PARTIAL TONES

But beside the over-tones, which sound with every good, simple sound, there are other partial tones, which, like the long-known combination tones, do not usually present themselves to our consciousness. Combination tones were first discovered in 1745 by the organ-builder, Sorge. By an act of concentrated attention one hears these tones at the accord of two different tones. They lie always lower than the interval to which they belong, and arise from the meeting of the nodes of vibration of the tones producing the interval. The node of vibration is the name of that place where, after every completed vibration, the sounding body returns to its former position. When, for instance, we give the third c¹ e¹, we hear the c, lying an octave lower than the third, sounding at the same time as a combination tone. For the tone c¹ a string has two vibrations, while in the same space of time e¹ has three. The vibration node of the c¹ will thus, after two vibrations, coincide with the vibration node of the e¹. By the coincidence of these nodes of vibration is produced the number of vibrations requisite for the c below. Besides these combination tones there are summation tones, discovered by Helmholtz, which arise from the vibrations collectively (Gesammtzahl) belonging to the above interval, and are higher than the interval. Both kinds of partial tones have again their faint over-tones.