In the early 1960s, Murphy also met pianist Bill Evans and became a close friend and confidant until Evans' death in 1980. Murphy’s second daughter, born in 1964, was named Miriam Evan, after Evans. Murphy became the chief transcriptionist for Evans’ solos, playing Evans’ records at 16 rpm to make sure he got every note. Many of these transcriptions were published and performed by other artists such as classical pianist Jean-Yves Thibaudet, who recorded a 1996 album entitled "Conversations with Bill Evans".