The
Greek philosopher Pythagoras, in about 500 BC, discovered that the
musical scale was closely related to mathematics. Plucking a taut
string sounding C for instance, he noticed that another string twice
as long and equally taut, sounded a note just one harmonic octave
below the first. Starting with any string, you could go down the scale
by increasing its length according to simple fractions. So, 16/15
of a C string would give the next lower note B, 6/5 of that B note
would give A, 4/3 of it would sound a G, 3/2 of that G would give
F, 8/5 of F gives E, 16/9 of E gives D, and exactly twice the first
C gives C again, one octave lower. Pythagoras' experiment is only
valid with strings of the same gauge and equally taut. If a harp were
made that way, it would be too tall, and almost impossible to play.
By having strings of different gauges musical instruments are easier
to handle. The correct gauging of strings is very important, and is
determined by complicated calculations beyond the scope of this book.
The
gauge of the strings is very important, as each string has a different
gauge, and it must be of even thickness throughout its entire length.
They are graded with great precision and cannot be mass-produced like
fishing lines! The correct grading follows:
