But no sonorous body vibrates in one single rate; a taut string vibrates as a whole, which gives its fundamental tone, but also in halves, in fourths, etc., each giving out a weaker partial tone, in harmony with the fundamental. And according to the different ways in which a sonorous body divides, that is, according to the different combination of partial tones peculiar to it, is its especial quality of tone, or timbre. The whole complex of fundamental and partial tones is what we popularly speak of as a tone,--more technically a clang. These physical agitations or vibrations are transmitted to the air. Omitting the account of the anatomical path by which they reach the inner ear, we find them at last setting up vibrations in a many-fibred membrane, the basilar membrane, which is in direct connection with the ends of the auditory nerve. It is supposed that to every possible rate of vibration, that is, every possible tone, or partial tone, there corresponds a fibre of the basilar membrane fitted by its length to vibrate synchronously with the original wave-elements. The complex wave is thus analyzed into its constituents. Now when two tones, which we will for clearness suppose to be simple, unaccompanied by partial tones, sounding together, have vibration rates in simple ratios to each other, the air- waves set in motion do not interfere with each other, but combine into a complex but homogeneous wave. If they have to each other a complicated ratio, such as 500:504, the air- waves will not only not coalesce, but four times in the second the through of one wave will meet the crest of the other, thus making the algebraic sum zero, and producing the sensation of a momentary stoppage of the sound. When these stoppages, or beats, as they are called, are too numerous to be heard separately, as in the interval, say, 500:547, the effect is of a disagreeable roughness of tone, and this we call discord. In other words, any tones which do not produce beats are harmonious, or harmony is the absence of discord. In the words of Helmholtz,<1> consonance is a continuous, dissonance an intermittent, tone-sensation. <1> _Lehre v.d. Tonempfindungen_, p. 370, in 4th edition. Aside from the fact that consonance, as a psychological fact, seems positive, while this determination is negative, two very important facts can be set up in opposition. As a result of experimental investigation, we know that the impression of consonance can accompany the intermittent or rough sound- sensations we know as beating tones; and, conversely, tones can be dissonant when the possibility of beats is removed. Briefly, it is possible to make beats without dissonance, and dissonance without beats.