# Lecture 4: Determining the Fundamental Frequency

The trigonometric Fourier series can be used to represent any periodic function.
In periodic functions, every frequency in the Fourier series representation
is an integral multiple of some fundamental frequency. Such frequencies are
said to be
**
harmonically related
**
. The ratio of any two harmonically related
frequencies is a
**
rational number
**
(i.e., a number which can be represented
as the ratio of two integers). (Interesting mathematical fact: there are more
irrational numbers than there are rational numbers. ) Any number which involves
a transcendental number such as
or
,
or which involves square roots which cannot be simplified down to ratios of
integers (such as
)
is an irrational number. For functions which are harmonically related, the fundamental
frequency is the greatest common divisor of the frequencies.