Neo-Riemannian theories consider pitch spaces as a set of operations which works on a chord or a tonality, regardless of a tonal context regulated by a central point. Because these theories don’t presuppose tonal grammar but lead to it, they are particularly appropriate to describe a kind of tonality in which tonal hierarchies don’t express themselves in a same way as in the18th or 19th century.
However precisely because they focus on the functioning of the tonal system, transformational theories don’t make tonality identification a priority. In a particular way, transformational approach is linked with the world of monotonality, that is, from a certain viewpoint, atonality. Then it does without a category which is able to lend itself to segmentation. Indeed, the description according to successive and chronological events, doesn’t usually allow to go beyond microstructural scale, because the underlying criteria aren’t directly transferable to a wider scale. This statement is particularly relevant for the music of the later 19th or the earlier 20th centuries, whose musical works are based on complex and developed structures, composed of non-symmetrical recurring units.
Transformations and harmonic progressions however offer other observable aspects. Among them, polarization on the circle of fifths and modal direction of the pitch sets, as well as voice leading should allow a significant contribution to bypass the issue consisting in the irreducibility of structure’s different levels. On the one hand, intervallic distances depend on the transformations modal direction as well as polarization on the circle of fifths in any hierarchy level. On the other hand, voice leading creates pitch spaces which embody and outweigh the abstract concept of tonal event subsequent to transformational theories. By observing several fragments of post-tonal works, this lecture is trying to define the tonality in an interaction between the different levels of structure as a conjunction of intervallic distance, polarization, modal direction and voice leading of the harmonic progressions.