I will add a few lines for you - Pratipada is like birth, Dwiteeya is like sustenance in this world and Truteeya is like the end. Pooja's begin from the fourth with Ganapati, then we worship Bharati (Saraswati) or Sri, we progress to Kartikeya and other warrior Gods and Goddesses on Shasti including Naga. Then the desire for well being dawns and the Sun is worshipped on Saptami. Astami is for Bali Karma and Navami for the Dharma Devata led by SRI RAM. Dasami is for the Devi and other such strengths that give us success. Ekadasi is to pray for world peace after the war of dasami is over. Dwadasi is for progress that follows peace and Trayodasi is for wealth that follows peace and progress. Chaturdasi is to save us from the sins that we make after wealth has come and Poornima is to pray for Mukti after realising that all this was but a Drama for our understanding. So say HARI OM TAT SAT.
In fact there is a close correlation between the kalachakra and the devata which your Guru's will teach you in due course. I am happy to see your progress and sincerity.
With best wishes
The first tithi of the new moon7 is known as the day of Murukan's birth. Tai Amavasya in January-February and Ati Amavasya in July-August are significant new moon days usually accompanied by ritual bathing and other purification ceremonies of a special order. They are the new moons of the first full months after the winter and summer solstices respectively and constitute the lunar beginnings of the bright and dark halves of the solar year. These two new moons relate to the agricultural season as in January-February the winter rice crops have just been harvested and in July-August the summer rains have come and the new crops recently planted.
A second tithi important in the cultus of Murukan is sasti, the sixth stage of the waxing moon. Sasti was one of the malevolent attendants of Murukan; Devibhagavat Purana also refers to her as a spouse of Skanda, also known as Devasena, and grants progeny to the childless. Sasti is also worshipped on the sixth day in a home where a new child is born. She represents all forces that can cause disease to the mother and child. Sasti is also associated with the killing of the asuras and Murukan is remembered on Skanda Sasti day by re-enactment of the battle and to celebrate his triumph over the cosmic forces of evil.9
The third tithi important in Murukan cultus is the full moon.10It symbolises completion, fulfilment and total maturity. The full moon connotes the zenith of the cosmic cycle and the maturity of the deity. Along with appropriate asterism, nakshatra and the month, the festivals are held accordingly.11