SA Issue 3: The Cage Issue: The Number Pieces
John Cage's Number Pieces
It can be dangerous to attempt to sum up a specific period of a composer’s output in a couple of paragraphs. However, if we were going to attempt such an exercise, John Cage’s Number Pieces, composed between 1987 and his death in 1992, would not be such a horrible choice. As with much of Cage’s oeuvre, the Number Pieces have a specific working methodology and a specific aesthetic. Everything is relatively explainable and easily diagrammed, and for those familiar with his use of chance operations to derive musical material (not familiar? Here’s a dense but serviceable introduction) can grasp the basic form, content and aesthetic of the pieces relatively easily.
It’s important to make this caveat before we begin, however. Though the form, content, and aesthetic idea of these pieces may share similar qualities, it’s important to take each composition on its own in terms of its musical character and sound world. This is a point that seems especially important when looking at the compositional output of Cage, which tends to be placed neatly into “periods” of his compositional methodology. The fact of the matter is that the Number Pieces do share a common general aesthetic: that of stasis, lack of narrative or linear time, silence, space. However, even a cursory listen to different pieces from this period or multiple versions of the same work reveal a tremendous diversity in timbre, pacing and overall feel. The information below is just intended as a basic primer to the general tools that John Cage used to make these pieces. The enjoyment is in taking the time to discover the slight deviations in the composition of the individual works and, as we’ve been talking about specifically in this issue, differences in interpretations in multiple performances.
All of the Number Pieces are titled in a way that readily distinguishes them from the rest of the Cage’s compositions and provides the basic information about the ensemble size and the piece’s place within the series. Each title consists of a written out number (i.e. One, Five, Seven, etc.). This denotes the number of performers needed for the composition. In addition to the written number, sometimes there is an added numeral at the end of the title (Two2, Five3, etc.) The numeral denotes the fact that the piece is the 2nd or 3rd piece in the series of compositions for that number of players (i.e. One4 is the fourth composition for a single player).
Beyond the obvious titles of these pieces, arguably the greatest distinguishing musical factor in the composition of the Number Pieces is Cage’s use of time brackets to set the musical content within the form. For a simple explanation of the concept we offer the following:
In regularly notated music, notes are placed on a staff using different rhythmic values to show in what order and when the pitches should be placed and how long they should be played given a certain tempo. This allows the performer a limited amount of possibilities for phrasing of melodic material and a very strict construction of harmony.
In Cage’s time brackets, the note or notes are placed inside a bracket, and are to be performed within a range of time given in seconds by the composer, and up to the performer’s discretion within that time frame. This allows for multiple overlapping harmonies amongst players and a great deal of flexibility for the performer to shape the melody of the piece.
There are two kinds of time brackets used in the number pieces. The first is flexible, which means the note can start and end within a time period, i.e. start time = 30”-52.5” and end time = 45” – 1’07.5”. The performer can start the sound anywhere between 30 seconds and 52.5 seconds and then, of course end that same sound between 45 seconds and 1 minute and 7.5 seconds.
An example of a “flexible” time bracket from Four
The other time bracket is “fixed”. “Fixed” time brackets do not give a period in which the note starts or the note ends, but gives a definite range within which the sound should happen. For example, a “fixed” time bracket may look like this: 1’30 – 2’. In this example, the three pitches should happen between those two times, with the first sound starting exactly at 1’07.5” and the last sound ending at exactly 1’22.5”.
An example of a “fixed” time bracket from Four
There are two periods of Number Pieces and they are delineated specifically by how Cage came up with the lengths and placements of his time brackets. During the first period, from 1987 to 1989, the construction of the time brackets fell into a series of categories based on start and end time spaces (i.e. 15 seconds, 30 seconds, etc.) and where they were placed in the composition was based solely on either Cage’s composerly intuition or his use of chance operations like the I Ching.
During the second period, between 1990 and 1992, Cage relied on Andrew Culver’s “TBrack” computer software to come up with the lengths and placement of the time brackets. This allowed the composer to be presented with more complex possibilities within the creation of the brackets, while still maintaining the feeling of compositional detachment achieved using chance operations.
Each of these time brackets have to contain material, of course, and Cage didn’t stray far from his previous methods of choosing his pitches. Cage had admitted his general disinterest in harmony as such on many occasions and very frequently used the I Ching to help him in choosing which notes each instrument would play (for an example of how he did this see this short analysis of his chance techniques in composing Music of Changes), creating seemingly random harmonic and melodic combinations. In the Number Pieces, he uses a similar process to provide the material inside his time brackets, thus combining older and newer processes.
For these pieces, note choices came generally from Cage writing down a range of pitches that will be used for each instrument, for example, the flute’s range may consist of one octave from C1 to B1. Each of the pitches within that range were given a number. He would then use the numbers to consult the I Ching, as to which pitches would appear in each time bracket.
For example, in the case of the piece featured on this page, Seven, Cage first gave a one-octave range to the flute, then numbered each of those pitches. He then used the processes of the I Ching to select the first tone, say a C, then used the I Ching again to decide if that tone would repeat or would vary. When he went to the next time bracket, he would exclude the C from his choices of pitch and work through the I Ching again using the smaller number of pitches he had left.
Essentially, two of the major building blocks of composition have been taken care of at this point, form and content (time brackets and chance selected pitches). It is the performance choices, such as articulation, dynamics, and timbral considerations tend to provide a lot of the subtle differences between Cage’s individual works from this period, and so they should be mentioned as well.
Cage’s decisions about performance choices varied from work to work during this period. In some pieces, Cage left these performance practices up to the performers themselves, others were relatively strictly notated, although the decisions, more often than not, were again derived from the I Ching or some other chance operation. In many cases, simple rules such as “short notes are played loud, long notes soft”, or “piano plays with the sustain pedal” were applied to the piece in toto.
Now that the dry explanation of how the pieces are made is over, it’s our pleasure to be able to stream one of our favorite performances of a work from this period. The composition is Seven from the early period of the number pieces (1988). It was recorded here in 2002 and released on the incredible Edition Wandelweiser label, which we feature in DRAM.
The performers in this version of Seven are:
Normisa Pereira da Silva-alto flute
As you’ll be able to hear, beyond the structural building blocks of the time bracket form and the seemingly disconnected way of choosing pitched material, Seven is a fantastically beautiful, meditative and thoughtful piece of music when performed with rigor by talented musicians. It is also distinctly different from Two2 , written for two pianos, and recorded for Mode Records by Rob Haskins (featured in this issue of SA) and Laurel Kalrlik Sheehan, which we are featuring as our incentive for becoming an individual subscriber. Also worth comparing is the JACK Quartet’s rehearsal of Four which is featured in this issue to Mode’s recording of the Arditti Quartet doing the same work. Even a cursory listen to these three pieces will make clear the range of musical space Cage could occupy using the same means.
This is what made John Cage special. He took a stayed way of making music, a compositional style that had hit its maximal limits of control with the hyper-serialism of Babbitt and others, and set it free, to use hyperbole. This was something that was philosophically part of the time period in which he was working, but the beauty of Cage is that he just found a new way to create order, not a strict order, but a natural order, one that shifts and provides multiple possibilities and musical answers, and the work he did in structuring the Number Pieces is a stunning example of how effective that new musical order could be.