Another important ingredient of music is tone. The pitch of a
tone is the listener’s evaluation of the frequency (number of
vibrations per second usually shown in Hertz) and is perceived as
how high or low a note sounds. The higher the frequency , the higher the pitch. The
lower the frequency, the lower the pitch. Pythagoras discovered
that the frequency (pitch) of a vibrating string is proportional to
its length. Doubling the length of a vibrating string lowers the
pitch by one octave. Standards of exact pitch have changed
many times over the centuries. The United States and Great Britain
eventually adopted A = 440 hertz to be the standard pitch in the
20th century and that is what all piano tuners use as a
basis for tuning.
How loud a tone is the listener’s perception of the
amplitude. The larger the amplitude, the louder the tone. The
smaller the amplitude, the softer the tone. There is a set
of characters which tells how loud or how soft to play the part.
The loudest is fff. That means to
play very very loud. It goes down in eight steps, which are:
fff, ff, f, mf,
mp, p, pp, and ppp.
They range from very very loud to very very soft. These marks
are called dynamics.
Knowing the frequency of Middle A is 440 Hz, what is the
frequency of of the A below Middle A?