João Carlos Pacheco


On the academic year of 2014/2015 a possibility to go to the Darmstadter Ferienkurse Für Neue Musik was given to the students of the Masters in Contemporary Music, as long as they would participate in a research project by professor Michel Roth. This project was centered around the figure of David Tudor, the works that some composers wrote specially for him, and his idiosyncratic characteristics as an interpreter. I would participate in the project by creating a version of Variations I by John Cage. For me, the project was one of the highlights of that year. I always appreciated John Cage as a composer and thinker and never had so much time to prepare a version of his open score pieces.

When doing research on the piece and on the interpretation of open forms and graphical scores I realized that there are not so many texts written on this field. I decided that this Master Arbeit would be centered on the process of creating of a version of Variations I for three reasons: I would like to have a document that would describe the work I had done, I would like it to be research material for other people attempting the same task and I would like to analyze the work I had done for the reason that in a way it shifted some of my ideas on interpretation. The opportunity to write about this as my Master Arbeit seemed to incapsulate these conditions.

Notice that this paper will not focus on biographical aspects of John Cage or his work. It will be focused specifically on Variations I and the process of interpreting the piece.


The Score and its text
Variations I was written by John Cage (1912-1992) in January 1958. A late birthday gift for the pianist David Tudor, it is also the first of eight pieces that Cage would write on this series during a period of ten years. This series would constitute a major example of indeterminate music and graphical scores of the second half of the 20th century.

Variations I material consists of squares of transparent plastic, five squares with lines, one with different sized dots and an introductory text, giving the guidelines to how the piece should be interpreted.

The most important part of the score is its explanatory text. Without this text the lines and dots would be mere symbols without value and relation between each other and the piece would lose its strength and core essence.

Image 1 - John Cage’s text for Variations

Image 1 – John Cage’s text for Variations I

This text serves the purpose of explaining the possible ways to read the transparent squares by giving the following indications

This text serves the purpose of explaining the possible ways to read the transparent squares by giving the following indications:

  • What the score is composed of
  • Definition of the dots
  • Definition of the lines
  • Relation between dots and lines
  • Instrumentation

Interpreting the text is not an easy task. On one side it seems to state simple and logical ideas, but on the other side the way Cage uses written language to explain the musical process is not the most simple and clear. Therefore, there are many different interpretations everywhere. In Darmstadt, during the final performances of the piece by the students of our Masters in contemporary music, one could see many different paths and ideas taken from the same text and score. That is one of the most beautiful aspects of the piece, and it is to a large extent what separates this type of scores from more traditional and closed ones.

It is difficult to state if Cage wanted this explanation to have an unclear meaning or if the arrangement of words to explain the piece was for him very clear. I can only say that in my experience it took a long time and many failed attempts to start writing a version but after reading the text many times, and going back and forth between ideas, I found a basis to start sketching an interpretation. Notice that after reading it one year later I keep finding new ways that I could have followed to interpret the score. So, the version I created of Variations I is, to some extent, just a continuation of the readings done one year ago. A new version could start with a different approach. For that reason this paper is descriptive of a possible journey and not a definite compendium of ideas about the piece.


After a period of reading and studying the text I arrived to some conclusions. The first was related to the ending: ‘’Any number of performers; any kind and number of instruments’’. After a long time considering the idea of not using percussion, which is my main instrument and area of work, I decided that I would do a computer version of the piece. I had started to program and use electronics more regularly about one year before beginning this project and thought this could be a good test to see how I could workout a creative way to use the computer as a musical tool. In this chapter I will not go into detail about how the computer was used. The computer’s role will be understood in later chapters when describing the treatment of sound sources and the building of a playback program.

The function of the dots and their size is the most clear element of the text. Dots are organized by size in order to determine how many sounds are played when interpreting a specific dot. The function of the lines is also a clear one, they determine five characteristics that will shape the dot’s sounds. What is open then is to choose which transparent sheet of lines to use. The definition of which characteristic each line takes is also opened to interpretation. I decided I would overlap the dots with a square of lines that came to my hand. The dots were then overlapped with page 5 of the squares. A function was also given to each line.

Image 2 - example of the Least Duration line and overlapping of the transparent sheets

Image 2 – example of the Least Duration line and overlapping of the transparent sheets


By this point the basis for interpretation were set and certain criteria were defined:

• Computer as instrument

• An overlapping of dots and lines as graphical score

• Distance from dots to lines as definition of sound characteristics

Other elements were to be defined or developed later and would constitute the core thinking process for this version:

• Measurement of distances vs observation

• Sound material

• Playback program

These departure points may seem simple but in fact they were not. It is safe to say that these conclusions only appeared on a third meeting for the project (meetings were held with the project organizer, Michel Roth, to record the process of our work). I discarded the ideas presented on the first meetings after entering a phase of development. They all seemed to go into dead ends. Either they were not coherent between interpretation and score, once re-analyzed, or technical issues arrived and could not be fixed.

The problems of the first ideas were based on the fact that they carried too much information during an early stage of the process. I had already made assumptions about sounds, treatment of sounds and building difficult programs to execute all I thought about but without paying closer attention to the text, therefore giving space for the incoherences and problems mentioned before.

This simpler and more compact starting point proved to be the best solution for a solid beginning.


As seen on the explanation of Variations I, John Cage describes two paths to follow in order to measure the distance between points and lines. One can either observe the distances or measure them. I decided to find out the exact distance from each point to the lines. Although this system functioned in a fine manner there was one point to take in consideration: as the lines are not going through the entire square I had to consider how to measure points that were past the end of the line. In this case I measured them to a point near or in the end of the line. Other solutions could have been found, like extending the lines ad eternum and measure perpendicular lines from the points to those extensions. This last solution only came to my mind after the first performance of the piece. If I would rewrite my version, I would use that measuring system.

Image 3 - Measurements of Simplest Overtone structure

To store the data recovered from the measurements I decided that all points would be named and I should create a table containing the values of each characteristic of the sound. The points were named according to their size, therefore also to the amount of sounds that each contains:

Points with 4 sounds: ”A” (A1, A2, A3, A4)

Points with 3 sounds: ”B” (B1, B2, B3)

Points with 2 sounds: ”C” (C1, C2, C3, etc.)

Points with 1 sound: ”D” (D1,D2,D3, etc.)

After concluding the measurements I grouped all the recovered data and created a table with all the distances from points to lines for each of the characteristics of a sound. After having this table organized, ordinal numbers (1st,2nd,3rd, etc.) were given to organize this characteristics. Ex: Point ”A1” is 9th on the occurrence in timeline, 9th sound with least duration, 15th sound with lowest frequency, 16th sound with simplest overtone structure and 15th sound with greater amplitude After all distances were measured and analyzed a final table was found, containing all the necessary numbers to create each sound and respect their relation to other sounds

This gradation of each characteristic was of great help for further compositions because of the simple way it offers to organize sounds according to their specific nature.

Image 4 -Final Measurement’s Table

Image 4 – Final Measurement’s Table




’I believe that the use of noise to make music will continue and increase until we reach a music produced through the aid of electrical instruments…’’ – John Cage – The Future of Music: Credo in Silence (1961)

One of the motivating aspects to create this version of Variations 1 was the possibility to get away from my previous percussion experience and dive into a more broad sound world permitted by means of electronic and digital manipulation, much inspired by the transcribed quote from John Cage.

As a percussion player one has the freedom to work with a immense palette of sounds, and percussion was always a major subject in Cage’s music, so it would make perfect sense to use those means to create this version. With the development of noise, and with the time percussionists invested in this development, one lives in an era where percussionists are the type of musician that a composer will ask for if he wants to find and manipulate new sounds. But those sounds are still created in the analog world, the real world. On the other hand, playing with a computer takes sound production one step forward. With the means offered by the digital world you can create new sounds or manipulate sounds from the analog reality and then turn them into an imaginary sound creation before bringing it back to the ”real world” with ‘’new clothes’’ and qualities.

The freedom offered by means of a computer motivated my choice, but soon I found out that I would need to establish some boundaries to take benefit from these means. To establish those boundaries I should ask myself a few questions.

This idea of asking pre-compositional questions seemed to be a good beginning for the fact that ‘’Cage was still involved in a certain structuralism‘’ (Wiggins, 2009) and used to ask himself a few questions regarding musical events before writing his pieces, as Steven Schick wrote: “For all of the apparent freedom in compositions from his indeterminate period, he remained committed to the need for discipline and process in composition. “Anything goes as long as nothing else matters,” he said once in a public lecture. He was also undeniably attracted to chance – to the inevitability that what would actually happen in a performance of music could not be completely foreseen by him or anyone else.”(Schick, 2006)

Image 5 - ( page 3, one of the pieces analyzed for this project

Image 5 – (…000…).pt page 3, one of the pieces analyzed for this project

My questions were the following:

  • How could I bring a personal character into the version?
  • If I wanted to include a personal input, what were the recurring sounds I used in my previous compositions?
  • Even if these sounds were personal, how could they reflect the figure of John Cage?
  • Would this be a very active version, or would it be a version with more subtle nuances?
  • How would the choice between active or subtle nuances shape the choice of sounds?
  • Would this be a version for electronic sounds only, sampled sounds, or a combination of both?
  • Which sounds could I choose that would let me use the characteristics taken from the measurements and play around them?

I believed that finding answers to these questions would eventually lead to encounter sounds that would respect composer intentions, and yet be personal, shape the piece’s character and take advantage of a computer while still maintaining some characteristics of human performance.

As I started to think about the possibility of bringing my personal input to the piece, and since the piece was to be performed in a lecture about David Tudor and the way that he brought input through his playing techniques and sounds into the pieces he interpreted, I decided that the sounds I would use should be somehow personal. Knowing that, I started to answer my second question and I went into an interesting process of analyzing works that I had written before. This turned out to be one of the most exciting points of the entire process, for the fact that it made me criticize my own work in a way I had not done before and then coming to the realization that there are in fact recurring sounds and manipulations that I tried to include in my pieces, even if some were more or less conscious choices.

From the analysis process I realized that these were the most important features:


  • White noise
  • Sine tones

Modified samples and recordings

  • Voice
  • Field recordings
  • Sampled percussion sounds

I also noticed that some techniques were recurring:

  •  Filtering
  •  Looping
  •  Distortion/Overdriving

Once I found these answers, it seemed logical that using the sounds that are recurrent in my previous experiences and finding a way to make it aesthetically close to John Cage’s work would be a good path to follow.

It seemed like an exaggeration to analyze all of Cage’s work and get it all as he would do it, it also seemed to be the wrong way to go because a personal interpretation, or a personal sound world, would be out of the question in that case. Taking this in consideration I decided to read Cage’s books, listen to interviews, documentaries and putting that together with the aural knowledge that I had previously acquired from playing and listening to much of his music.

I restricted myself to a few characteristics of Cage’s figure and work that I specially enjoyed:

  • Humor
  • Silence
  • Chance
  • Noise

Image 6 - John Cage’s smile. A trademark of his personalityImage 6 – John Cage’s smile. A trademark of his personality

Regarding the idea of having a very active version or a version with more subtle nuances I chose the second. The purpose that lead me to that was the fact that I could play around with very small tweaks and make slight modifications of the sound material by means of the computer. These type of small changes would not be possible in a percussion version, thus this idea seemed to take advantage of the means that I was going to use. From this thought derived the idea of making changes that are so small that our ear can not perceived them, as well as using correct interpretations of the score, according to the table created with the measurements, that result in an illusion that what we hear is incorrect. For example , by taking absolute values of amplitude without any regard for pitch one will perceive a high sound to be louder, even if its amplitude is slightly lower than the one of a low sound. This idea was much influenced by a documentary on the making of John Cage’s chess video piece where he plays a chess match against Marcel Duchamp’s wife. While talking to the camera man about how the camera works he asks that the young man places the focus on a number for one shot and then on a number very close to it for the next one. The young man answers that there is no difference between having the focus on either of those numbers because the image will appear to be the same. To this answer John Cage says: ‘’ I’m not concerned with what we see, I’m concerned about being able to tell you where to put it. ’’

The choice of having a version with subtle nuances immediately gave me the idea of using drones as the main musical material. I expected that by creating different drones I would be able to come up with a piece that would be more on the side of a still soundscape than of an active piece with much dramaturgy. By defining that drones would be created as the main sound element I started to focus on the next question.

After analyzing the recurrent sound elements of my other pieces, as I talked about before, it was clear that a version with sampled sounds as well as very pure electronic sounds was to be created. This way I could use field recordings that I had, something that would fit Cage’s ideas about freedom of sounds such as in traffic, create long drones of sine tones and use the ‘’airy’’ sounds of filtered white noise. I could imagine that these choices of sound would also be great material to experiment and play around the information I had gathered from the measurements.

After these answers were found I decided that the following would be used as sound material:

  • Samples of John Cage’s voice (taken from ‘’19 questions’’ and ‘’About silence’’ – documentaries with John Cage)
  • Two distorted field recordings of trains
  • Organ-like sine tones
  • Filtered white noise
  • Glitch sounds


In this question/answer pre compositional process I found it interesting to notice how answering one question could immediately give answers to other questions, create more subquestions and how one decision could affect an entire chain of thought.

On treating the raw material

Once the sound materials were found one needed to find ways to treat them and make it fit to the table of measurements. In this chapter I will explain how these processes functioned for each characteristic of the sound. But before, the reader should know that just when starting to treat the sounds I came up with the idea of randomizing the playback between sound materials.

At this point I played with the idea that the program used to play the piece should be able to decide from which material it would play the next sound event. I would then make all the sounds with each sound material. This meant that now I had to do five times more sounds than originally planned. Now A1 could come out as a sample of Cage’s voice, C3 a filtered white noise, B2 an organ like sine tone etc.. Any material could come out, so every dot should be represented in each sound material. This way of playing back Variations I could be seen as having 5 pieces within a piece. Here, I also decided that I would use the glitch sounds as a way to create the amount of sound events that each dot contains. This means that on all sound materials I added three initial ‘’clipping’’ sounds for every dot with four sounds (1 sound from the layer + 3 clipping sounds = 4 sounds), two for dots with three sounds, one for dots with two sounds and the the dots with just one sound were made out of their according sound material. These clipping sounds are very recognizable in the piece and were meant to give a certain structure to a version that plays from different sound materials.

This was the point where most artistic freedom was taken. Now the sounds would be related as a whole, and follow Cage’s rules, but the machine would choose which layer it would play from. As there was no perfect relation between each layer the rules were now more flexible and in some cases even broken. Nevertheless I decided that this freedom could be taken and still be in accordance to other ideas that were ruling this version. I came to this conclusion by thinking that this decision takes Cage’s musical work in consideration for, on a more or less conscious level, I was taking concepts that he used on his pieces with radios. One can consider the random change of layers do be equivalent to the changing of radio stations on Cage’s pieces. It is as if 5 pieces are simultaneously running and we are jumping between them. On the most recent version of the patch one can also choose to listen to a version with only one sound material or the mix of sound materials. Notice that versions with only one sound material are in complete accordance to the score and its rules.

Sound material and treatment of each characteristic

Many times it happens that different layers have different processing of sound. Here are the processes used to treat each characteristic of a sound event, according to sound material. To realize these processes Apple’s Logic Pro 9 (DAW) and Cycling 74’s Max6 were used.

Notice that least duration and earlier occurrence in a given upon time are explained later.

Sine tones

  •  Greatest Amplitude

The amplitude of the sine tones, as already mentioned before, is a proportional representation of the measurements. Using the multiplier object in the synthesizer that was built with MAX6 to create the organ-like sounds I controlled the amplitude (from -1 to 1) of each sound event.

  •  Lowest frequency

This characteristic was treated as a direct representation, on the fundamental pitch for each sound, of the order of the data gathered during the measurements.

  •  Simplest overtone structure

To control this characteristic I used addictive synthesis. The fundamental sound was always the most present and the amount of overtones of the composed sound was defined according to the table of measurements. The simplest overtone structure of all is therefore composed of only one sine tone and then each of the more complex received added sine tones on top of the fundamental.

Image 7 - a graphical representation of a sine toneImage 7 – a graphical representation  of a sine tone


White Noise

  •  Greatest Amplitude

The amplitude of the white noise layer was treated in the same fashion as the sine tones. It is a proportional representation of the measurements. Using a multiplier object in MAX6 I controlled the greatest amplitude of each white noise event.


  •  Lowest frequency

To define the Lowest frequency a hi pass filter was used. According to the order of the table, each track was filtered in order that the lower frequencies were cut off. The lowest in frequency was therefore cut at a lower frequency and the higher track was cut at a higher frequency.

  •  Simplest overtone structure

To define the overtone structure a low pass filter was used. According to the order of the table, each track was filtered in order that the higher frequencies were cut off. The hi pass filter used to define the lowest frequency and the low pass filter used to define the overtone structure work together as a band pass filter. The sounds with a more complex overtone structure possess a broad band of frequencies and the sounds with a more simpler overtone structure are fit to a shorter band.

Image 8 - Filtering of sound D1 (white noise layer)Image 8 – Filtering of sound D1 (white noise layer)


Field Recordings of Trains

  •  Greatest Amplitude

The amplitude of the field recordings was controlled with the gain of each track. The samples with lower amplitude were always lowered on the gain of Logic (DAW used to create the final samples). The sample with greatest amplitude was not altered and the following were put down by a certain amount of decibels according to the table of measurements.

  •  Lowest frequency

The process of getting the lowest frequency was the same used for the white noise layer. A hi pass filter was used to cut off each samples low frequencies according to the table.

  •  Simplest overtone structure

To get the overtone structure the same system used for the white noise layer was also put to practice. A low pass filter was used to cut off each samples high frequencies and create a band pass.

Samples of John Cage’s Voice

  •  Greatest Amplitude

The amplitude of John Cage’s Voice layer was controlled in the same fashion as the field recordings of trains, simply by using the gain of each track to define it.

  •  Lowest frequency

In this layer I took the concept of frequency literally and did not relate it to pitch. I took frequency as the number of occurrences of an event. In this way I managed to use the process of looping that is characteristic in some of my own compositions and contradict an immediate pitch interpretation of the sound characteristic presented on the score. Each sample was looped according to lower or higher frequency. Samples with higher frequency were looped more times than ones with lower frequency. This decision affected the duration of each loop in order to maintain coherence with the already defined duration of the final sound sample. Final samples with high frequency but short duration were made out of a very small loop and sounds with low frequency but large duration were made out of longer loops.

  •  Simplest overtone structure

This was the most difficult characteristic to work with. Out of a lack of imagination I decided to use the same process that was used on other layers. A low pass filter was used in order to cut off the higher frequencies of each track. Sound events with simpler overtone structure were therefore cut at a lower frequency than events with more complex structures.


Image 9 - Looping of John Cage’s voice samples to control frequencyImage 9 – looping of John Cage’s voice samples to control frequency

It was also in this part of working on Variations 1 that I took the characteristics of Cage’s figure and work that I previously chose (Humor, Silence, Chance, Noise).

Humor is mostly present on the way I interpreted John Cage’s indications of sound characteristics. On the recordings of Cage’s voice I interpreted frequency as being the amount of times an occurrence repeats itself instead of relating it to pitch and on the the sine tones I interpreted amplitude as being the amplitude of the wave form and not real dynamics, to take an example.

Silence is presented by the choice of the duration of the piece vs the duration of each sound event. I made decisions for these in order that long silences would happen during the performance.

Chance, besides the randomization of the playback, it was used to define many of the values within the features of a sound. Most of the filtering as well as some frequencies for sine tones were chosen using chance, within the possible limit that would still keep it in accordance to the other sound events, for example. It was also used to take which moment each sample would be cut from Cage’s interview that I used as the basis for the layer of his voice.

Noise was taken in consideration on the choice of sounds (white noise and distorted field recordings).

With the exception of Least Duration and Earliest occurrence within a decided upon time all characteristics are more or less particular to each sound material. These two are common to all for the sake of coherence. In order to have more coherence in a version with mixed layers I decided that these would be transversal to all.

After this treatments were applied all sounds were finished and only a playback device was missing. Next chapter will describe the building of this device.

Final Stage – building a devic

To be able to play this version of Variations I without human intervention and to be able to automatize some ‘’on the spot’’ decisions one would need to create an original program to play the piece. If this was a fixed media version (ex.tape) any cd player or computer program would be able to play the piece. On a more flexible version, such as this, I decided to design a special playback machine using Max6. Notice that Max6 patches were already used during the creation of the final sound samples, mostly to take care of chance procedures and/or to automatize tasks that would either be very time consuming or difficult to realize manually.

During this paper it was many times referred that the playback device would have determined characteristics, that it would perform certain tasks. It is also relevant that during the creation of the device some other ideas came up and were implemented like, for example, randomized panoramic (sound samples are randomly placed more to the left or right speaker). As this paper does not focus on the technical aspects of building this machine, but rather on the interpretation aspects and decisions taken while creating this version I will resume this last chapter to describing the main characteristics of the playback device. One with the need to analyze how the patch technically works can open it and go through that process.

The main characteristics of the patch are:

  •  Polyphonic playback

This program has ability to play more than 1 sound event at the time. This is a very simple programming task but it is of great importance for it allows that the sound events overlap according to the timeline prepared in advance.

  •  Internal timeline

A stopwatch clock which represents the timeline is embedded in the program. Since the patch was created for a 10 minute version of the piece this clock stops and resets after 600 seconds.

  • Triggering of events on the decided upon time

An automatic sound file launcher was programmed so that the sounds are played according to their correct placement on the timeline.

  • Randomization between layers or choice of one layer

The last version of the patch permits six different listening modes. A mixed wersion where new sound events can be of any sound material or a version that always plays from the same material. Versions with only one sound material follow the rules of the score and versions with mixed layers are more flexible within those rules, as it was said in previous chapters.

Image 10 - Layer displayImage 10 – Layer display

  • Randomization of panoramic

During the performance the program is prepared to distribute the sound files around the two speakers. Once a file is to be played the program automatically divides it more to the right or more to the left speaker.

  • Displays

The program also has displays such as the current count in seconds, name of the last triggered event, layer selector and volume control.

Image 11:12

In sum one can state that this playback device works as an organizer of sound in the moment of performance. It is intended to create a performance that is not ruled by the emotions and feelings of the self but rather place it in a more abstract and contemplative scenario. I believe this fact serves as a possible example for John Cage’s idea that ‘’if this word “music’ is sacred and reserved for eighteenth- and nineteenth-century instruments, we can substitute it for a more meaningful term: organization of sound.’’(Cage, 1961)


After reflecting on this paper I found some answers for questions that still persisted in my mind. It made me realize that my version, even though it was created by modern means, is faithful to the practice of the time when the piece was released. It sounds like a very open and almost improvised piece even if a lot of determination was put into it. It also has a sound world that is dear to me but organized in a fashion that resembles a John Cage piece. By any means would I write a piece like this, but it satisfies me as an informed interpretation practice. If I had to do a new version I would, most likely, do it all different. But the essence of the piece would still be there. It was said during the paper that one answer lead to another as if a chain of thought in a cause/effect process. I strongly believe that this version represents that. A chain, a path, a way to do it, but definitely not the only way.

As a composer I will take many of the strategies I used in this project as means to organize ideas and specially sounds. I believe that the organization of sound by characteristics and material was a very important phase. The thought given to small elements that work as a way to give coherence to the sound events was also very important.

As an interpreter I learned and organized a lot of ideas by creating this version. It strongly solidified the thoughts that I already had about the importance of context in interpretation (historical information, knowing the composer, etc.), using the technical means available to provide the best possible result and it broadened the horizons of how to use creativity as a way to test the boundaries of a score while remaining faithful to it.

Variations I is a landmark in open scores. After doing this realization of the piece I think I better understand why. It definitely made and impact on me and made changes in the way I approach musical practice.

It is my hope that this paper has synthesized the thought process present in my version and that it has shown the reader how amusing it can be to ‘’organize the sounds’’ for this fantastic example of indeterminate music.