First off, this is no longer ‘complete’ if it ever really was – Glass has apparently written a 6th quartet. (Also, there are other pieces he has written for string quartet that do not appear here, but they are not numbered among his string quartets, apparently.)
Glass’ first quartet is a really great piece of music, in part because it doesn’t sound so Glassian as almost all of the rest of his music does. My guess is this was written so early in his development that he had failed to fully establish his style. And normally one might assume that such an early work would be derivative (it may well be, I don’t exactly have an encyclopedic knowledge of 20th century ‘classical’ music) or immature, but I don’t get that. What I hear sounds to me like the work of a great composer in the mid 20th century, bridging the gap between minimalism and other supposedly avant garde ‘high art’ music, even if it is very brief.
The second quartet feels a lot more Glassian – though it’s still not blatantly so compared to some of his work – and is even shorter. Though it’s pretty, it’s the most incidental of these works and the most obviously in line with the tradition of quartets, and so I am inclined to say it is the most derivative. And it just sort of peters out at the end, rather oddly.
The ‘Mishima’ quartet may be his most famous (just a guess) because of its inclusion on a soundtrack and also because it is far and away the most obviously Glassian of his quartets up to the time of its composition. As such, what you think of it likely depends on whether or not you like Glass. I think it’s great, though I am inclined to rate the first quartet higher, but I also have become quite the Glass fan recently. It’s as a good place as any to enter into Glass’ oeuvre, as it’s short enough but representative enough to give you an idea of whether or not he’s for you.
The ‘Buczak’ feels a little less significant, perhaps because it is also so very much of his style. It’s the second longest, and so (at least to my knowledge) much more in line with modern quartet lengths. It just doesn’t stir me like some of the others. I can take it or leave it.
The 5th quartet is an interesting one in that it seems to me to be a clear attempt to bridge Glass’ own very identifiable style with some other ideas, and as a result I think it is probably his second most successful, behind his first. It’s still very recognizable as Glass’ work, but it feels more mature than the middle quartets, which all feel as if they are just Glass’ music in quartet form – nothing wrong with that, just less interesting than this one.