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Intonation in musical strings is the attribute that causes one string gauge (core wire) combination to change pitch at a different rate from another gauge when fretted at the same lenght.
Thicker gauge strings tend to note sharper then thinner strings because of the heavier string gauge(s) greater resistance to being stretched. (Siminoff Lutherie).
The above statement comes from Roger Siminoff a master lutheir. His explanation is brief and to the point. Naturally, different guitars have different ways to set intonation. Simply, most electrics have adjustible string saddles to set intonation. To correctly set intonation a Conn or Peterson strobe should be used. The over the counter tuners (some are good) are insufficient to exact intonation.
On Acoustic, or classical, guitars, compensated string saddles aid intonation, but if intonation is seriously off then the bridge placement itself requires an analysis.
For additional in depth article on "intonation" go to article titled: GUITAR TUNING & INTONATION.