The overtones arrange themselves in a definite order, as follows: (1) the fundamental or prime tone; (2) an overtone one octave above the fundamental; (3) an overtone a fifth above No. 2; (4) an overtone a fourth above No. 3 (two octaves above the fundamental); (5) an overtone a major third above No. 4; (6) an overtone a minor third above No. 5. There are others in still higher range but those indicated are easily demonstrated on the piano. For C they would be as follows:
Experiment I
Step to your piano, noiselessly press and hold down the key of No. 2, then strike the fundamental No. 1, with force and immediately release it. As a result No. 2 will sound clearly, and if your ears are keen you will at the same time hear No. 6. In succession hold down the keys of 3, 4, 5, and 6, while you strike and release the fundamental No. 1. If your piano is "in tune" you will probably hear No. 6 when holding the key of any other note of the series.
In a musical tone of rich quality the overtones just indicated are present in their fulness, while tone that is weak and thin is made so by the absence or weakness of the overtones. I have stated that the quality of a tone depends on the form of its vibrations, and that the form of its vibrations is determined by the character of the resonator. We can now amplify this by saying that while the relative presence or absence of overtones determines the clang or color of a tone, their presence or absence is determined by the character of the resonance.
An English writer records that he was once in the garden at the back of a house while a gentleman was singing in the drawing-room. The tone-quality was good, and the pitch so unusually high he hastened to learn who sang tenor high C so beautifully. On entering the room, instead of the tenor he had supposed, he found the singer was a baritone, and the note sung was only middle C. The fundamental tone had not reached him in the garden but the first overtone, an octave above it, had. Concrete illustrations will make the subject still clearer.
Experiment II
If an ordinary tuning-fork when vibrating is held in the hand its intrinsic tone is too weak to carry far. Rest the handle of the vibrating fork on a bare table or the panel of the door, and the sound is greatly augmented. The vibrations of the fork have by contact induced similar vibrations in the wooden table or panel which reinforce the primary tone.