Q: Can you write a history of popular music, that ""paradigm of American culture,"" and not mention George M. Cohan? A: No, you cannot, and Tony Palmer just did. He also skips Harold Arlen, Butt Bacharach, Laura Nyro, James Taylor, and John Denver--and relegates Aretha Franklin, Peter, Paul and Mary, and Stevie Wonder to photo captions. Not to worry. Palmer has the latest on Led Zeppelin and 18th-century British recruiting jingles; check out the war-song chapter, the one without ""Over There."" What's going on over here? A personal discourse-harangue, that's what; not necessarily--as Alec Wilder proved--a bad thing. But with gift-and-reference book trappings and a panoramic table of contents, one expects thorough research, eclectic enthusiasms, more musical analysis, less pseudo-sociology, and fewer obsessions. Arbitrarily partitioned essays (circumscribing jazz, blues, country, swing, rock, and a half dozen others) fail to acknowledge blends and overlappings, and Palmer seems to doze half the time. Musicians' bottles, needles, and sorry ends, however, find him endlessly fascinated. So does the motif of ""the white man"" stealing black music--an arguable notion but relentlessly pursued to the exclusion of any other approach. A third tired chord: Judy Garland, ghoulishly portrayed as the spirit of decaying vaudeville, denied her movie-musical niche. For encores, Palmer turns faintly anti-Semitic (""The monopolistic greed of a white, Jewish-dominated, New York-oriented clique""), garbles the plot of Finian's Rainbow and indulges in TV-award-show phrasemaking (""Psychologists were her parents, the camera her lover"" . . . ""The Beatles became an abstraction, like Christmas""). His knowledgeability in the rock-of-tomorrow field may deserve a hearing, but not as part of a long, droning concert played on a curiously angled and out-of-tune calliope.