The scale designer is better equipped for his task, however, if he possess a working knowledge of the principles upon which the science and art of tuning are based. This is the justification for the space and time devoted to the exhibition of certain of these principles in the earlier portion of this book. As a further contribution to this useful body of knowledge, we shall point out here the general scheme whereby the tuner proceeds to the execution of his important, indeed essential, portion of the whole work.
The practical work of tuning is performed by the aid of certain acoustical phenomena which enable the tuner to distinguish between sounds that are very nearly in unison. As the Equal Temperament requires the slight roughening of all the intervals with the exception of the unison and octave, it is clear that there is great value in a method of estimating, not only the unisonal or non-unisonal condition of two sounds, but also the exact amount of difference that may occur between them. The phenomena mentioned are called “beats,” and it is well that their physical basis should be described here.
From what has been said before, it is clear that musical sounds, generated as they are by the periodic agitation of the air according to fixed laws, are but the audible manifestations of a peculiar form of air-motion. The particular form of air-motion can best be described as a wave. Whenever a sonorous body is excited into vibration it causes the surrounding atmosphere to make motions that correspond to its own. A vibrating body such as we have described (together with the segments thereof) partakes of a motion that may be compared to that of a pendulum. There is a rhythmic swinging back and forth of the body and its segments, with the result that the immediately adjacent layers of air are excited into alternate states of compression and expansion; or, more correctly, of condensation and rarefaction. This rhythmic motion is imparted by the layers of air adjacent to the sonorous body to the next adjacent layers, and so on. The result of this is that a wave is formed, the length of which varies inversely as the number of vibrations performed by the sonorous body. This wave is called a sonorous wave.