The 30 Tithis
A tithi is the time the moon takes to gain twelve degrees on the sun. Thirty of them make a lunar month: fifteen while the moon waxes (shukla paksha) and fifteen while it wanes (krishna paksha).
Because the moon does not move at a constant speed, a tithi is not a fixed length. It runs from roughly nineteen hours to roughly twenty-six, which is why a tithi almost never lines up neatly with a calendar day, and why a panchangam prints the moment it ends rather than pretending it fills the day. The convention nearly all panchangams follow is that a day is named for the tithi running at sunrise.
Each tithi has a presiding deity and belongs to one of five groups that muhurta uses to judge what a day suits. Those two facts together are what makes a tithi useful for planning: they tell you whether a day favours beginning, building, contesting, clearing or completing.
Shukla Paksha
The waxing fortnight, from the new moon to the full moon.
Krishna Paksha
The waning fortnight, from the full moon to the new moon.
The five tithi groups
The thirty tithis fall into five repeating groups of three. This classification is older than most of the festival calendar and is the first thing a purohit checks when asked whether a day suits a particular act.
Nanda — joyful
Tithis 1, 6 and 11. Celebration and beginnings.
Nanda means 'delight'. These tithis favour festivity, auspicious openings, art and anything undertaken in good spirits. They are ruled in the muhurta scheme by Friday, and work begun on a Nanda tithi that falls on a Friday is held to be doubly favoured.
Bhadra — auspicious
Tithis 2, 7 and 12. Steady, constructive work.
Bhadra means 'good' or 'fortunate'. These are the workmanlike tithis: good for building, for trade, for study and for the ordinary business of a household. Their weekday is Wednesday.
Jaya — victorious
Tithis 3, 8 and 13. Contest, courage and resolve.
Jaya means 'victory'. These tithis favour anything competitive or confrontational — litigation, examinations, negotiations, and acts requiring nerve. Their weekday is Tuesday.
Rikta — empty
Tithis 4, 9 and 14. Avoided for beginnings; good for clearing.
Rikta means 'empty'. These tithis are traditionally avoided for weddings, housewarmings and other auspicious beginnings. They are not bad days — they suit demolition, dispute, medical treatment, settling debts and clearing out what is finished. Their weekday is Saturday.
Purna — full
Tithis 5, 10 and 15. Completion and fulfilment.
Purna means 'full' or 'complete'. These tithis favour the conclusion of things, ceremonies, journeys, and acts of charity and devotion. Their weekday is Thursday.