The tone of a stringed instrument is to a great extent depending on the resonance of the overtones in the strings you don't play upon. If you mute all strings but one on a stringed instrument, very little tone is left when you play on the remaining string.

The overtones are so important for tone that pianos are deliberately tuned false* to sound good. Due to inharmonicity the overtones of a piano is namely too high. That why the octaves of pianos are stretched out, they are tuned a little too high, so the inharmonc overtones in the adjacent octaves will resonate easier.

When a fretted instrument is intonated, the overtones in the strings you don't play upon can resonate much easier. For certain, guitars and other stringed instruments have inharmonicity, but it is far less than on pianos because the strings are considerably thinner. While a non intonated instrument loses its tone when the strings get old, an intonated instrument continues to sing with old strings. It is namely the highest, most inharmonic overtones that first disappear when a string is aging. Personally I only change strings when they eventually break.

* A piano technician might not agree that he/she is tuning false, but if you play a note in the highest treble  with a note in the deepest bass on a piano, anybody can hear that the two notes are not in tune due to the stretching.