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PART 1 - 1.1 - Genesis of the analytical model :: 1.2 - Description of the analytical model :: 1.3 - A practice of analysis in the tonal harmonic discourse from Bach to Wagner :: 1.4 - By way of a general conclusion

1.1 - Genesis of the analytical model|| 1. Origin :: 2.Sources


Through the lectures of Rosette Renshaw, a remarkable and formidable pedagogue taught by Nadia Boulanger, I soon had at my disposal a whole arsenal of prefabricated material consisting of a collection of capsules of harmonic vocabulary (named as such, it seems, by Nadia Boulanger). These formulas proved valuable in my first attempt to grasp the harmonic reality from Bach to Wagner, but at the same time I had to account for the presence of a latent, underlying, immanent principle to which Professor Renshaw referred us on occasion and which we found sporadically in a few treatises on harmony in the form of a vague and preliminary mention of an indisputable aphorism which in modern terms could be stated thus:

It was necessary to understand from the outset that in this case, this maxim does not refer to the principle which governs the relationships between consecutive tonalities in the tonal system by ordering the sequence in which the sharps and flats appear (a phenomenon which is reduced to what we call more precisely the circle of fifths of tonalities or keys).

Figure 1


Rather, it refers to the relationships between the chords belonging to a single key, thus describing a circle of fifths of functions: I-IV-VII-III-VI-II-V-I.

Figure 2

Figure 3


However, how is it possible to reconcile the systematic order of this progression of functions with the reality of certain formulas of harmonic vocabulary such as:

V - VI - IV - V - I
III - IV - V - I
V of IV - IV - V - I
I - IV - II - V - I

While I was painstakingly trying to resolve these contradictions, the answer struck me like a bolt of lighting upon meeting Richard Franko Goldman, or more precisely upon reading his remarkable book Harmony in Western Music, published in 1965 by Norton in New York. Here, Goldman accomplishes a masterful demonstration of the pertinence of the descending circle of fifths as the foundational structure of the harmonic discourse from Bach to Wagner. At the same time, he addresses the most frequent discrepancies concerning this structure and elaborates a theory capable of integrating these apparent inconsistencies. Faced with the collection of harmonic formulas inherited from Nadia Boulanger through Rosette Renshaw, I now held, ready to be tested, the embryo of a solid and coherent explanatory model that I then sought to develop and perfect.

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II - Description of the analytical modeld