Exploring Transfer Functions in Evolved CTRNNs for Music Generation

  • Steffan IanigroEmail author
  • Oliver Bown
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11453)


This paper expands on prior research into the generation of audio through the evolution of Continuous Time Recurrent Neural Networks (CTRNNs). CTRNNs are a type of recurrent neural network that can be used to model dynamical systems and can exhibit many different characteristics that can be used for music creation such as the generation of non-linear audio signals which unfold with a level of generative agency or unpredictability. Furthermore, their compact structure makes them ideal for use as an evolvable genotype for musical search as a finite set of CTRNN parameters can be manipulated to discover a vast audio search space. In prior research, we have successfully evolved CTRNNs to generate timbral and melodic content that can be used for electronic music composition. However, although the initial adopted CTRNN algorithm produced oscillations similar to some conventional synthesis algorithms and timbres reminiscent of acoustic instruments, it was hard to find configurations that produced the timbral and temporal richness we expected. Within this paper, we look into modifying the currently used tanh transfer function by modulating it with a sine function to further enhance the idiosyncratic characteristics of CTRNNs. We explore to what degree they can aid musicians in the search for unique sounds and performative dynamics in which some creative control is given to a CTRNN agent. We aim to measure the difference between the two transfer functions by discovering two populations of CTRNNs using a novelty search evolutionary algorithm, each utilising a different transfer function. The effect that each transfer function has on the respective novelty of each CTRNN population is compared using quantitative analysis as well as through a compositional study.


Continuous Time Recurrent Neural Network Novelty search Audio synthesis Generative music 


  1. 1.
    Ianigro, S., Bown, O.: Plecto: a low-level interactive genetic algorithm for the evolution of audio. In: Johnson, C., Ciesielski, V., Correia, J., Machado, P. (eds.) EvoMUSART 2016. LNCS, vol. 9596, pp. 63–78. Springer, Cham (2016). Scholar
  2. 2.
    Ianigro, S., Bown, O.: Investigating the musical affordances of continuous time recurrent neural networks. In: Proceedings of the Seventh International Conference on Computational Creativity (2016)Google Scholar
  3. 3.
    Ianigro, S., Bown, O.: Exploring continuous time recurrent neural networks through novelty searchGoogle Scholar
  4. 4.
    Eigenfeldt, A., Bown, O., Pasquier, P., Martin, A.: Towards a taxonomy of musical metacreation: reflections on the first musical metacreation weekend. In: Proceedings of the Artificial Intelligence and Interactive Digital Entertainment (AIIDE 2013), Conference, Boston (2013)Google Scholar
  5. 5.
    Van Den Oord, A., et al.: WaveNet: a generative model for raw audio. In: SSW, p. 125 (2016)Google Scholar
  6. 6.
    Kiefer, C.: Musical instrument mapping design with echo state networks (2014)Google Scholar
  7. 7.
    Mozer, M.C.: Neural network music composition by prediction: exploring the benefits of psychoacoustic constraints and multi-scale processing. Connect. Sci. 6(2–3), 247–280 (1994)CrossRefGoogle Scholar
  8. 8.
    Lambert, A.J., Weyde, T., Armstrong, N.: Perceiving and predicting expressive rhythm with recurrent neural networks (2015)Google Scholar
  9. 9.
    Eldridge, A.: Neural oscillator synthesis: generating adaptive signals with a continuous-time neural model (2005)Google Scholar
  10. 10.
    Beer, R.D.: On the dynamics of small continuous-time recurrent neural networks. Adapt. Behav. 3(4), 469–509 (1995)CrossRefGoogle Scholar
  11. 11.
    Bown, O., Lexer, S.: Continuous-time recurrent neural networks for generative and interactive musical performance. In: Rothlauf, F., et al. (eds.) EvoWorkshops 2006. LNCS, vol. 3907, pp. 652–663. Springer, Heidelberg (2006). Scholar
  12. 12.
    Dahlstedt, P.: Creating and exploring huge parameter spaces: interactive evolution as a tool for sound generation. In: Proceedings of the 2001 International Computer Music Conference, pp. 235–242 (2001)Google Scholar
  13. 13.
    McCormack, J.: Eden: an evolutionary sonic ecosystem. In: Kelemen, J., Sosík, P. (eds.) ECAL 2001. LNCS (LNAI), vol. 2159, pp. 133–142. Springer, Heidelberg (2001). Scholar
  14. 14.
    MacCallum, R.M., Mauch, M., Burt, A., Leroi, A.M.: Evolution of music by public choice. Proc. Natl. Acad. Sci. 109(30), 12081–12086 (2012)CrossRefGoogle Scholar
  15. 15.
    Yee-King, M.J.: An automated music improviser using a genetic algorithm driven synthesis engine. In: Giacobini, M. (ed.) EvoWorkshops 2007. LNCS, vol. 4448, pp. 567–576. Springer, Heidelberg (2007). Scholar
  16. 16.
    Bown, O.: Player responses to a live algorithm: conceptualising computational creativity without recourse to human comparisons? In: Proceedings of the Sixth International Conference on Computational Creativity, p. 126, June 2015Google Scholar
  17. 17.
    Bown, O.: Performer interaction and expectation with live algorithms: experiences with Zamyatin. Digit. Creat. 29(1), 37–50 (2018)CrossRefGoogle Scholar
  18. 18.
    Husbands, P., Copley, P., Eldridge, A., Mandelis, J.: An introduction to evolutionary computing for musicians. In: Miranda, E.R., Biles, J.A. (eds.) Evolutionary Computer Music, pp. 1–27. Springer, London (2007). Scholar
  19. 19.
    Lehman, J., Stanley, K.O.: Exploiting open-endedness to solve problems through the search for novelty. In: ALIFE, pp. 329–336 (2008)Google Scholar
  20. 20.
    de Castro, L.N., Timmis, J.: An artificial immune network for multimodal function optimization. In: Proceedings of the 2002 Congress on Evolutionary Computation, CEC 2002, vol. 1, pp. 699–704. IEEE (2002)Google Scholar
  21. 21.
    de Franca, F.O., Von Zuben, F.J., de Castro, L.N.: An artificial immune network for multimodal function optimization on dynamic environments. In: Proceedings of the 7th Annual Conference on Genetic and Evolutionary Computation, pp. 289–296. ACM (2005)Google Scholar
  22. 22.
    Abreu, J., Caetano, M., Penha, R.: Computer-aided musical orchestration using an artificial immune system. In: Johnson, C., Ciesielski, V., Correia, J., Machado, P. (eds.) EvoMUSART 2016. LNCS, vol. 9596, pp. 1–16. Springer, Cham (2016). Scholar
  23. 23.
    Ableton live, February 2019.
  24. 24.
    Cycling ’74, February 2019.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.UNSW Art and DesignPaddingtonAustralia

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