In spite of the famous Riemannian criticism concerning Jean-Philippe Rameau’s chord generation, the works of the latter offer a number of theoretical instruments to explain chords and chordal progressions variant to the model of the ‘stack of thirds’. But historians also face a striking discontinuity in Rameau’s analytical use of instruments like ‘supposition’, ‘accords par emprunt’ or the interpolation of additional roots. The thoughts of Johann Philipp Kirnberger and Simon Sechter, represented by their books Die Kunst des reinen Satzes in der Musik (1771) and Die Grundsätze der musikalischen Komposition (1853/54) can be regarded as attempts to integrate some of Rameau’s ideas into closed systems of fundamental bass theory. Their achievements and newly formed problems are discussed using the example of incomplete chords.