Founded in London in 1963 by singer Phil May and an original Rolling Stone, guitarist Dick Taylor, the Pretty Things took their name from a 1955 Bo Diddley single and covered four of his tunes on their debut LP. The Pretties also supercharged Diddley’s iconic shuffle and tremolo strum into an avenging-R&B mayhem — caught right away on the 1964 45s “Rosalyn” and “Don’t Bring Me Down” — that was the delinquent model for garage rock, punk and glam (David Bowie covered both songs on 1973’s Pin Ups). That would have been legacy enough for most bands. But the Pretties were impatient modernists, carrying that blues zeal to psychedelia (1967’s “Defecting Grey”), rock opera (ahead of the Who, on 1968’s S.F. Sorrow) and progressive rock (1970’s Parachute) with spectacular if commercially dire results. This grand box takes that tale, across 11 studio albums and a feast of extras, up to the present day: a 2012 throttling of the Beatles’ “Helter Skelter.” Taylor’s old band may cast the longer shadow, but this one is determined to have the last word.