Atomic Decomposition offers interesting possibilities for musical applications:
Iterative Approximation. Control over degree/resolution of the model
Approximation is based directly on the signal rather than signal descriptors
Dictionaries can be arbitrarily designed and combined (sample libraries, field-recordings, etc.)
Model is naturally polyphonic (juxtaposition and superposition of sound grains)
Constrained Matching Pursuit (constraint-based control over distribution of sound grains)
Process leaves a “residual” – Multiple iterative decompositions (serial, parallel) of the same target are possible, e.g. for different orchestrations
OM-Pursuit was awarded the CIRMMT Director’s Interdisciplinary Excellence Prize.
In a recent project we have employed OM-Pursuit for the notation of musical audio:
The notation of musical audio (such as a tape-part in electroacoustic music) is typified by two extremes on a continuum: On the one end are signal-based notations, such as sonograms, waveforms, etc. -which however don’t provide information about musical semantics. On the other end are symbolic notations, such as icons, characters, etc. -which in turn don’t provide information about the sonic details. Both aspects, however, are important for the interpretation of a musical work, in particular for contemporary music, which does not rely on common musical idioms. Using dictionary-based approaches (OM-Pursuit) an audio signal can be analyzed / transcribed based on a user-defined collection of smaller-scale sound files (so-called ‘atoms’). The individual atoms can be associated with arbitrary visual representations (symbolic, iconic, etc.). The user can then design simple programs to algorithmically arrange these visual elements on a 2D-canvas into a kind of cartographic map of the higher-level sonic content in the signal. Below are some screenshots from early experiments with the system. There’s also one from my piece for 2 pianists and tape “6 Fragments on 5’05” – 1 Act of cleaning a piano”.
This work was presented at the 1st Symposium on Music Notation at Université IV, Paris Sorbonne, organized by AFIM/MINT-OMF workgroup Les nouveaux espaces de la notation musicale.
See the set on soundcloud for some audio examples.