Sergei Taneev’s Vertical-Shifting Counterpoint

In his 1909 treatise Podvizhnoi kontrapunkt strogogo pis’ma (Movable counterpoint in the strict style), Sergei Taneev reconceived invertible counterpoint as a type of “vertical-shifting” counterpoint, in which the voices move higher or lower in pitch but do not necessarily cross. The conditions on vertical shifting at all intervals operate according to the same mathematical principles; Taneev’s system allows these conditions to be efficiently calculated. This article introduces Taneev’s terminology and method in order to demonstrate how his work generalizes, refines, and extends the insights of prior theorists. I apply the method analytically to investigate shifts at uncommon intervals in one of Taneev’s fugues, and I extend the method to account for Taneev’s compositional use of counterpoint alla riversa , or “reversible” counterpoint, in which the voices are flipped upside-down in melodic inversion.