Listening plays a fundamental role in jazz improvisation; but is it necessary for each player to hear all others in a successful improvisation? To better understand the interactions and dynamics of improvisation, a two-part project was started. The project is pursued with hopes for symbiosis between pragmatism (musical experiments) and theory (mathematical models).

Experiments were conducted to provide guidance in developing a mathematical model to describe how jazz musicians listen and process information during an improvisational session. Four musicians participated in a total of nine improvisational sessions. Each piece was created through a different controlled listening network structure that dictated who could hear whom.

The most widespread example of controlled listening in jazz is overdubbing. Overdubbing is a process by which musicians record their parts in layers at different sessions. Perhaps the bassist records their part and then individually the parts of the other musicians are recorded, each hearing only the bass part. Alternatively, subsequent parts could be recorded in succession. In overdubbing the recording is not in real time; the information only flows in one direction. Overdubs also allow the musician to hear the original recording as many times as needed, creating a carefully reactive and not interactive performance. In other words, there is no real-time feedback.

In this paper we focus on the experiments, and an additional paper, which is in progress, will outline the mathematical model.

Related Work

In fields like economics and philosophy of science there is somewhat similar work. Major questions pursued include the formation of information sharing networks [1], the flow of information on networks [2], and achieving consensus on a network [3]. A network in these contexts is a set of vertices and directional edges that represent individuals and the flow of information between them. In our project this is the same; the network is the controlled listening structure. That modeling focuses on collaborations that lead to truth: cases where there is only one “answer.” We hope to generalize this by contributing models that focus on many “right answers.” In terms of jazz a “right answer” is ambiguous and we explore several interpretations of it in the modeling. For example, a “right answer” could be a decision by the “audience,” or it could be the consequence of group consensus at different time-scales of the piece. Our model also involves path dependency; the creation of the piece is part of the piece.

Methodology

The first set of experiments were conducted in the summer of 2015. We brought together four improvisers, M.F.A. students at the University of California, Irvine’s program in Integrated Composition, Improvisation, and Technology (ICIT): Anthony Caulkins (guitar), Molly Jones (saxophone), Anna Okunev (violin), and Jordan Watson (guitar). As a graduate cohort, the musicians already had two years’ experience improvising together in various configurations.

Each improviser was isolated in a separate space, with no acoustic or visual communication. Each space was acoustically treated to prevent sound from carrying.  Each improviser was given a set of headphones through which they could always hear themselves and sometimes other players, depending on the network setup.

The improvisers were told that all musicians would be playing in every piece but that they might not hear everybody. They were not told which network structure was being used. The improvisers had no additional information.

Sessions

The sessions below were tested in a random order (with the control first), but they are grouped below to discuss different network structures. Where appropriate we have made preliminary notes below; however, each network requires further analysis, as discussed in future work.

Control

This is a standard improvisational session. Everybody can hear everybody else.

One node removed

Removing one instrument’s input doesn’t appear to create a clear group musical impact. Halfway through the track we can hear an idea played on saxophone carried to the violin and end up back at the acoustic guitar, showing musical information carry through the formation.

Star

The star is a network with a central performer who sends and receives information from the three other musicians, while the other musicians are not connected. This network presented some of the clearest distinctions between experiments. In the version with the electric guitar leading, the performer started first and maintained the same idea throughout the improvisation. They did not alter their performance throughout, possibly as they were unable to isolate any musical ideas to use from the three unrelated streams of musical material. This strongly contrasted with the tenor saxophone version, where the performer instead chose to play very sparsely and attempted to interpret all the unconnected incoming information.

Star with Circle

Preliminary analysis did not show significant differences between this network and the network with one node removed (described earlier).

Single Direction Circle

In this network the information travels in a circle. For both sessions the music is chaotic for a few minutes before noticeable convergence of ideas is clearly heard. We have split the music into three sections: the chaotic beginning, the moment of organization, and the remainder. Each section of the pieces is being analyzed further.

Disconnected Guitar

In this network the guitar receives no input and is essentially playing a solo piece of music. However, their musical information is being leaked into the violin player’s earphones in real time. The purpose of this is to see if the other players realize that there is a stream of musical information coming into the piece that they have no power in altering. They must integrate this musical informational or else succumb to noisy musical disagreement. We observed successful integration of the guitar’s piece in the smaller circle of musicians.

Future Experiments and Directions

The first round of experiments, as described in this paper, has guided the development of a simple mathematical theory. To test results of the theory we will simplify future experiments to include only percussion instruments. The theory keeps track of the flow of musical ideas under different network structures. By limiting the instruments to percussion, we are reducing the complexity of the output of the experiments. We can then apply mathematical tools to analyze the binary sequences that result from the experiments and relate these results to the theory.

Far into the future, once the theory has been fully refined, the goal is to integrate the theory into computer programs to have “intelligent” and “creative” computer improvisers.

References

[1] Bala, Venkatesh and Goyal, Sanjeev. A noncooperative model of network formation. Econometrica, 2000.

[2] Rowe, Robert. Machine musicianship. Massachusetts: MIT press, 2004.

[3] K Zollman. The communication structure of epistemic communities. Philosophy of Science,

74:574–587, 2007.

[4] Zollman, Kevin. Social Network Structure and the Achievement of Consensus. Politics, Philosophy, & Economics, 11:26-44, 2012.

Santiago Guisasola is a doctoral candidate at the Institute for Mathematical Behavioral Sciences at the University of California, Irvine. His research touches on group cooperation, collaboration, and creativity. On the side he plays with music and music technology.

Richard Savery is a music technologist, composer, and improviser performing on saxophone, clarinet, and flute. He completed an M.F.A. in Integrated Composition, Improvisation, and Technology at the University of California, Irvine and is continuing graduate studies at the Georgia Institute of Technology. His research focuses on artificial improvisers, robot musicianship, and machine learning. www.richardsavery.com