"Good Vibrations" doesn't use basic chords. The bass line in the chorus is conventional, but the chord progressions throughout the song are more complex than many "standard" rock songs. But these atypical chords aren't what set the song apart.
"Good Vibrations" is a "studio song," which means that it was pieced together through multiple complex recording sessions. And it was this process that produced the song's distinctive musical character.
Numbers tell part of studio the story: six months, 17 recording sessions, 100 hours of tape, $50,000. But another aspect of the song's charm and success is the creative use of new technologies, old instruments, and even non-instruments. New technology was used to create the spooky, vibration-simulating whine that appears for the first time about 25 seconds into the song.
Many have identified this technology as a Theremin, an older electronic gizmo played by waving one's hands in front of two antennas. But actually, the device used was an early version of a Tannerin, or Electro-Theremin. Unlike the Theremin, the Tannerin is physically touched while being played. The musician/technician slides a lever along the instrument to produce the sound. Its sounds can be more precisely controlled, as it contains a keyboard; by sliding the lever between two notes on the keyboard, the operator can determine the range of the sound being produced.
Just as the Theremin was named after inventor Léon Theremin, the Tannerin is so called because of its designer, Paul Tanner, a trombone player turned inventor. The device used in recording "Good Vibrations" was an early version of Tanner's machine. Tanner and his Electro-Theremin box were in great demand to provide sound effects during this pre-synthesizer period. Eventually, Tanner's creation was modified and given its current name, the Tannerin.
This new technology was combined with an older, more classical instrument, the cello. According to Brian Wilson, the cello that saws off the last several bars of the song was the first to make an appearance in a rock song. And new and old were joined by even more unconventional rock instruments. At various points in the song, a Jew's harp, sleigh bells, and a harpsichord are played.