Pitru paksha

 Tradition of Pitru Paksha/Shradh 

As per the Hindu calendar, Pitru paksha or Shradh fortnight is observed during Krishna paksha of the lunar month of Bhadrapad (immediately after Ganesh Utsav) for those following the Amanta system.

For those following the Purnimanta system (For North, East India and Nepal) it will be the lunar month of Ashwini, Shukla paksha.

It begins on the Pratipada (first day of the fortnight) and ends with the no-moon day known as सर्वापित्री अमावस्या, Pitri Amavasya, Peddala Amavasya, Mahalaya Amavasya.

Rituals associated with Pitru paksha/Shradh, are mentioned in Rgved and are observed to this day, with changes and modifications. 

But why was this month and date selected and not any other?

As I had said most of our Hindu festivals/ rituals are based on celestial events, indicating a change of season/Ritu/elapsed time and actions to be taken by all given the cosmic event and what to expect further.

 This was a method of timekeeping, by performing periodic rituals, in consonance with the celestial event.

In Hindu tradition, the north celestial sphere is consecrated to the gods (deva) and the south celestial sphere is consecrated to the ancestors /pitṛ. However, Devayāna देवयान and पितृयाण are not in active calendric use any longer but do form the basis for Pitṛpakṣa.

With this as the backdrop, during Vedic times(referred to in Rgved) the Summer solstice commenced on Bhadrapad full moon, so that the dark half of the lunar month of Bhadrapad was the first fortnight in पितृयाण, therefore, naturally became the first fortnight in the Ayana of manes, or the dawn of Pitrupaksha (The year was counted from W solstice to W solstice, solstitial year)

The ritual of paying obeisance, to the ancestors/Pitr is carried out during this time, as the Sun is in pitralok. This also marked Varsha Ritu's end and Sharad Ritu's beginning.

Incidentally, the Parsis celebrate their feast to manes around the same time. Their year starts from the month of Fravashinam.

Based on the Buddhist and Tao traditions of China, the ghost festival or Yulan festival is celebrated on the 15th day of the 7th month of the calendar between August and September.