These are also known as partials or overtones. They can be viewed in the spectral window.An overtone series over a fundamental note looks like this:

Here are the individual tones that make up one particular note, immediately followed by
two versions of the same note that the partials create. In each note, different harmonics are emphasised. The pitch of the note stays the same but the timbre or tone colour is affected.

Filtering

before

after

Filters can be applied to boost or reject certain frequencies. Examine the full range of the church organ (audio file) in the spectral view (on the screen).

Then listen to it when everything is filtered out  (audio) except the note A. Here is the
spectral view (on screen).

Composers of electronic music often use noise as a source of sound waves. They use Subtractive Synthesis to filter out some harmonics and build their own timbres by boosting or rejecting frequencies.