Polynomial Functions in Žuraj’s Changeover
- Polynomial Functions in Žuraj’s Changeover
When listening to changeover, an orchestral piece composed by Vito Žuraj in 2011, one hears trajectories of motion that span over many measures and often over many different instruments in the ensemble. These trajectories are across the dimensions of time, pitch, and temporal density (i.e., durations between notes). In this analysis, I plot and investigate these trajectories in search of a deeper understanding of their structure. Often, what can be clearly heard by a listener is not clearly seen in the score because of the quantization in the time and pitch domains required for representation in musical notation. Furthermore, the traditional layout of orchestral scores does not offer a clear time-to-pitch graphical interpretation. This paper analyzes most of the material in mm. 1–86 of Žuraj’s Changeover, which is presented here in chronological order. The analysis is limited to these measures as they include the music that has the most audible trajectories. Each trajectory analyzed was initially identified through listening, then for analysis, abstracted through manual data entry into code or spreadsheets, before being processed in Python using the Numpy, Scipy, and Matplotlib libraries. The content of each section’s [End Page 179] analysis was driven by the musical materials themselves, pursued as the author felt they implied further investigation. These analyses first seek to visually clarify the sonic trajectories being created by Žuraj, thereby secondly allowing for a deeper investigation and understanding of their construction. These investigations are often made by fitting polynomial functions to the trajectories heard in the piece and using these functions to theorize how Žuraj used algorithms to compose the trajectories. It is possible that some of the trajectories heard in the piece were not composed algorithmically, but instead created intuitively by the composer. My analysis seeks to answer how Žuraj may have composed them algorithmically. Some of the analyses suggest more strongly than others that the trajectories in question were composed algorithmically.
Žuraj on His M-Matrix
Many of the methodological and heuristic choices made in this analysis come from a conversation I had with Žuraj about his compositional process. He explained why he uses algorithms when composing, saying,
In the normal process of composing, there are way too many decisions to be made. . . . Some decisions are secondary, like if there’s an eight-note chord and two of the voices have to move, whether it moves to the violin or the English horn is secondary. . . . The technology is a way to free myself of the tons of calculations that would drive my main idea away. When I’m composing, if I have a main idea and then get disturbed by some technical thing, it would get me off road. The computer is a performer of large amounts of basic calculations.
(Moore)
The framework in which Žuraj does his calculations is custom software made in Max, which he calls M-Matrix (Example 1) (Moore). He says that it, “has the benefits of Open Music,1 but in Max” (Moore). When using M-Matrix, Žuraj can input MIDI data through a MIDI keyboard, which then is processed or manipulated in various ways before being sent to the Finale notation software via internal MIDI ports as MIDI data (Moore). Explaining why this workflow is important to him he says, “I am a pianist, I like to improvise, when I wanted to play something I had to do it by ear—this training helped me a lot to develop spontaneous flow of music—to control the flow of music” (Moore). His interest in real-time, expressive data entry is further expressed in his plan for a future development of M-Matrix: [End Page 180]
I wish I had more time to work on voice input into the software. That’s one of the next projects. Every piece I write needs to have one technical improvement.
(Moore)
During our conversation, Žuraj emphasized the use of randomness in his algorithms saying, “I started simple experiments with arpeggios, I found that there are some aspects that work best with randomness. It freed me from some of the decision making that needed to be done...
