Stufentheorie and Function theory

We are planning descriptions of European theories of harmony (and tonality). Among these, the most important may be the Stufentheorie (Theory of Degrees) of Simon Sechter (and several others) and Hugo Riemann’s Function theory. These descriptions should be articulated under several headings.

One possibility would be to articulate the description under the names of theorists. The Stufentheorie has an ancient tradition, which can be traced back to the 18^th century and the earliest usage of Roman numerals (not to mention other systems of numbering the degrees). Riemann’s theory, on the other hand, obviously cannot predate Riemann himself (although it may have been prepared earlier); but has been modified since. If this organization of the article is chosen, then we may begin by listing the theorists – keeping in mind that other ones could be added at any point.

We may also organize the description according to more specific problems and the solutions given, for instance:
• Ways of figuring. Roman numerals (from I to VII) and other numbering systems, vs letters (T, S, D, etc.) and other signs giving additional information.
• Ways of considering the role of the elements. For instance, there exists a tendency to consider the Theory of Degrees as denoting six or seven functions, instead of three in Riemann’s theory. However, signs added to the letters might be considered to increase the number of fuctions.

Insofar as the conceptions have been changing, we will still have to consider varying versions of either theory by different writers, which would lead us back to the first possibility described above, that of articulating the descriptions by theorists. I personally think that this first possibility would be the best. But what do you think?

Nicolas Meeùs, November 26, 2021

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