This piece was part of my work towards M.F.A. in ICIT. For more details on the overall work go here
This piece is completely improvised by the computer and human performer, with a short computer composed melody the only set material. The computer part is represented through the sounds of an electric guitar, bass and drum set, each of which carry their own musical identity that interacts with the human performer. These musical sounds are based on the mathematical formula of the Henon Attractor which creates chaotic unpredictable results. At two stages melodies are composed by the the computer and given to the human performer via the iPad.
Two recordings Henonistic are below. The two different takes should give an impression of the variance between performances (if you use the “I” to get a free download you can listen to a much higher fidelity version).
Below is an excerpt from my thesis paper discussing this piece. Read the full paper here
In my own work I have used the Hénon map (created by Michel Hénon) to create a musical improvisation partner, utilising the orbit of the Hénon map to create every musical component. Additionally, I use the Hénon map to decide musical directions and impact the overall structure. The Hénon map is a two-dimensional map that takes a point and moves it to to a new location using the algorithm below.
The Hénon map is an example of an iterative process and is a discrete dynamical system that shows chaotic results. A discrete dynamical system moves at chosen time intervals, and continually uses the same formula to move to new locations. Chaos within mathematics applies to systems that through slight variations in their initial conditions can show drastic changes. More importantly to my own use is the tendency of chaotic systems to create highly structured orbits, with a logic that is not often easily discernable. The Hénon map is particularly effective for musical patterns because it displays a regular orbit, albeit with chaotic results that contain intermittent outliers. By using an underlying formula such as this, I believe it is possible to create the illusion of an intelligent organised system that has somewhat predictable results, but does show occasional creativity through the chaotic movements, reaching beyond the more predictable patterns.
I would argue that developing a balance between predictability (the regular orbit) and unpredictably (the chaotic results) is key a part of Western music, assuming repetition itself is not the aesthetic basis of the piece. Pierre Boulez describes all Western music as ‘caught up in a “dilemma” involving repetition, variation, recognition and the unknown’. Iterative processes can be considered a form of musical composition through their internal repeating process which creates recognisable patterns. With the addition of chaotic results as the ‘unknown’ these formulas can be used to create musically effective output.
Through experiments substituting the Hénon Map with alternate formulas or with random values, it became apparent that this use of an iterative formula did contain musical significance. While my use of the Hénon map does produce defined harmonic and rhythmic characteristics, this sound is never identical in subsequent performances. I would liken its output to that of a performer reinterpreting improvisational guidelines in each performance. I use multiple iterations of the Hénon map in my composition, with each version operating at a different speed of output. This has the effect of parameters (such as harmony, rhythm and structure) moving at different speeds. I intend for this to allow for very direct mappings from the variables created by the Hénon map to musical parameters, without sacrificing musical interest.
My piece uses three conceptual instruments (drums, bass, and guitar) performed by the computer with a bass clarinet performed by the human player. I divide the piece into three layers (demonstrated in Figure 2), although the layers communicate between each other and they are all highly intertwined. The bottom layer creates the decisions of each instrument using musical ideas generated from the Hénon map and an interactive component from the bass clarinet part. The middle layer decides how each instrument will interact, using a game-like system developed for the piece; this is the only section that doesn’t rely on the Hénon map. The top layer acts as a greater structural conductor and decides on instrument combinations (solos, duets, trios or quartets) and when key moments of melodic unison should begin. The top layer combines the output of a Hénon map with the input from each instrument to decide the overall direction.
I also have a global harmonic foundation underpinning the work based on the scaling of both the x and y values of the Hénon map to a note in the Western chromatic scale. I then divide the distance between these two notes and add a note halfway between (creating a triad) before adding a 7th on the chord using the distance between each note. This creates a sequence of four note chords that each run for 16 beats, which defines the harmonic progression for each improviser. The choice of 16 beats is arbitrary in nature, as rhythmic ideas cross and accents are articulated with different placements, no meter is ever perceived.
Each instrument uses the Hénon map in a slightly different way, but one common characteristic is to use the x and y values to create rhythmic lengths. As a basic variation each value of x and y could be multiplied by 100 to create a note length (in ms) and once these notes end the next point in the map is created to output the new note lengths. By using this internal structure from the Hénon map across multiple iterations, combined with the input of a live performer, it is possible to create many unique and changing improvising environments.