In 1987 Joseph Straus outlined four necessary conditions for the existence of prolongation: the consonance/dissonance condition, the scale-degree condition, the embellishment condition and the harmony/melody condition. Most schemas of post-tonal prolongation fail to meet these four criteria, but the idea of post-tonal prolongation remains compelling to many analysts.

This paper assumes post-tonal prolongation must exist somehow, and proposes to redefine prolongation as any compositional technique by which structurally important notes are compelled toward mental retention when not literally present. Per the adjusted definition, four principles of post-tonal prolongation are proposed: extrication through one or more (but preferably more) non-pitch domains has the power to prolong notes; fixed-register reiteration of the same pitch has the power to prolong it during intervention; the projection across time of a sonority in the form of gradually accumulating constructive elements confers upon those elements hierarchically prolongational power as they travel from less complete to more complete; and the projection across time of a sonority in the form of elements that produce self-replicating and subordinate levels of hierarchy confers upon those elements hierarchically directional prolongational power as each element travels toward the next hierarchically superior element.

Building on Edward Pearsall's 1991 prolongational analysis of Webern, Six Bagatelles for String Quartet, Op. 9, No. 2, these four principles are applied to the same to arrive at a background. The four principles are also applied to the first movement of Stravinsky's Movements for Piano and Orchestra, revealing a three-tier background structure informed by registral fixation and invariant pitch associations.