Simple Models of Music Cognition

The above image is taken from a crude, 3-dimensional model of pitch perception based upon Fred Lerdahl's theories of pitch perception (see A Generative Theory of Tonal Music, Cambridge, MA: MIT Press, 1983 or Tonal Pitch Space, New York: Oxford University Press, in press for detailed information). We are presently working to instantiate a much more extended and sophisticated model, using the IRCAM program "patchwork" coupled with RTcmix to generate a real-time auditory rendering of the pitch-space model.

One of the features of these models is their ability to concretize tonal relations in a manner allowing easy exploration through the interface. The following three images show snapshots from a "virtual excursion" through one such constructed space:

Neural Net Research

We are also exploring the use of neural-net models of auditory perception and music cognition. The image at right is a screenshot from a simple network trained to differentiate between different classifications of timbre. The classification occurs through a spectral analysis (FFT) of the incoming signal. The net is given a training set of several thousand spectra with particular characteristics, and it rapidly learns to differentiate between timbre-classes based on these characteristics.

Although the network model is rather crude, the system actually can learn to identify timbral features. Timbre remains one of the most poorly-understood areas of music theory and music cognition. Much current research is being done in an attempt to understand more completely how we "make sense" of complex and evolving sounds.

Artificial Life

We are also using contemporary a-life research to gain insight into how sounds are constructed. The following three screen-shots show successive stages of an evolutionary system working to build a sine wave:

generation 5
generation 100
generation 500

The system works by following very simple rules for 'drifting' towards an optimum solution (the sine waveform). When rules for 'mutating' the population are included, the system evolves much more rapidly (so long as a definite fitness criteria is rigorously applied).

This particular application not only demonstrates the type of research we are doing towards the goal of creating new sounds, it also exmplifies a method for "auralizing" a particular model -- it is very easy to hear how different evolutionary factors affect the a-life model; where these effects are much more diffcult to apprehend through other perceptual modalities.