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Through a new examination of historical events and the related literary sources, the author connects the construction of the temple of Hercules Musarum in Circo Flaminio to an attempt to reform the calendar and to the appearance of two close astronomical phenomena (eclipses of 190 and 188 bc). Consequently, the chronology of the aedes is tackled again in order to demonstrate that the Hercules Citharoedus of the Circus Flaminius and the Camenae of the Roman tradition, as well as the Greek Muses, were called to fix with music the «harmony of the spheres» of the Pythagorean tradition. In fact, harmony and time (the latter regulated by the motion of the stars and marked by the calendar) appeared probably to have gone lost in the years of the Aetolian war. The unusual architecture of the complex, where significantly M. Fulvius Nobilior deposited his Fasti, are consistent with the aforementioned philosophical and religious framework, which had been conceived with a decisive intervention of Ennius. In particular, as in other known cases, the circular plan of the temple alluded to the circularity of the celestial planisphere. The study also considers the renovations of the sanctuary carried out by L. Marcius Philippus. He was a descendant of Q. Marcius Philippus, who had built the first horologium solarium, adjusted to the meridian of Rome, during his censorship in 164 BC. On the grounds of a number of observations and comparisons, the author concludes that the semicircular schola located behind the aedes Herculis Musarum was equipped with a monumental sundial.