Computational musicology is the fruit of two factors that were brought to florescence in the twentieth century: modern mathematics and computer technology. The mathematical contribution can be attributed to an incredible expansion of the mathematical concept architecture, reaching far beyond simple numbers and functions. The culmination of this development can be concretized in the theory of topoi that was initiated by Alexander Grothendieck and ultimately unites geometry and logic in a revolutionary restatement of what is a space, namely, that concepts are understood as being points in a conceptual space. Mathematical music theory has drawn substantially from topos theory, as has become evident with the publication of The Topos of Music (Mazzola 2002). A concrete consequence of this development has been a computational description and modeling of fundamental topics of music theory: harmony, rhythm, melody, counterpoint, performance, and composition.

But it became evident very soon that such computational approaches could only be related to existing musical works with powerful computational tools, much as modern physics cannot be developed without impressive experimental devices, such as particle accelerators and their computational background machinery. In fact, a melodic analysis of a one-page composition can easily imply billions of comparisons of motivic units. This suggests a future musicology that might move in the direction of big science when it comes to understanding major works in music, be it in the Western classical score-driven tradition, in the Indian raga tradition, or in free improvisation. This is why music software has been developed to calculate quantitative results that reflect the theoretical models of computational musicology. The RUBATO software (Mazzola and Zahorka 1994) was one of the first tools that offered comprehensive analytical machinery for computational harmonic, rhythmical, melodic, and performance-theoretical investigations. It is not by chance that such investigations were first conducted in collaboration with a statistician (Beran and Mazzola 1999) since experimental science cannot be realized without statistical methods. Statistics in musicology has become a fascinating new field of research (Beran 2004). These investigations have revealed significant relations between the