In his seminal works on North Indian classical music theory, V. N. Bhatkhande (1951, 1954) classified about two hundred raags (fundamental melodic entities) by their seven-note parent modes known as thaats. However, assigning raags to thaats is not a straightforward task. Each raag is defined by a collection of melodic features that guide a performer's improvisation. Although these features sometimes point to a unique thaat, in other situations they either give incomplete information (too few notes) or give conflicting information (too many notes). Our goal in this paper is to construct geometrical models that help us to better understand the relationship between thaats and raags. Following the principles of geometrical music theory (Callender, Quinn, and Tymoczko 2008), we locate the thirty-two “theoretical thaats” in a five-dimensional lattice. Jairazbhoy's “Circle of Thaats” connecting common thaats embeds within this lattice (Jairazbhoy 1971). For a given raag, our geometrical representations show which theoretical thaats contain the notes used in the raag's various melodic components separately. We have written Matlab code that produces images of a database containing a number of raags. Our models reveal graphically some of the problematic aspects of Bhatkhande's raag classification system.