What is Mazzola's "Topos of Music" about? Disclaimers: I am neither a musician, nor I want to discredit Mazzola's work. Corollary of the first point: please use a plain style, without technical terms in the area of Music Theory. Corollary of the second: don't take my disbelief in Mazzola's work as an offense. ;)
So, the question is: what is Mazzola's "Topos of music" about? Is the considerable required amount of advanced Mathematics a necessary tool to achieve the goals of the book? Can a discrete knowledge of those mathematical prerequisite shed some light to the mathematical approach to music theory? Does somebody out there managed to apply Mazzola's ideas (if there are some, sensible to be applied) to a "concrete" situation?
Thanks!
 A: Ich habe bisher den Teil lokaler Strukturen gelesen und bin ein sehr großer Freund der Idee, dass sich Musik insbesondere durch die vielfältigen Arten und Anwendungen von Symmetrie "ordnen" lässt.
Egal ob Ohrwürmer oder Konzerte, der geübte Hörer leitet die Struktur aus seiner bisherigen Hörerfahrung ab und bildet somit das Stück auf seine bisher "gepspeicherten" Musik-"Teile" ab; weshalb wir etwa auch Probleme haben fremdländische oder ethnische Musik aufzugreifen; sie ist uns fremd.
Die Darstellung der Materie folgt insbesondere in dem Buch "Topos of Music" nicht unbedingt DEM Standard der Algebra, weshalb ich vermute, dass Herr Mazzola einige seiner Leser verliert und daher vielmehr sein Werk Geometrie der Töne empfehlen darf.
Ob Komposition seinen Methoden folgen darf, muss genauso bejaht werden, wie umgekehrt der Umstand, ob Kompositionen seinen Methoden folgen muss, verneint werden muss.
Ich denke aber, dass der Autor sich dazu sehr deutlich genau so geäußert hat.

Rough translation:
I have so far read the part on local structures, and like the idea that music can be "ordered" in particular by the manifold types and applications of symmetry.
Whether earworms or concerts, the experienced listener derives the structure from their listening experience and thus maps the piece to the previously "stored" music-"parts"; which is the reason why we have problems to pick up foreign or ethnic music - it is alien to us.
The presentation of the matter in particular in the book "Topos of Music" does not closely follow the standard of algebra, whence I surmise that Mr. Mazzola loses some of his readers and rather recommend his work "Geometry of Tones".
The question whether composition may follow his methods must be answered with yes, just like conversely the question whether it must follow his methods must be answered with no. But I think the author himself has clearly stated exactly that.
A: the theory has been applied in my composition software presto for atari (google it, it is still available for PC emulation), and for the universal software rubato for composition, analysis, and performance. These software were also used to compose music, see mazzola's homepage www.encyclospace.org, and go to CV there. Best, Guerino Mazzola
