There are a couple of interesting points about this piece. First, it's an important milestone in Cage's work as, supposedly, it's his first use of time-bracket notation. I say "supposedly" because I'm unclear what those timings were in For Paul Taylor and Anita Dencks if not time brackets. But I've read in a few places that time brackets proper started here.
With the use of time-brackets, it's immediately tempting to connect this to the Number Pieces. Personally, I would be wary of that temptation. I'm not sure there's all that much continuity between this and the Number Pieces. You can see an important difference in the title alone. Thirty pieces. Five orchestras. Whereas the main feature of most Number Pieces, even the ones involving large numbers of musicians, is simplicity and stillness, the focus here is on multiplicity, complexity, extravagance. This is as related to something like HPSCHD as it is to the Number Pieces (in both cases, not much).
Another notable difference is its use of repetition. In almost all the pieces, there is at least one instrument repeating a single note. None of these seem to be following any particular rhythm. It reminds me a little of Hymnkus, though the music here feels much more organic, and because of the short length of each piece (there are thirty pieces in about thirty minutes), none of them have a chance to develop gradually like Hymnkus does. Just as you're feeling tempted to describe it as "minimalist", the music is cut short and some new part starts. Again, Cage's focus here seems to be multiplicity. Cram in as much as possible. Quantity creates quality. Don't be afraid of waste. (I should note that Cage crams in plenty of silence and quiet parts, too. This is not nearly as loud and chaotic as HPSCHD.)
Second, I think, though I may be wrong about this, that this was also the first time Cage derived his compositional method from his visual art, here the series of paintings On the Surface. I'm not sure if I've ever seen On the Surface. I have a few collections on Cage's visual art, but not on me where I am right now; and I couldn't find anything on a brief search on Google. So I can't say whether the music feels similar to the artwork.
Nevertheless there is something more generally interesting to note about the use of paintings here. Visual art is, of course, a medium that necessarily exists in space; music, on the other hand, is generally seen as being an art of time rather than space. Cage felt that any strict division here would be a mistake. Granted, time is essential to music; but space need not be neglected. Indeed, it's impossible to neglect space entirely: where the musicians are placed, where you are in relation to them, what kinds of room is used, etc, will make a difference to the sounds you experience no matter what composition is being played. Even so, very few composers have shown much concern with space. Questions such as "where to place the musicians?", "what kind of room should this be performed?" are not traditionally ones with which composers have concerned themselves. Cage, however, was deeply concerned with space, especially during his later career. He tried to erode the boundaries between time-art and space-art. And I think that his use of paintings in his music composition was very much an expression of this concern.
(Re space and music in general: here's an interesting talk by David Byrne about the significant influence that venue - space - has on music. Cage's interest in space had some justification.)
Importantly, the use of space extends to the music itself. The five orchestras are placed apart from each other and arranged in a pentagon around the audience. Unfortunately, I can't really comment on this aspect of the piece, as it's obviously impossible to preserve it in a recording. It's one of the things that makes being a fan of Cage somewhat frustrating. Much of his work is not really suited to recordings (which is one of the main reasons why Cage himself was fairly hostile to recordings). I will probably never hear anything more than a cheap imitation of Thirty Pieces for Five Orchestras.
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