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.