Complexity Measurement in Music

These past two weeks, i've been in Scandinavia, at Sound and Music Computing conference in Stockholm, and visiting the Intelligent Instruments Lab in Reykjavik. The project that I presented at SMC was on measuring complexity in time series, using a new technique called Random Projection Complexity (RPC). These are the slides from my presentation:

The paper is here:

Kiefer, C. 2023. Dynamical complexity measurement with random projection: a metric optimised for realtime signal processing. Sound and Music Computing, Stockholm, Sweden, 12-17 June 2023. (

and for a more digestible version, here's the poster from the conference:

The project started out a few years ago, with the CoFlo project, using complexity metrics to manage the behaviour of the feedback cello.

Kiefer, C., Overholt, D. and Eldridge, A., 2020. Shaping the behaviour of feedback instruments with complexity-controlled gain dynamics. In 20th International Conference on New Interfaces for Musical Expression (pp. 343-348). (

Complexity metrics seem to be good at detecting saturated feedback, and then you can use this information to change the gain of the feedback instrument to help it to stay in playable place. The metric, ETC, that we used for the original CoFlo study, has poor realtime performance, so the SMC paper is about a new metric, RPC, which is significantly faster than ETC for realtime signal processing.

There's C++ code available for the RPC algorithm (, and there's also a SuperCollider UGen in this repository.

This week at IIL, i've been trying out the algorithm, with Giacomo Lepri's Chowndolo and the lab's own Proto-Langspil.

This is a short demo of the Langspil - it's set up as a feedback instrument, and CoFlo is catching the emerging feedback and damping the feedback loop. As a result, you hear a cyclic push-pull between the feedback and the compressor.

When we plugged the RPC analyser into the Chowndolo, it showed some potentially interesting reflections of the movement of the instrument.

I spent a while making recordings of the Proto-Langspil, using complexity analysis as part of different feedback systems - more on this soon.