Have you ever thought about why different instruments sound different, even when playing the same note in the same register? How can you instantly tell a clarinet from a cello, or even two different violins apart?
The different timbres (tone colours) of different types of instruments (and even between different violins) are due to the different ways the note is produced, and therefore the different ratios of harmonics and overtones created.
But what are harmonics and overtones?
Whenever a note is produced on an instrument, what we hear is one fundamental tone (for example an C). What we don't hear clearly, is that there are many other tones above the fundamental - ringing at the same time. All these tones are called overtones. The different strengths of each overtone created by an instrument produces the particular timbre that we hear .
String instruments are built in a particular way, so as to create particular types of overtones. The overtones in violins and violas are notes in harmony with the fundamental tone, and are therefore known particularly as harmonics. These harmonics create the rich beautiful tone that is so lovely to listen to.
Here is the harmonic series showing the fundamental tone as 1 (low C in bass clef), and following harmonics in order.
As you can see from this, the first harmonic in the series is the octave (C no 2), followed by the fifth (G no 3) etc...
Within the first 4 tones of the harmonic series, you also find the intervals of an octave (C-C), a perfect fifth (C-G) and a perfect fourth (G-C), the 3 most perfectly harmonious intervals in music.