 Some theorists developed hybrid views. Ptolemy (c. 100—c. 170 CE) is a case in point, as he explicitly faults both Pythagorean and Aristoxenian approaches (Harmonics, book I, 2). His philosophical outlook is clearly Pythagorean. For instance, he defends at length the notion of cosmic harmony, tracing parallels between musical and cosmological entities (Harmonics, book III, 9). However, he attempts to develop mathematical constructs that are better adherent to musical practice than the ones proposed by Pythagoreans, thus addressing a concern characteristic of the Aristoxenian approach.