Current discourse on a "historical informed music theory" focuses on the 15th to 18th century, while the 19th and 20th centuries are rarely considered in this context. Rather, nineteenth- and twentieth-century music theory is frequently conceived as representative of "systematic" music-theoretical concepts. Nineteenth-century music theory effectively seems to be separated from eighteenth-century
... [Show full abstract] music theory by a categorical rupture that can be traced in the origins of the German tradition of "Harmonielehre". These origins were closely connected to the breakdown of a professional music education supported by aristocracy and church institutions during the ancien régime. In the young bourgeois society the instruction of composition changed its social context: many representative German theorists of harmony, such as Gottfried Weber and Adolf Bernhard Marx, were autodidactically trained music amateurs with only a rudimentary compositional and music-theoretical basic knowledge. Weber transferred a notion of "scientific scholarship" based on logical deduction and analogy ("Folgegleichheit") that he had encountered during his study of law to music theory - a notion that he does not recognize in the "vexatious figured bass manuals". In a mechanistic and systematic manner the principles of scale degrees and inversions are expanded into vast combinatorial matrices of possible chord progressions. This highly speculative method removes music theory significantly from compositional practice, thus supporting the idea of impenetrable artistic decisions attributed to the musical genius and their independence from musical craftsmanship. Weber's "mathematical" exploration of pitch space is representative of the "combinatorial space" (Catherine Nolan) characteristic for nineteenth-century music theory that finds its logical consequence in Arnold Schönberg's "method of composing with twelve tones which are related only to one another".