Two oscillations, one along the x-axis and the other along the
y-axis, when added together produce a two dimensional figure. If the
ratio of the frequencies of the two oscillations is some simple
fraction, the figure is quite pretty.

**
MUSICAL
SCALES**

The various tones of a musical scale are not selected at random, it
was found very early by many different cultures that if two tones
were played together, the combination would sound pleasant (__consonan__t)
if the ratio of their frequency (__the interval__) was given by a
fraction of integer numbers.

Because of this, adding the oscillations of two tones from the
musical scale will produce a pleasant lissajous curve.

**
**

The various tones on a scale are traditionally given letters and
names; the ratio of their frequencies is given below for the major __just
scale.__

**
DO RE MI FA SOL LA TI DO’**

**
C D E F G A B C’**

**
1 9/8 5/4 4/3 3/2 5/3 15/8 2**

The intervals in the __well tempered__ scale do not correspond
to a simple ratio of integers, because of this the combination of some
of the tones is not consonant and the lissajous curve is not as
pretty.