One possible way to find hints to answers of questions raised in Muzzulini's report such as: what exactly distinguishes the diatonic major scale from any arbitrary one, or: what exactly is the musical relevance of Mazzola's mathematical structures, is to apply the theory. So I started defining harmonic structures differing more or less from classical theory and investigating them  partly with mathematical methods, partly in form of musical experiments. Some results are listed in the table below.
Ma  Mu (Terms of use) 

OnToSû,
SoNaTa A composition (sounding a little oldfashioned) based on a structure that differs only slightly from classical harmony. With this piece as an example, the underlying theory is explained in detail. 
Midi File Score (PDF) 
Scale 57 A slightly more exotic harmonic structure with only one cadenceset. 
57_1.mid Not finished yet (latest version: 20010320) and performed badly  but you can already hear the modulations. 
Wholetone scale Yet another harmonic structure, quite bizarre this time: based on the wholetone scale, but with similar properties as harmonic minor. 

Wholetone scale in 19tone equal temperament A first example for the natural application odf the theory in alternative tunings. 
Gon Dance (MP3) 
Literature:
 Mazzola, G.: Geometrie der Töne, Elemente der mathematischen Musiktheorie, Birkhäuser, Basel 1990.
 Muzzulini, D.: Musical Modulation by Symmetries, Research Report Mo. 9002, Juli 1990, SAM ETH. Also appeared in: Journal of Music Theory, Volume 39
 Schönberg, A: Harmonielehre (1911). Universal Edition, Wien 1966.
 Mazzola, G.:The Topos of Music, Geometric Logic of Concepts, Theory, and Performance, Birkhäuser, Basel 2002.