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I’ve talked there and there about the Number Pieces of John Cage, mainly to expose some ideas about how these works could be analyzed.

John Cage

In particular, I’m advocating a statistical approach to the analysis through the random selection of the starting and ending times of the different time-brackets. In my view, this allows to take into account all the possibilities which can arise during a performance. Note however that the results depend on the model used for selecting the time marks: the random selection process I’ve used is probably not characteristic of human behavior and having a process which could model the musicians’ choices more accurately would also change the resulting probability distributions of length, temporal location, etc. There is one particular example, though, where time marks were selected in advance at random, and that’s the performance of $\text{103}$ conducted by Petr Kotik (you can find the recording there, though it seems to be out of stock). There would be much to say about why Kotik didn’t let the musicians choose the time-marks themselves (though he did let them choose the ending time), but I’ll probably keep it for another time. If you’re really interested in that, you can read Steven Shlegel’s dissertation:

• “John Cage at June in Buffalo, 1975”, Steven Shlegel, State University of New York at Buffalo, 2008

wherein he shows that, although some of Cage’s scores seemed to allow performers to do whatever they want, this was not the case from Cage’s point of view. Apparently, an angry John Cage (!) (if you can imagine that) said: “Over and over again, no matter how many times I say, “You can’t do anything you want, but anything goes,” everyone interprets it as “I can do any GOD DAMN THING I WANT”

So, the random selection process and statistical framework is useful for analysis, but it can be used for the automated generation of Number Pieces too. You can thus determine every part of a Number Piece algorithmically and assemble them for a final performance. I’ve recently written a small Java program to generate MIDI files of some works, which can then be rendered using a software sampler into a final music file.
Here’s how it works in detail:

• We determine each part independently from each other. Again, this is a considerable assumption, as it supposes that performers are not influenced by each other. This probably would not be the case in real life, and I’d be curious for a model of the performer’s interactions during the Number Pieces.
• In each part, we determine each time-bracket successively, as was exposed in the previous posts.
• In each time-bracket, we determine pitches (when there are many of them in a single time-bracket) by successively choosing time-marks at random (see picture below).

Determining multiple pitches at random in a single time-bracket. Time-marks are selected successively.

The Number Piece $\text{Five}$ was written by Cage during 1988 and is dedicated to Wilfried Brennecke and the Wittener Tage. This piece is written for five voices or instruments or mixture of voices and instruments. Each part contains five time-brackets, the third one being fixed, and the time-brackets are identical for all players. Some of them contain just a single pitch, others multiple, though not more than three.

I chose to make a version for one flute, two clarinets and two violins. I recorded samples of my own instruments, then used them in a MIDI sampler to render the Java-generated MIDI files. You can listen to 20 different versions at the following adress, and I plan to upload more, in an attempt to give an idea of all the possibilities offered by this piece.

You’ll notice on this website that there is a similar page for another Number Piece, $\text{One}^4$, with 10 different versions. This is a very peculiar Number Piece, and I’ll talk about it in a separate post.