Hi Diemo and Karim,
Emmanuel’s definition of the spectral negative, as I had said in an earlier post on this, amounts to nothing more than a particular case of image sonification, i.e. it’s just the audio output of a sonified (photographic) negative of a spectrogram. It can easily be achieved using apps like Photosounder, which has been around for quite a while.
An interesting definition of the mirror/negative of a sound can perhaps be attained by appealing to Audio Descriptors (e.g., IRCAM’s own ircamdescriptors), i.e. for a given Audio Descriptor phase space (Timbre Space) one could define by symmetry the mirror/negative of a sound (for the given Timbre Space), and then proceed to synthesize it. I have no idea, however, if any of these proposed mathematical symmetries have any pyschoacoustic or cognitive significance on their own, or if they’re just an alternative way of parsing and probing the world of sound/timbre.
Concerning Duchamp’s own musical game, it’s very easy to implement it in OpenMusic: one just needs to choose as universe a temperament (and mode/scale), and pick the complementary sublist for any given note or list of notes. Basic example: taking as universe the chromatic C major scale (i.e., (0 2 4 5 7 9 11) in Z12), a C major chord (0 4 7) would then give a D minor 6th chord (2 5 9 11.)
All the best,