This is a fact which no argument can destroy.  Two double basses, placed in the above-named conditions—­conditions of vicinity and tonal identity—­far from adding up their individual result, are thus reduced each to a quarter of its own sonority, which in the sum total, instead of producing a double sound, produces a sound reduced to half of that given individually by each instrument taken alone.  This is how a power plus an analogous power equals together with it but half a power; and thus we are forced to admit that one and one do not necessarily make two.

I have carried the experiment still farther; in the instrument which gained me a first-class medal at the exhibition of 1854, I was enabled to put thirty-six strings of the same piano into unison at once.  Well!  All these strings, struck simultaneously, did not attain to the intensity of sound produced by one of them struck singly.  All these sounds, far from gaining strength by union, reciprocally neutralized one another.  This is not logical, I admit; but we must submit to it.

Logic must be silent and reason bow before the brutal force of a fact to which there is no objection to be raised.

Since we are on the subject of the phenomena of sonority, let us draw another illustration from it, quite as overwhelming in its illogicalness as the former.

When two similar phenomena differ from one another on any side, the discord brought about by this difference is more apparent and more striking by reason of the closer conjunction of these phenomena.  By way of compensation the dissimilarity is less appreciable in proportion as these phenomena are farther apart from each other.

This is rigorously logical and perfectly conformable to reason; yet there are cases where we must affirm the contrary.  Thus the same sound produced, I will suppose, by two flutes not in accord with one another, forms those disagreeable pulsations in the air which discordant sounds inevitably produce.  There seems to be no doubt that by gradually bringing these discordant instruments together, the falseness of their relation must be more and more striking, more and more intolerable.  Wrong!  For then, and above all if the mouths of these instruments be concentrically directed, a mutual translocation is produced between the two discordant sounds, which restores the accuracy of their agreement.  Thus the lower sound is raised, while the higher one is lowered, in such a way that the two sounds are mingled on meeting and form a perfect unison.  Now, here are contrasts, which, contrary to all rational data, so far from being exaggerated by contact, diminish gradually, until they are utterly annihilated.  Thus, then, given two instruments of the same nature, if the harmony which they effect be true, they enter by reason of their conjunction into a negative state which neutralizes their sonority; while the contrary occurs in the case of false unison.  Here the instruments become identical with one another, the sonority is increased and the tonal deviation is corrected to the most perfect harmony.