David Temperley (2007) has described instances of melodic-harmonic independence or divergence in rock music as “stratified pitch organization”. We have found similar organization in other genres of popular music, suggesting that it may be a widely-distributed phenomenon. Since it has only recently been considered theoretically, further study is needed in order to understand the functions of stratified tonal music and how they compare to those of the ‘unified’, common-practice music that has set the terms for tonal theory. Our paper will give examples of stratified or layered organization in jazz, beginning with clear, relatively-simple cases in order to establish our terms. We then will give an overview of Four, a composition by Eddie ‘Cleanhead’ Vinson (made famous by Miles Davis) that not only exhibits this feature but brings up a number of interesting issues related to it. Our method of analysis is suggested by Temperley’s notion of stratification. We thus divide the music into at least two layers: melody (or main voice) and accompaniment. Each layer is understood to envelop tonal forces and play a distinct formal role. Having analyzed each in isolation, we consider the products of their interactions. We provide the rationale for our analytical method by outlining a theory of layered formal functions, based, in part, upon a selective reading of the theories of Arnold Schoenberg.