Q: “How can I achieve that ‘chiming,’ jangly rhythm guitar sound I hear on old Byrds records from the 1960s (and from R.E.M. in the 1980s and 90s)?”
A: The Byrds readily acknowledged that their admiration of Beatle George Harrison’s use of an electric 12-string guitar led to their own trademark sound. The “chiming” effect came from the extra strings, tuned an octave higher than normal guitar strings. This sound was revived in the 1980s by R.E.M. and other bands and has been used extensively in pop recording.
If you don’t have a 12-string (electric or acoustic) there’s another way to achieve a convincing jangle: have your rhythm guitarist lay down two or three different guitar tracks, each playing different inversions of the chord changes (i.e., play the chord in different positions on the fingerboard). On each track, different notes and harmonics will tend to ring out. You can use an equalizer to emphasize those frequencies, and mix the combined tracks to your liking. The result will still sound like one guitar, but it will be one GREAT guitar!
A different approach is to try an acoustic guitar sound employed in some country music arrangements. The Nashville “high-strung” technique is based around on a six-string guitar, in which the bottom 4 strings are tuned an octave higher than normal. Again, the unique harmonics that result from this can create a psycho-acoustically enhanced instrument sound that blends perfectly into a mix, often with little need for additional processing.
Incidentally, there is a GigaStudio sample library featuring these instruments. Jim Corrigan’s Nashville High-Strung Guitars recreates up and down chord strums and single notes from a high-strung acoustic.