Trayodashi

Trayodashi is the thirteenth tithi of the bright fortnight, a Jaya tithi in the fivefold grouping, associated with victory. Its presiding deity is traditionally Kamadeva, the god of love, though its most widespread observance is Shaivite: the Pradosha vrata, kept on the thirteenth tithi of both fortnights, is dedicated to Shiva and observed in the twilight hour of pradosha, held especially favourable for his worship. The waxing Moon by now is nearly full. In the panchanga Trayodashi is read as generally auspicious, and it carries a strong current of Shaiva devotion through the Pradosha observance. These are the conventions of the calendar and festival tradition, anchored to the count of thirteen lunar days from the new moon.

Kamadeva's association with the thirteenth tithi sits somewhat apart from the tithi's dominant Shaiva colouring through Pradosha, and the two associations coexist without being reconciled in most sources, an example of how a single numbered tithi can accumulate more than one deity assignment from different strands of tradition without any attempt to unify them. Pradosha itself is timed not simply to the calendar date of Trayodashi but to the specific twilight period, roughly an hour and a half before and after sunset, that falls within it, so the observance depends on a sub-division of the tithi by clock time in addition to the tithi's own boundary, a level of temporal precision the panchanga applies to relatively few observances.

Reckoning a tithi means measuring elongation, the angular distance of the Moon from the Sun, and cutting that circle into thirty equal twelve degree arcs. Trayodashi occupies the arc from 144 to 156 degrees of that separation. Because the Moon travels an elliptical orbit its angular speed is not constant, so that twelve degree arc is crossed in anywhere from roughly nineteen to roughly twenty six hours. The convention that resolves this is simple and consequential: the civil day takes the name of the tithi that is running at sunrise. A tithi shorter than the interval between two sunrises can therefore be skipped entirely, which the tradition calls a kshaya tithi, and one longer than that interval can carry its name over two civil days, an adhika or vriddhi tithi. Both occur in the ordinary course of a year, and both are why an observance can appear on two dates in the same almanac.

Each tithi is halved again, and each half carries a karana, so the first half of Trayodashi carries Kaulava, the third, and the second Taitila, the fourth. Seven of the eleven karanas repeat, cycling eight times through the month, while four are fixed to particular half tithis at the month's opening and close.

The Moon is waxing through this arc, setting later each evening and carrying about 93 per cent of the disc lit. That figure is a consequence of the definition rather than an observation added to it: elongation fixes the phase, so naming the tithi already names how much of the disc is lit.