"He (Feiten) was not the first musician to be unhappy with prevailing intonation theory. In 1939 musical acoustician L.S. Lloyd wrote in Intervals, Scales, and Temperaments (St. Martin’s Press), “What [musicians] particularly dislike about equal temperament . . . is the false intonation of the thirds and sixths.” Unfortunately luthiers didn’t listen, maybe because tackling the series of harmonic relationships on a guitar, which are vastly more complex than on the one-string/one-note piano, seemed too daunting."
The first part of this statement is absolutely correct, and impossible to resolve, any more than you can make 2+2=5. The natural harmonic major third is represented by the ratio 4:5 and the harmonic minor third is the ratio 5:6. However neither of these intervals will resolve as multiples within an octave, so it’s impossible to create a scale of fixed pitch which incorporates correct thirds relative to all other notes in the scale. The equal temperament intervals are slightly expanded and compressed respectively. Musicians sensitive to dissonance have always expressed dissatisfaction with equal temperament while nevertheless recognising that it is the only practical solution to the the problems of creating a fixed pitch scale in a hostile harmonic environment.
What Buzz has failed to identify correctly is that the problem is one of music, harmony and perception rather than of guitar construction. All equal temperament instruments are affected by the discrepancy between the natural harmonic intervals which we strive to hear and the equal temperament intervals which sound slightly less than perfect to us. Equal temperament succeeds if its rules are respected, as pianists and other keyboard players do, and the instrument is tuned correctly. The problem for the guitarist is that they are saddled with the problem of tuning their instruments themselves and as most guitarists get by with a minimal musical education they lack the knowledge and understanding of what is happening when they follow the advice of their ears and everything then sounds wrong...
