The voice will follow the thought as surely as the hand will reach the object aimed at. The extreme anterior part of the nares, or head cavity, is the chamber of resonance farthest from the vocal cords. Therefore, if the voice be directed through that chamber of resonance all the others must be passed in reaching it, and hence all must be accessible to the vibrating column of air. It is a law of acoustics that any given cavity of resonance will resound to that pitch to which its size corresponds, and to no other. This law of sound secures the appropriate resonance for every pitch much more accurately than it could be secured by an effort to develop chest, middle, and head registers through calculating the differences. Again, we need the higher chambers of resonance to reinforce even the low pitch, because every note has its overtones that enrich it, and if these cannot find their proper resonance the tone is impoverished. It may be well to explain our use of the term "overtone."
This word "overtone" is used unscientifically by many. The significance of its use is somewhat varied among teachers, but it generally means head resonance, or a tone "sent over" through the head cavities. The term is used here technically, not arbitrarily. Overtones are not confined to the voice, but are those constituent parts of any tone which are produced by the vibrating segments into which any vibrating cord will divide itself.
Any cord, or string, stretched between two given points, when struck will vibrate throughout its entire length in waves of a certain length and with a certain degree of rapidity, according to the tension of the string. This vibration of the entire length of cord gives forth the tone heard as the fundamental pitch or tone. Besides this fundamental or primary vibration, the movement divides itself into segments, or sections, of the entire length. These sections also have vibrations of their own which are of shorter length and more rapid motion. The note given off by these subdivisions is, of course, on a higher pitch than that produced by the fundamental vibration of the cord; hence, they are higher tones, or overtones. It will be remembered that pitch depends upon the rapidity of the sound waves or vibrations. This subdivision of the vibrations is incalculably multiplied, so that it may be said to be impossible to determine the number of overtones accompanying the fundamental tone. What the ear hears is the fundamental pitch only; the overtones harmonize with the primary or fundamental tone, and enrich it. Since this is a law of vibration, it is unscientific to speak of giving an overtone, for all tones contain overtones. Where these overtones are interfered with by any imperfection in the instrument the result is a harsh or imperfect sound.