I haven't seen the Pixies documentary loudQUIETloud, but I know the band is said to have influenced Nirvana and a number of other '90s grungers with the remarkable innovation of dynamics (think of the verse-chorus contrast in "Smells Like Teen Spirit").
Now, I can take or leave about 50 percent of the Pixies' work, though "Here Comes Your Man" remains one of my favorite pop singles of all time (yes, I said pop), and when they were good, what distinguished them--and was not widely imitated--was their innovative song structure, not their use of dynamics. Sure, their harmonies are nicely jagged and worthy of further study (see below), but what hits me most about their songwriting is their odd elongations and elisions of form. Almost every pop or rock song you could name has a kind of couplet/quatrain format, with verses and choruses grouped in four, sometimes two lines; and this binary form, as natural to us as breathing out and breathing in, or our heartbeat, or walking on two legs and having four limbs, is built deep into most songs' DNA, so that there are often also two or four or eight bars, and two or four or eight beats per bar, and so on.
So when a song violates that rule of fours, it stands out. I think of the irregular three-line pre-chorus of Kelly Clarkson's "Since U Been Gone," which makes the chorus a consistent surprise, or the beguiling three-line verse of the Beatles' "Every Little Thing." The Pixies do this sort of thing so often it's almost a tic. Try to count along with the sweeping "Velouria," for instance. An even better illustration is the terse, brilliant "Is She Weird," the verse of which has four sections, but with an odd shape--they're all in 6-bar lines, except for the last line leading into the chorus, which has an extra two bars to create a more standard 8-bar line. This has a very imbalancing effect, and it sets us up for an equally odd chorus, also consisting of six-bar sections of three lines apiece ("Is she weird, is she white/Is she promised to the night/And her head has no room"), and that triple phrase is repeated...three times rather than four. And I'm not even addressing the stunning bridge from nowhere (roughly at 1:30). This is a raggedy performance, but it's all there:
This kind of art rock takes real confidence to pull off this offhandedly well, but I would have taken 10 bands that followed this kind of lead, in whatever style of rock, for every sweaty Stone Temple Pilots knockoff.
UPDATE: I checked out the harmony. This is art rock, as studiedly dissonant and architectural as early 20th-century "classical" music. The whole thing is built on a majestically rising progression of F#, A, C#, E, which swells for four bars, then folds back down for two bars on B and C# to create the song's weird flow-and-ebb gait. The vocal line, and the guitar noodling throughout, explore the chromatic possibilities of that progression (the first two notes of the melody are A# and A-natural), but the most haunting harmony of the song is on the final word of the chorus: "And her head has no" is sung on a D# over a B chord, then "room" is a D-natural over a C# chord--an extremely jagged dissonance that not only lodges this song in the brain but functions as a spur to push the song forward, as dissonances usually do. And the final resolution is a great payoff: The vocal repeats "head has no" on the D note but the accompaniment moves to a D chord, then the vocal and the accompaniment drop to B and B minor, respectively. Beautiful.
Again, this is not my favorite Pixies song or even their most ambitious, but it's a great reminder that from the ashes of punk and prog rose a mutant rock phoenix that variously inspired the likes of the Pixies, Sonic Youth, Nirvana, and the best of the grungers, before finally morphing into Radiohead. (In addition to my own work, I consulted this page.)