner wove into his compositions every combination of which ordinary musical instruments are capable. Again, we have the Swiss musician who went into
