The Number Pieces of John Cage (4)

Each piece in John Cage’s “Number Pieces” corpus of works is unique, and One4 is no exception. This piece was written in 1990, and as its name indicates it is written for a solo musician (the score is published by Peters Edition, with the reference number EP67349). More specifically, the piece is written for a percussionist playing on a drumset. It is dedicated to the Swiss percussionist Fritz Hauser, who originally commissioned it.

The structure of \text{One}^4 is peculiar. As for the other Number Pieces, John Cage uses the system of time-bracket for organizing the sounds in time, which I have explained precedently. Let’s recall that a typical time-bracket shows up as such on a score


and indicates that the content of the time-bracket (here, a single F pitch played piano) should be started anywhen between 0’00” and 0’45”, and stopped anywhen between 0’30” and 1’15” (the performer(s) are encouraged to use a clockwatch or similar). To represent the structure of \text{One}^4, I will use the following graphic representation of a time-bracket


where the blue bars represent the starting and ending time-intervals (also pictured in black), and the red part shows the internal overlap between the two. Consecutive time-brackets in the score can overlap as well, and these external overlaps will be represented with a darker shade of blue, as such


Though \text{One}^4 is written for a solo musician, there is in fact two sets of time-brackets, one for the left hand with six time-brackets, and one for the right hand with eight time-brackets. The total length of the piece is 6’55”, and the temporal structure of the time-bracket can be depicted as such


As compared to other Number Pieces, for example \text{Five}, \text{One}^4 is much more asymmetrical. The time-brackets themselves, for example, can be asymmetrical: observe the last one in the right hand part, or the second one in the left hand part. But the external overlaps are also peculiar, especially in the right hand part.

We can also see that the right hand part is denser, especially at the beginning of the piece. Some time-brackets even start right in the middle of the previous one: observe for example the time-brackets 2 and 1, or 5 and 4 as well as 6 and 5. Cage singled out these time-brackets in the score, and encourages the performer in the score instructions to find a suitable solution to accomodate these time-brackets together.

But the real peculiarity of \text{One}^4 lies in the sonic content of the piece. Not every percussion instrument is acceptable, as the percussionist should only use cymbals and/or drums from a drumset. Each time-bracket contains a number, which corresponds to one cymbal or drum in the chosen set-up, and which also corresponds to a single sound per time-bracket. Here comes the first oddity. In total, we have 14 single sound events played in 6’55”, which amounts roughly to 30 seconds per sound events. In other terms, the sonic density of this piece is very low, and this is all the more surprising for a drumset piece ! When we think of a solo drum piece, we might be used to stuff like this :


So Cage goes to the other extreme by presenting us with a piece with almost no sounds, and certainly without rhythm.

But there is more. The score instructions say that the sounds should either be long, i.e. a tremolo with individual attacks which should not be heard, or very short, “without resonance, completely stopped“. This means for example that a single hit on a cymbal (or a drum) which is allowed to ring after is not an acceptable sound for \text{One}^4. Fritz Hauser confirmed it to me in a private e-mail conversation, and having these two types of sound was important to Cage. You can find more information about this in the DMA essay of Kevin Arthur Nichols :

  • “Important works for drum set as a multiple percussion instrument”, Kevin Arthur Nichols, DMA Essay, University of Iowa, 2012, available here.

A damped cymbal (either with a piece of cloth, or by hand) or a muffled drum would be acceptable in this piece. On the other hand, a cymbal roll with soft mallets would satisfy the requisites for a long sound. We thus see the second oddity in this solo drum piece: the performance calls for sounds which do not usually belong to the “traditional” way of playing drums (see above video). Using short sounds also has consequences for the interpretation of time-brackets. Indeed, if very short sounds are used, they start and finish almost at the same time and therefore can happen only in the internal overlap of the time-bracket. A long sound can be of any length and can thus be started and ended anywhen within the time-bracket according to its rules.

In a sense, \text{One}^4 could be seen as the “anti” drum set composition: no rhythm, and very extreme types of sounds. It seems that Fritz Hauser was thinking the same, as he mentions that ” (…) it creates a very intense counter-point to most other drums set pieces I know which mostly keep the performer quite busy” (see reference above). Being scarce, the piece also helped Hauser to appreciate the special timing of sounds and their relation with silence.

To finish this note, I’d like to present my own version of \text{One}^4, which I developped algorithmically following the ideas presented in a previous post. In selecting the sounds, I’ve made an extreme choice: this version would be played on a single ride cymbal (a Sabian XS20 Medium ride). Indeed, a particular configuration of the drumset could be having ten identical cymbals to play from (the score instructions mentions cymbals and/or drums), corresponding to the ten different sounds in the score, which amounts to playing everything on a single cymbal, though the ten sounds should be all different from each other. The selected sounds are:

1. Damped drumstick on the outer rim
2. Damped marimba mallet on outer rim
3. Undamped brushes tremolo
4. Damped timpani mallet on outer rim
5. Damped drumstick on bell
6. Damped marimba mallet on bell
7. Damped brush stroke
8. Undamped timpani mallets tremolo
9. Undamped drumstick scraping
10. Damped scraping with an Allen key

When I exposed this idea to Fritz Hauser, he was somewhat reluctant with it as he felt that this did not really went with Cage’s concept. However, he said that if one could indeed produce ten different sounds on a cymbal, Cage would probably have liked it. So here it is anyway, feel free to comment. You can find ten different versions of \text{One}^4 with the above set-up at the following adress, and I plan to upload more in the future.

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