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Yes, the drummer of Jefferson Airplane was Charlie Chaplin’s nephew, a fact I learned in passing last year when I read a biography of Chaplin. The fact was never called out—I just saw the kid’s name (quick mention of his participation in a party in his famous uncle’s mansion in the early 40s) and did a quick Google. Actually, the drummer’s father was Chaplin’s half-brother by the same mother, hence the different surnames. Dryden never told any of his bandmates or anybody else about it (I’m sure he had plenty of good reasons—not wanting to be overshadowed, not wanting people to expect him to carry on those “comedy genes,” not wanting to be associated with someone who was generally regarded in LA as a beast and a rogue and communist, and so on and so forth).
About Spencer Dryden’s role in Jefferson Airplane. No, he wasn't one of the creative principals in the group, and he, like most drummers, was pretty low-key and invisible. His name is essentially a bonus question in a 60s-rock trivia contest. From everything I've read, he was just about the freest spirit of the bunch, and the least connected with the whole Haight-Ashbury scene (he was always perceived by the other members as the "LA guy" on drums). But he directly influenced the Airplane's lead singer, main personality, and resident looker.
Grace Slick wrote/sang the wonderful, overlooked, funny ballad “Lather” about Dryden, who was her primary squeeze during the 1967-68 creative sweet spot, spanning “Surrealistic Pillow,” “After Bathing at Baxter’s,” and “Crown of Creation.” “Lather was 30 years old today/They took away all of his toys/His mother sent newspaper clippings to him/About his old friends who’d stopped being boys.” An overgrown child, or lost child, or tripping child.
When I think of his contribution to the band, I primarily think of the “bolero” drum progression of “White Rabbit,” and also the charging percussion of "Somebody to Love" (I've heard Grace's prior versions of both songs from her pre-JA band, Great Society, and can assure you that JA's versions are much better, thanks in no small part to Dryden's excellent drumming).
I also think of Dryden's acid-drenched free-association riff called "A Small Package of Value Will Come to You Shortly," on "After Bathing at Baxter's": especially him barking out the phrase: "No man is an island/No man is an island/He's a peninsula" (one of my absolute favorite double-entendres of all time--think of Florida--also look into the word "peninsula" for five letters in the correct sequence, and strip away the four unessential letters to reveal the hidden word).
I wonder what Dryden had been doing with his life since the 70s (he was in country-rock band New Riders of the Purple Sage for several years). As you can tell, I’m a huge Jefferson Airplane fan. One of the most memorable events of my life was a brief, accidental meeting with Grace Slick and Paul Kantner in Detroit in 1981. Somehow, I prefer their artsy noodlings to the Dead. I’m sure they don’t remember the encounter. I got their autographs. Lost ‘em.