(2) The presence of harmonics up to the sixth communicates force and brilliancy and character to the tone. Of this kind are the notes of the piano and organ-pipes more strongly blown.
(3) If only the uneven harmonics, viz. the first, third, fifth, etc., are present, the sound acquires a certain nasal character.
(4) If the higher harmonics are strong, then the sound acquires great penetrating force, as in the case of brass instruments, trumpet, trombone, clarionet, etc.
(5) The causes of discord are beats having a frequency of 30 to 40 or so, taking place between the two primary tones or the harmonics of either note.
The pleasure derived from the sound of a musical instrument is dependent, to a large extent, on the existence of the desirable harmonics in each tone, or on the exclusion of undesirable ones.
In the next place, let us consider a little the means at our disposal for creating and enforcing the class of air-waves which give rise to the sensations of musical tones. Broadly speaking, there are three chief forms of musical air-wave-making appliance, viz. those which depend on the vibrations of columns of air, on strings, and on plates respectively.
One of the oldest and simplest forms of musical instrument is that represented by the pan-pipes, still used as an orchestral accompaniment in the case of the ever-popular peripatetic theatrical display called Punch and Judy.
If we take a metal or wooden pipe closed at the bottom, and blow gently across the open end, we obtain a musical note. The air in the pipe is set in vibration, and the tone we obtain depends on the length of the column of air, which is the same as the length of the pipe. The manner in which this air-vibration is started is as follows: On blowing across the open end of the pipe closed at the bottom a partial vacuum is made in it. That this is so, can be seen in any scent spray-producer, in which two glass tubes are fixed at right angles to each other. One tube dips into the scent, and through the other a puff of air is sent across the open mouth of the first. The liquid is sucked up the vertical tube by reason of the partial vacuum made above it. If we employ a pipe closed at the bottom and blow across the open end, the first effect of the exhaustion is that the jet of air is partly sucked down into the closed tube, and thus compresses the air in it. This air then rebounds, and again a partial vacuum is made in the tube. So the result is an alternate compression and expansion of the air in the closed tube. The column of air is alternately stretched and squeezed, and a state of stationary vibration is set up in the air in the tube; just as in the case of a rope fixed at one end and jerked up and down at the other end. The natural time-period of vibration of the column of air in the tube controls the behaviour of the jet of air blown across its mouth, the energy of the jet of air being drawn upon to keep the column of air in the tube in a state of oscillation. Thus a flutter is excited in the air in the tube, which is maintained as long as there is a blast of air across its mouth, and this communicates to the air outside a wave-motion. We have, therefore, a musical note produced, the wave-length of which is four times the length of the closed tube across the mouth of which we are blowing. Accordingly, a very simple musical instrument such as the pan-pipes consists of a row of tubes closed at the bottom, the tubes being of different lengths. A current of air from the mouth is blown across the tubes taken in a certain order, and we can obtain a simple melody by that process of selection.
Fig. 57.—A closed organ-pipe.