A tithi is a lunar day: the time it takes for the angle between the Moon and the Sun to grow by twelve degrees. A full cycle from new moon to new moon contains thirty tithis.
The first fifteen belong to Shukla Paksha, the bright fortnight, ending in Purnima. The next fifteen form Krishna Paksha, the dark fortnight, ending in Amavasya.
Because the Moon’s speed varies, a tithi can last from roughly nineteen to twenty-six hours. It does not begin at midnight or sunrise, it can start at any moment.
The tithi prevailing at local sunrise usually names the day. Sometimes a tithi begins and ends between two sunrises and is skipped (kshaya); sometimes it spans two sunrises and repeats (vriddhi). This is why a festival can fall on different dates in different cities.
