Amavasya

Amāvásyā (Sanskrit: अमावस्या) means the lunar phase of the New moon in Sanskrit. Ancient Babylonian, Greek and Indian calendars used 30 lunar phases, called tithi in India.  The dark moon tithi is when the Moon is within the 12 degrees of angular distance between the Sun and Moon before conjunction (syzygy).  The New Moon tithi (called Pratipada or Prathama) is the 12 angular degrees after syzygy. Amāvásyā is often translated as new moon since there is no standard term for the Moon before conjunction in English.

In Sanskrit, "amā" means "together" and "vásya" means "to dwell" or "cohabit". It also means "na" +"ma"+"asya" meaning to "na" = "No, "ma"=Moon, "Asya"="There" in turn meaning to There is no Moon i.e., Moon is not visible.

In the pūrṇimānta māna Hindu lunar calendar used in most parts of the Indian subcontinent, the lunar month starts on the day following the full moon or purnima and therefore Amāvásyā always falls in the middle of the month. However, in the amānta māna calendar used in some places, the lunar month starts on the day of the new moon, making Amāvásyā the last day of the lunar month in those places. Many festivals, the most famous being Diwali (the festival of lights), are observed on Amāvásyā. Many Hindus fast on Amāvásyā.

Few Pancha-Gauda Brahmins have month from next day of Purnima (day) to Purnima (day), that is Purnima is last 29/30 days (Purnimanta). Pancha-Dravida have month from next day of Amavasya to Amavasya . Amavasya is last 29/30 days (Amanta) . Śhukla paksha is called as the bright half as the Moon changes from New Moon to Full Moon while in Krishna paksha it changes from Full Moon to New Moon. Hence it is seen that same Amavasya has same festival all over the country. Ujjain, Allahabad, Orissa, Bihar Brahmins are one few Pancha-Gauda Brahmins have month from 1 day after Purnima (day) to Purnima (day)(Purnimanta), While the people of Karnataka, Maharashtra, Goa, Gujarat, Kerala and Andhra Pradesh the Pancha-Dravida have month from 1 day after Amavasya to Amavasya. Amavasya is last 29/30 days (Amanta). Since Kanchipuram Mutt where the Adi Shankara lived and all the Pancha-Gauda and Pancha-Dravida use to visit hence Tamil Nadu developed a mixture of Panchangam and saka calendar. Similarly the place where Pancha-Gauda and Pancha-Dravida are living together as Rajasthan, Madhya Pradesh, Southern Uttar Pradesh and Chhattisgarh also show the mixtures. Also the people following Jainism follow Pancha-Dravida calendar, Amavasya is last 29/30 days. 

In old Indian culture and beliefs, irrespective of religions, Amavasya is considered a time of great power. In Tamil, though Amavasai is commonly used in religious spheres, the pure Tamil scholars prefer the term Puthuppi Rai  Fast is observed to propitiate both the Sun and Moon Gods.  Except for the Karttika Amavasya (Amavasya of Diwali), the Amavasya is considered inauspicious.

Reference

https://en.wikipedia.org/wiki/Amavasya