- Here is a very succinct pictoral description of what is meant by tonal space and the torus.
- Here is an example of a piece of music moving about in tonal space.
- Here is a whole page of some more animations of musical stimuli projected onto a toroidal model of tonal space
- Overview of how an audio signal maps onto the torus (using the jlmt)
- We use the IPEM Toolbox developed by Marc Leman and colleagues as a front end to convert the audio signal, and a weight matrix trained as a self-organizing map to go from the last stage of the IPEM Toolbox (periodicity pitch images) to the toroidal representation of tonal space.
- We then use a quantitative description of how music moves in that space to figure out what parts of the brain track the changing melodies and harmonies in the music as people listen to it.
- We use this technique to study music-evoked autobiographical memories.
- The best way to learn more about it is to watch some animations and then read some papers about it.
Temporal (Metric/Rhythmic) We are also interested in modeling the temporal structure in music. Here again we use the IPEM Toolbox for the early processing stages and then custom code to implement a bank of reson filters (damped oscillators) which perform the periodicity analysis.
Timbral How many complex sounds can you hold in mind at the same time if you can't easily associate them with an instrument or any other sound that you have a memory for? It turns out that not very many, as we show in our work on working memory for timbre.