The Overtone Series (colour code chart here)

Musical instruments create overtones (notes other than the fundamental).
The shape and structure of an instrument determines which overtones are more prominent.

The overtones vary with different instruments and the prominence of certain overtones are what give an instrument its timbre.
When a note is played, that one note is registered in our minds as the loudest, we say it’s the note C, C#, A whatever, however that note is the result of other notes co-existing with it which are called overtones. The overtone series is a direct result of other notes vibrating in sympathy with the original note which within this context we shall call the fundamental. The notes vibrating in sympathy have an intervallic structure just like scales. The intervallic structure of the overtone series is, in the case of the note A:
Fundamental A
Octave A
Fifth E
Fourth A
Major 3rd C#
Minor 3rd E
Minor 3rd G
Major 2nd A

1 With the guitar pluck an open A string -------- Fundamental A
2 Place the 1st finger of left hand and lightly touch the A string at the 12th fret and pluck -------- Octave A
3 Same thing same string 7th fret -------- Fifth E
4 Same thing same string 5th fret -------- Fourth A
<5 Same thing same string 4th fret -------- Major 3rd C#
6 Same thing same string 3rd fret -------- Minor 3rd E
7 Place the 1st finger of left hand and lightly touch the A string inbetween the 2nd and 3rd frets (in line with the dot fretmarker or whatever markers you have on your fretboard) and you should find --------Minor 3rd G

What all this means is that when you pluck an open A string all those and more harmonics vibrate in sympathy with the open A to create the overtone series. The overtone series is endless but as you proceed along the series, the overtones become less identifiable because the frequencies exceed the audible spectrum. The choice of the major scale as a basis for elementary and advanced music education resides in the fact that the note order of the major scale creates a consonance that is pleasing to the human hear.