If the laying of the bearings has been accurately performed, the chords that are produced by the combination of the various sounds will be found to have very nearly the same roughness and to generate approximately the same number of beats. The best work is that which most closely approaches this standard.

After the bearings have thus been laid, it is necessary to continue the tuning of the instrument above and below the octave already treated. Now, since the octave to any given sound has exactly double the frequency of the former, and since octaves are to be tuned purely, it follows that we need only tune the remainder of the instrument by octaves up and down from the “bearings.” The consonance of an octave is determined by the absence of beats, and, consequently, we have only to follow this rule to reproduce, in all parts of the piano, deviations from purity relatively the same as those which we have been at such pains to secure.

Of course, the actual number of beats in any given interval varies as the frequencies, and, consequently, the frequency of the beats increases regularly in the higher registers, while it similarly decreases in the lower portions. Thus the deviations from purity become much greater in the higher portions of the compass and incorrect laying of the bearings is, therefore, productive of more and more disagreeable results as the scale ascends. On the contrary, in the lower register these inaccuracies are less productive of irritation, as the frequencies of the beats become continually less.

Such, then, is the process of tuning the pianoforte in Equal Temperament. We have made no attempt to go into those practical details that are concerned with the ear-training, the manipulation of the hammer, or other cognate matters. These are entirely “ex provincia” of this work.

Nevertheless the person who digests the foregoing statement of the laws and methods of the art will be well equipped to pass upon the correctness of tuning, and this is sufficient for our purpose.

The work of tone-regulation opens up varying but not entirely dissimilar fields of research. The material of which the pianoforte hammer is constructed has an important influence upon the coloring of the sound that it draws from the string. In order that the influence of the pianoforte hammer in tone-coloring may be understood clearly, we shall investigate the matter with some completeness.

We have already investigated the compound nature of the sounds excited by the pianoforte strings. We know that the nature of these sounds varies as the method of excitement and as the nature of the resonance apparatus that surrounds the strings. Now the pianoforte strings are excited by being struck, and we have already noted that the point of striking must be carefully chosen. Further, we know that the amount of metal framing, the manner of adjusting the bridges, the nature of the sound-board and innumerable other details must be taken into consideration.

But by the time that the pianoforte comes into the hands of the tone-regulator, it is out of his power to affect the construction in any fundamental points. He is able to change only two things. These are the striking point and the condition of the hammer-heads. Even the former cannot be changed to any great extent. In the highest treble, however, it often becomes necessary to bend the hammer-shanks slightly in order that a more correct striking point may be obtained. But this must be done with great discretion and caution.

The object of tone-regulation is to ensure an agreeable tone and perfect evenness of quality throughout.