Krishna Trayodashi

Krishna Trayodashi is the twenty-eighth tithi overall, the thirteenth day of the waning fortnight. Like the bright-fortnight thirteenth it carries the Pradosha vrata, the twilight observance dedicated to Shiva, so the fast recurs on the thirteenth tithi of both halves of the month. In the fivefold grouping it is a Jaya tithi. The Dhanteras observance that opens the Diwali season falls on the dark-fortnight Trayodashi of Kartik. The waning Moon is now a hairline crescent near the Sun, soon to vanish. The panchanga reads the thirteenth tithi as generally auspicious, carrying a strong Shaiva current through the Pradosha vow. These are the conventions of the calendar and festival tradition.

Dhanteras, opening the multi-day Diwali observance on the dark-fortnight Trayodashi of Kartik, is dedicated to Dhanvantari, the physician-god who is said to have emerged from the churning of the cosmic ocean bearing the nectar of immortality, and the day's strong association with purchasing gold and new utensils draws on his identity as a bringer of wellbeing and prosperity rather than on the tithi's own Pradosha character, which continues to apply independently on this date as it does on every thirteenth tithi of either fortnight. The convergence of Dhanteras and Pradosha on the same waning Trayodashi in Kartik is a case of two separately timed observances, one keyed to the specific month and one recurring every fortnight regardless of month, falling together.

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. Krishna Trayodashi occupies the arc from 324 to 336 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 Krishna Trayodashi carries Gara, the fifth, and the second Vanija, the merchant's karana. 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 waning through this arc, rising later each night and showing about 7 per cent of the disc lit. The phase follows from the elongation and not the other way round, so the tithi and the shape of the disc are two readings of one measurement.