<Bhairav> ....... </Bhairavi>

Very good question. I knew there was Purandara Dasa's influence on the choice of Mayamalavagowla (over Kharaharapriya) and I found this info on the net:

The Modern period of Carnatic (Karnatic) music begins with "Purandaradas" (1484-1564). He was the pioneer who blended the rich musical streams of Dravidian and Aryan music into a single stream called Karnatic music. This synthesis of cultures resulted in the hybrid variety, a highly rich traditional and classical musical system.

Sri Purandaradas born at Purandargarh near Pune in Maharastra, finally settled at Hampi (Vijayanagar), a border area for both Northern and Southern cultures. The aesthetic beauty of both the Northern and Southern flow of music attracted him as similar ragas and 'thalas' exist in both the systems in different names. The Aryan system was more prevalent in princely courts whereas the Dravidan system was prevalent in the temples of South India.

Sri Purandara Das decided that "Malava gowla" of the South was most suited for beginners. The corresponding Raga in the North is called "Bhairav". In "Malavagowla" subsequently named as "Maya Malavagowla", the difference of pitch between 'Ri' and 'ga', and 'da' and 'ni' are the same and the notes sa-ri-ga-ma and pa-da-ni-sa are perfect concordant notes. That is why Purandara Dasa found Maya Malavagowla the best Raga to begin lessons in classical music. This system of music is called "Karnataka Music" as he belongs to that region and the music is very pleasing to the ears. He created several phrases of notes called "Sarali" "Janta", Hetchu-sthayi, "Thaggu sthayi" and "Datu" Swaras. He also simplified "Thala" system and moulded it into "Pancha-Thrimsathi" Thala system and composed "Alankaras" to be sung in those Thalas.

All these initial notes or Swaras are to be sung in Maya Malavagowla. The next phase of learning of a beginner is "Geetham" for which Purandaradasa created "Pillari Geetams" in Rag-Malahari" a derivative of Maya-Malava-Gowla . Gradually the Ragas and their notes are to be changed to acquaint the student with different notes step by step. Purandara Dasa was therefore, rightly called Karnataka Sangeeta Pithamaha.

Further Purandara Dasa said in his song "Vasudevana namavaliya" (Mukhari raga) that he composed 4,75,000 Keerthanas. About 800 of them are available now. As the original tunes are lost, people sing some of them in their own tunes.

Three schools influenced the beginning of the modern period of Karnatic music.

* The Vishnu Bhaktas of Dwaita school comprising Narahari Theertha, Sree Pada Raja, Vyasa Raja, Vadhi Raja Purandar dasa, Kanaka Dasa, Vijaya Dasa Jagannadha Dasa etc. and the compositions of all these Dasas, about 5,00,000 compositions in number, are called Dasara Pada Galu.

* Shiva sharanas of Veera Saivam such as Basaveswara, Akka Mahadevi, Channa Basaveswara, Nijaguna Shiva Yogi etc. had their compositions in poetry and vachanas, which contributed substantially to the enrichment of contemporary music

* Nayanars, Alwars and other Tamil writers composed varieties of songs called Thevaram (Devaram), Thiruppughaz, Arupti etc. The prominent composers of these were Manikkavachagar, Arunagirinather, Ramalingaswamy, Muthu Thandavar, Marimuthu Pillay, Papavinas-Mudaliar etc of the subsequent period.

Sri Purandara Dasa's life is a wonderful episode in human history showing how an initially miserly man was converted into a great Bhakta by the grace of Lord Vithala.

The earlier name of Purandara Dasa was Srinivasa Nayaka. In his earlier days he was miserly and cruel. His wife Sri Lakshmi Saraswati Bai was pious and kind to fellow human beings. The turning point in the life of Srinivasa Nayaka occurred at the instance of the Lord who in the guise of a poor brahmin begged for alms for conducting the sacred thread ceremony of his son. Srinivasa Nayaka in his customary style drove away the disguised brahmin who straight away went to his wife and repeated the drama. His wife being a very kind hearted one, gave away her diamond studded nose ring and the Brahmin went to Srinivasa Nayaka again and asked him to give some money in return for the diamond-studded ornament. Srinivas Nayaka identifying it as his wife's ornament kept it in his iron safe and went to his wife to enquire about the nasal ring. Bewildered at the turn of events Sri Saraswathi Bai decided to end her life and was about to take poison. But in that container Lord put a similar ornament to the utter surprise of Saraswathi Bai, who went ahead and showed the same to Srinivasa Nayaka as if nothing has happened. Surprised at this Srinivasa checked his iron safe and found the ornament kept by him in tact. This made him realise that the Brahmin in disguise was none else than Lord Vithala. He repented for his misdeeds, begged pardon of the Lord, and renounced all his wealth to become a saint and was called "Purandar Dasa". This inspired him to sing innumerable songs in praise of the Lord, which numbered about 4,75,000 of which about 800 survive.

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I know that "Madhyamavati" is peformed at the end of the concert since it is believed to "cure" all the mistakes committed by the performer during his/her earlier performances. Madhyamavati is called something like "Sarva-raga-dosha-pariharini". In any case, it sets a very peaceful mood and is very much suited at the end.

As far as Bhairavi is concerned, I am not sure of any "curing" power it has. I think it is the emotional quotient of the raga that makes it suitable for the finale. Also, it is one of the "all-time" ragas (like Pahadi, Dhani, etc.,) and hence has no problem with the time of the day.