One first step in any theory of harmony consists in representing each chord by a cipher denoting either its degree (usually expressed by its fundamental) in the key considered, or denoting its more abstract “function” in the tonality by a similar cipher or other symbol.
Rameau presented the fundamental bass of harmonic progressions that he analyzed, but his presentation remains rather descriptive in that it denotes the fundamentals by their note in staff notation – and, so doing, does not really abstract them from the particular key under consideration. It is true that the degrees often were labelled with names somehow describing they function, mainly “tonic,” “dominant,” “mediant”, more rarely “submediant,” but the real meaning of these names was not always clear.
Two main theories of harmony or of tonality deserve discussion here, the Stufentheorie often attributed to Simon Sechter, and Hugo Riemann’s theory of tonal functions. Both existed before and have been developed after their supposed main author. Both are characterized by a way of representing chords (or their functions) by ciphers: Roman numerals for the first, letters denoting functions for the second. They were preceded by other ways of ciphering the fundamental bass.
(To be continued.)