the big fundamental waves. Points of least motion, called nodes , form on the string, dividing it into two, three, four, five, etc., parts, which may be further divided by subsidiary nodes. The string, considered as halved by one node, gives the first overtone, or octave of the fundamental. It may also vibrate as three parts, and give the second overtone, or twelfth of the fundamental; and as four parts, and give the third overtone, the double octave.
Now, if a string be struck at a point corresponding to a node, the overtones which require that point for a node will be killed, on account of the excessive motion imparted to the string at that spot. Thus to hit it at the middle kills the octave, the double octave, etc.; while to hit it at a point one-third of the length from one end stifles the twelfth and all its sub-multiples.
A fundamental note robbed of all its harmonics is hard to obtain, which is not a matter for regret, as it is a most uninteresting sound. To get a rich tone we must keep as many useful harmonics as possible, and therefore a piano hammer is so placed as to strike the string at a point which does not interfere with the best harmonics, but kills those which are objectionable. Pianoforte makers have discovered by experiment that the most pleasing tone is excited when the point against which the hammer strikes is one-seventh to one-ninth of the length of the wire from one end.
The nature of the material which does the actual striking is also of importance. The harder the substance, and the sharper the blow, the more prominent do the harmonics become; so that the worker has to regulate carefully both the duration of