Physics-inspired algorithmic composition

Recognizable, yet unique, harmonic and rhythmic structures emerge from the models described above. This leads us to explore how these statistical mechanics models allow us to stochastically compose music. For example, a three-dimensional arrangement of tones, interacting via dissonance with their neighbors, quenches into a state with single-pitch domains. Neighboring domains tend to represent consonant intervals, and the lines along which three or more domains meet form a branching network of harmony. (This network is directly analogous to the "cosmic strings" that may have formed from a similar phase transition in the early universe.) By following a random walk along this network, we can obtain a harmonic progression. By choosing pitches along this walk according to the principles of musical voice-leading and counterpoint we can create melodies that harmonize. And these pitches can be arranged in time by a rhythm stochastically generated to conform to a regular beat, while also displaying variation. Some or all of these approaches can be combined with more traditional algorithmic composition techniques, such as markov chains, to produce a wide variety of musical composition.

Read more here about harmonies from "cosmic strings": Critical behavior and the Kibble-Zurek mechanism in a musical phase transition.

We have developed software to put these ideas into practice, along with tools for adding additional muscial structure and expression, and for vizualizing the output. In collaboration with Alex Cooke at the Cleveland Institute of Music, we are exploring new modes of combining human performance and composition and technology. We are grateful to Dean Ward and the CWRU College of Arts and Sciences Expanding Horizons Inititative for providing support for this work.

Here is a demonstration of the software, showing two pieces generated in real time, first for piano and viola, and second for a jazz ensemble:

We have explored several implementations of the composition algorithms. The initial impetus for developing these algorithms was to create music from physics-based models of harmony and rhythm. The model we developed of harmony as an ordered phase of sound yielded harmonies that were similar, yet somewhat different, from familiar western music. These pieces are usually at least somewhat atonal, as in this piece performed by Huan Zhang at the April 2022 performance “Crystals of Sound”:

By adjusting the parameters in the physics-based model of harmony, we can generate other musical systems as well, such as a microtonal 31-tone octave, used in this piece:

The same algorithm that generates harmonies from the physics-based model can also be adapted to take harmonies specified by other approaches, such as a Markov model. In such a model, the probabilities to change from one harmony to another are specified and the harmonic progression is set according to these probabilities. This allows for the shaping of harmonies to match particular genres of music, or particular composers. Just a couple of examples include a brass trio:

And this Halloween inspired piece:

Going even further, a particular harmonic progression may be specified as desired. This allows for algorithmic composition that will harmonize with a particular melody, or allows creation of a variation on a particular melody. For example, Berezovsky has developed several “Goldstone Variations” in which the parameters are set to mimic the style of one of Bach’s “Goldberg Variations,” while following the same harmonic progression used by Bach. One such Goldberg Variation is seen here, performed by Huan Zhang:

An example of algorithmic accompaniment is heard here, where Berezovsky is playing the tune to “I’ll be home for Christmas” along with an algorithmic piano accompaniment:

The algorithm also has the ability to adjust how closely a given melody and rhythm is followed as a motif, allowing one to generate variations on a familiar tune. That is done here, with Berezovsky playing along with some variations on “Somewhere Over The Rainbow”:

And many more compositions are available here. Or listen below: