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 20^th 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?

170 Hz
220 Hz
340 Hz