  Transformational music theory, pioneered by the work of Lewin, shifts the
music-theoretical and analytical focus from the "object-oriented" musical
content to an operational musical process, in which transformations between
musical elements are emphasized. In the original framework of Lewin, the set of
transformations often form a group, with a corresponding group action on a
given set of musical objects. Klumpenhouwer networks have been introduced based
on this framework: they are informally labelled graphs, the labels of the
vertices being pitch classes, and the labels of the arrows being
transformations that maps the corresponding pitch classes. Klumpenhouwer
networks have been recently formalized and generalized in a categorical
setting, called poly-Klumpenhouwer networks. This work proposes a new
groupoid-based approach to transformational music theory, in which
transformations of PK-nets are considered rather than ordinary sets of musical
objects. We show how groupoids of musical transformations can be constructed,
and an application of their use in post-tonal music analysis with Berg's Four
pieces for clarinet and piano, Op. 5/2. In a second part, we show how groupoids
are linked to wreath products (which feature prominently in transformational
music analysis) through the notion of groupoid bisections
