To give yourselves a clear idea of the production of beats, take two metronomes and set them almost alike. You can, for that matter, set the two exactly alike. You need not fear that they will strike alike. The metronomes usually for sale in the shops are poor enough to yield, when set alike, appreciably unequal strokes. Set, now, these two metronomes, which strike at unequal intervals, in motion; you will readily see that their strokes alternately coincide and conflict with each other. The alternation is quicker the greater the difference of time of the two metronomes. If metronomes are not to be had, the experiment may be performed with two watches. Beats arise in the same way. The rhythmical shocks of two sounding bodies, of unequal pitch, sometimes coincide, sometimes interfere, whereby they alternately augment and enfeeble each other's effects. Hence the shock-like, unpleasant swelling of the tone. Now that we have made ourselves acquainted with overtones and beats, we may proceed to the answer of our main question, Why do certain relations of pitch produce pleasant sounds, consonances, others unpleasant sounds, dissonances? It will be readily seen that all the unpleasant effects of simultaneous sound-combinations are the result of beats produced by those combinations. Beats are the only sin, the sole evil of music. Consonance is the coalescence of sounds without appreciable beats. [Illustration: Fig. 12.] To make this perfectly clear to you I have constructed the model which you see in Fig. 12. It represents a claviatur. At its top a movable strip of wood _aa_ with the marks 1, 2 ... 6 is placed. By setting this strip in any position, for example, in that where the mark 1 is over the note _c_ of the claviatur, the marks 2, 3 ... 6, as you see, stand over the overtones of _c_. The same happens when the strip is placed in any other position. A second, exactly similar strip, _bb_, possesses the same properties. Thus, together, the two strips, in any two positions, point out by their marks all the tones brought into play upon the simultaneous sounding of the notes indicated by the marks 1. The two strips, placed over the same fundamental note, show that also all the overtones of those notes coincide. The first note is simply intensified by the other. The single overtones of a sound lie too far apart to permit appreciable beats. The second sound supplies nothing new, consequently, also, no new beats. Unison is the most perfect consonance.