Number 9: Chester Alan Arthur
According to Guion, Arthur played the banjo and is probably the only banjo-playing President. He even posed next to one for a photographer.
Number 6, 7, and 8: John Quincy Adams, John Tyler, Woodrow Wilson
The author says that these three Presidents are tied. Adams played flute, while Tyler and Wilson played violin.
Number 5: Harry S. Truman
Truman played piano throughout his presidency and beyond. His performances were captured on film and are available on YouTube. His daughter Margaret had aspirations of becoming an opera singer. Truman’s rage against a critic who panned her performance is a legendary anecdote.
Number 4: Bill Clinton
Clinton played saxophone well enough to win first chair in his all-state band and consider music as a career. He continued to practice saxophone daily, and as a Presidential candidate in 1992, he appeared on the Arsenio Hall Show and played “Heartbreak Hotel” with the show’s band, wearing wraparound sunglasses and a colorful tie. He passed President George H. W. Bush in the polls for the first time shortly afterward.
Number 3: Richard Nixon
Besides being an accomplished pianist, Nixon played accordion and violin. Not only did he play three instruments, he is the first American President who composed any music that came to public attention. The following clip from the Jack Paar Show features Nixon performing a short piece he composed, accompanied by an ensemble of “Democratic violinists.”
Number 2: Thomas Jefferson
Jefferson, like Nixon, played three instruments: violin, cello, and clavichord. He practiced three hours a day in his college years. The royal governor of Virginia regularly invited Jefferson to play chamber music at his home. Music also played an important role in Jefferson’s courtship with Martha Wayles Skelton. She played piano, an instrument Jefferson had apparently not encountered before. He ordered a solid mahogany piano for her. After they married, he made sure his children became proficient musicians as well. His daughter Martha became so proficient on harpsichord that they traveled to Philadelphia and Paris to find teachers for her. Jefferson was an avid book collector and later sold his personal library to the Library of Congress. In 1783, he compiled a catalog of his music collection. There was chamber music for strings and harpsichord (especially that of his favorite composer Arcangelo Corelli), song collections, ballad operas, and orchestral music. He also acquired instruction books for violin, harpsichord, flute, and “musical glasses,” as well as books on music history and theory.
Number 1: Warren G. Harding
Harding played more instruments than any other president. He once remarked, “I played every instrument but the slide trombone and the E-flat cornet.” He played well enough to join the band that celebrated his nomination in 1920.
The author comments that three of the four most musical Presidents are remembered for the scandals that marred their administrations, though that's probably just a coincidence.