Two: another approach

In my last post, I described how I’ve been approaching the performance of the piano part to Cage’s Two:  by feeling my way through the brackets and making decisions on the fly, “by going inwards”, as Cage described it in his “Composition as process:  indeterminacy”.  That 1958 article described another approach to take:

Or he may perform his function . . . more or less unknowingly by employing some operation exterior to his mind:  tables of random numbers, following the scientific interest in probability; or chance operations, identifying there with no matter what eventuality.

In other words, I could allow some external chance-driven process to make all the decisions for me, and then just follow the results.  In this approach, I’d try to think like Cage and create a process that determines every aspect of the piece fully using chance operations.  Although this isn’t my natural inclination for this piece, I tried this out, too.   I’ve put the gory details of the process at the end of this post, to spare those who aren’t as into that sort of thing.  But suffice it to say that I had to spend some time framing the questions that would need answering, I generated lots of random numbers ( is a great resource for this), and thus determined the timing of all the chords.  Because the resulting timings have absolutely nothing to do with the way the chords appear in the score, it’s really impossible to perform such a version that way, so I wrote out the results by hand in music manuscript (well, I did it for about half the piece; it’s a time-consuming process).   The result is a precise, completely unpremeditated version of the piece that theoretically uses a wider range of possibilities than I would have thought of myself.

I played around with this version of the piece a little, but I haven’t kept up with it.  Learning the piece this way is a completely different experience from the “going inwards” approach that I’ve been taking.  It’s a matter of learning more or less precisely how the timing goes and playing it over and over until I get it right.  In other words, it’s very much like learning any new piece of music.  The sense of rhythm is different — it’s all clock-time based — but the process is pretty much the same.  I find that I pay more attention to the clock than to the notes while working on this version.  Some of the sequences are awkward and difficult, which is a sure sign that it has been done by chance operations.  It’s harder to play, that’s for sure.

But ultimately I don’t think that this approach is appropriate for Two.  It’s a style of playing that comes right out of Cage’s work in the 1950s:  it’s the way that David Tudor would have approached it back then.  And it’s the approach that is demanded in a piece like the Solo for piano from the Concert for piano and orchestra (1957-58).  But by the 1980s Cage’s style was different, and the precise working out of timings “following the scientific interest in probability” was no longer his way.  The number pieces are about a more casual form of indeterminate performance, and I believe that the intuitive, situational approach I’ve been taking is really the more appropriate one.

That said, I have tried a little hybrid version.  I found that there were a few decisions that I would overthink:  when to start a phrase within the bracket (early or late?), which hand to start with (right or left?), and the general pace of the phrase (fast or slow?).  I used some random numbers to generate several sets of ten answers to these questions, one for each phrase.  I printed these out in a shorthand form, little rubrics that I can put next to my score and follow while playing.  I treat them as disposable chance operations:  each time I play the piece I use a different one.  It helps keep me focused and keeps me from doing the same thing every time.

Trying out these two methods makes me realize that one of the breakthroughs of the number pieces is this simple indeterminate notation.    Technically, it’s nothing all that special.  But it can be handed to just about any conscientious professional musician, not just to a David Tudor, and a performance in line with Cage’s conception will come out of it.  In that way it is quite different from his indeterminate scores of the 1950s and 60s.  Two and all the following number pieces are works written by a composer who had a flood of commissions from all kinds of mainstream performers — even orchestras.   The kinds of things that Cage wrote in the 1950s just aren’t practical for a composer in that situation, and Cage was, in many ways, a very practical composer.

Process for determining timing & durations in Two

There are lots of different ways one could use chance operations to determine the durations in Two.  This is how I did it:

  1. Determine the total duration of each of the nine phrases with flexible time brackets.  I arbitrarily set a lower limit of 15 seconds for this (anything shorter would start to get unplayable for me); the upper limit is 75 seconds (per Cage’s notation).  These can be determined by generating random numbers between 15 and 75.
  2. Determine the starting time of each phrase.  The possibilities here depend on the duration.  If the duration is less than 30 seconds, the phrase will have to start no earlier than 30 minus the duration (in order to end within the given bracket), and as late as 45 seconds into the start.  If the duration is over 30 seconds, the phrase will have to start no later than 75 minus the duration (again, in order to end within the given bracket) and as early as the very beginning of the start bracket.  Generate a random number for each phrase that is within the constraints for each.
  3. Determine which hand will start each phrase and which hand will end each phrase.  I did this by generating two sets of ten zeroes & ones:  a zero meant the right hand, a one the left.
  4. In each phrase, for each hand, determine the remaining start and end times for each chord.  If the hand starts and/or ends the phrase, you already know the first start time and/or the last end time (they have to be the start and end times of the overall phrase).   Generate a set of numbers between the start/end time values of the phrase to give the rest of the start/end times of the chords.  Arrange these in ascending order to get the timeline for that hand.

That’s all there is to it.  As an example, here’s how the first phrase played out in my realization:

  1. Duration:  35 seconds
  2. Start time:  I chose a random number between zero and 40, which is the only range of possibilities for starting a 35-second phrase (any later goes past the latest end time of 1:15).  Result:   21.  So my first phrase runs from 0:21 to 0:56.
  3. Which hand starts/ends:  I got a zero and a one, so the right hand starts the phrase and the left hand ends it.
  4. Remaining start/end times for chords:  For the four chords in the right hand, I generated 23, 28, 34, 40, 43, 46, 55.  The first chord starts the phrase, so it begins at 21.  The start/end times thus are:  21/23, 28/34, 40/43, 46/55.  For the three chords in the left hand, I generated 30, 43, 50, 51, 56.   The last chord ends the phrase, so it ends at 56.  So the start/end times are:  30/43, 50/51, 56/56.  The last chord, therefore, is a grace-note (as short as possible).

I did the same thing for all the other brackets, except the fixed one.  For that, I skipped steps 1 and 2, since the duration and start/end times are already known.

A couple of interesting things that can happen with this method.  First, when generating the start/end times of chords (step 4) you might get the same number two or more times.  This means that chords might follow each other without pause or that they might have zero duration (i.e., are grace-notes).  This happened a number of times in my realization (see the example above).  The other situation that might happen is that a phrase might start before the previous one ends.  This didn’t happen in my realization, but it’s a possibility.  I have no idea if Cage ever considered this possibility himself — my hunch is that he didn’t.  But I see no reason that it shouldn’t be allowed.  Just one of the insights that chance operations can provide!

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