3 Environnements


1. Verhulst Populations 
2. ‘Vegetarian’ Lottka-Volterra Model 
3. Zombie Apocalypse

This composition explores three different ways separate musical elements can coexist, compete, fight each other in a musical space.

"Verhulst populations" (the first movement): a dominant species (Charleston-style moto perpetuo played by the pianist) takes up most of the space.  Many different other musical species try to settle in, most of them becoming quickly extinct.  The ecological models developed after Verhulst mainly predict that any ecosystem will have a carrying capacity to which the species will tend to stabilise either by reproduction (if it is under the carrying capacity) or sickness/sterility (if it is over it) or ; it is used for instance to choose proper harvesting quotas, but also predicts that humanity will face a major decline in population growth at some point. In this music, the 'piano species' declines (less Charleston, more of the other musical objects) very slowly towards a carrying capacity of roughly two thirds of the available space.  Towards the end all the present little things go extinct due to overcrowding (the system was apparently more stable with more Charleston).

"The 'Vegeterian' Lottka-Volterra" presents a predator-prey system with two species: piano + vibraphone (the predator), opposed to the other instruments - the prey.  The Hudson Bay Company, in the late 1800s have censused the populations of hare and lynx in central Canada for commercial purposes, and a few years later Lottka and Volterra independently established mathematical models that fit that data:  in short, when one of the species (say the prey) becomes too scarce, the other one starts declining (no more food), so that now that there is less predators around, it reproduces more easily, and again now that there is food, the predator population will start rising again, until there is too little prey left to eat, and so on.  The thing is in the music, I decided the 'predator' becomes vegeterian, stops eating the prey and both species now are in competition for the rest of the food, which causes proliferation and the extinction of both species.

The Zombie Apocalypse model (Mund, Hudea, Imad, Smith - Carleton University) was developed very recently as a classical epidemiologic model with a twist: the 'infected' individuals will die, but they may become undead and then contribute to infecting ('eat the brains of') other healthy individuals. In my composition, the zombies are represented by the drum-set, and the individuals being attacked (mathematically, the susceptibles) are played by the other instruments.  Of course, I opted for the scenario where they all become zombies, but in reality (well...let's hope not) in case of a zombie 'infection', all humans would die, and a fraction of them would turn undead.  The model does not predict what happens when there are no more tasty human brains for the zombies to eat...


  • The first movement was (by coincidence) composed just a few days before the Charleston shooting, June 2015 - the choice of this rhythm has no link with the event.
  • I do not have a negative opinion of vegetarism and/or vegeterians. 
  • I do not consider performers, DJs and composers of drum and bass or jungle music as potential zombies, or as a threat to anyone.

Premiered by Continuum on September 19, 2015.

André Ristic CA

André Ristic was born in Quebec city, completed his studies in Montreal (piano, harpsichord, composition, mathematics), then was pianist at the Ensemble contemporain de Montréal and the Trio Fibonacci.  He is currently pianist and keyboardist at Musiques Nouvelles (Belgium) and European contemporary orchestra (France), and splits his time between Canada, Belgium and eastern Montenegro. As a composer he has been frequently recognised by distinctions, and his catalog sports 6 major orchestral works, 7 string quartets, one opera (soon, another...) and many works for piano and chamber ensemble.  His music stands stands somewhere between process/repetitive-minimalism and multi-genre collage, with a preference for irony, humour, and unnecessary simplicity and complexity.

André Ristic