In the Antiquity, music was defined in terms of memory, not of temporality. By a writing artifice, Western music begins to consider itself as a temporal art. In the diastematic notation, duration is related to a line whose properties –divisibility, homogeneity, continuity– are assigned to the time gradually. Due to this relation, the number, the proportion and the geometric spirit can be applied to the duration. Only then a properly musical time starts to be discussed. With the development of the writing on musical staff, the fundamental philosophical problem for music is the rational construction of time. Throughout this essay, a historical pursuit is made to the process that gives rise to this construction. Also, the epistemological implications of this concept are put in evidence since the parallel between the concepts of time in the musical score and time developed by Western science.