Question: Pallavi Seshayyer was an expert of which form of singing in Carnatic music which allows the musicians to improvise to a great extent?

Context paragraphs:
Pallavi Seshayyar: Pallavi Seshayyer (1842–1909) was a composer of Carnatic music, who followed the traditions of the famous composer Tyagaraja.  Seshayyar was a singer in the court of the king of Mysore.  As a singer, he was an expert of the techniques of "Ragam-Thanam-Pallavi", a unique style of singing Carnatic music.  This expertise gave him his epithet "Pallavi" Seshayyar.  He could also compose exploiting rare "Ragas".

Kalpanaswaram: In Carnatic Music, Kalpanaswaram (also called swarakalpana, svarakalpana, manodharmaswara or just swaras), is raga improvisation within a specific tala in which the musician improvises in the Indian music solfege (sa, ri, ga, ma, pa, da, ni) after completing a composition.  This takes place during the Pallavi portion of a Ragam Thanam Pallavi.  E.g. SMR, SRMR, SRMPMR... It starts with a simple note SMR and extends all the way to SRMPMR.

Shanmukhapriya: Shanmukhapriya is a rāgam in Carnatic music (musical scale of South Indian classical music).  It is the 56th "melakarta" rāgam (parent scale) in the 72 "melakarta" rāgam system of Carnatic music.  It is called Chāmaram in Muthuswami Dikshitar school of Carnatic music.  It is said to be borrowed into Hindustani music from Carnatic music.

Anupallavi: In Carnatic music, the anupallavi comes after the pallavi and is usually the second section of any composition.  It is then followed by one or more charanams.  The anupallavi is optional.  In such compositions "pallavi" is followed by one or more "charanams".

Muthu Thandavar: Muthu Thandavar (1525 – 1600 CE) (Tamil:முத்துத்தாண்டவர்)was composer of Carnatic music.  He was an early architect of the present day Carnatic "kriti" (song) format, which consists of the "pallavi" (refrain), "anupallavi" and "charanam".  He lived in the town of Sirkazhi in Tamil Nadu.  His contributions to Carnatic music have been largely forgotten and not many of his "kritis" are in vogue today.  Muthu Thandavar, along with Arunachala Kavi (1712–1779) and Marimutthu Pillai (1717–1787) are known as the Tamil Trinity of Carnatic music.

Ragam Thanam Pallavi: Ragam Tanam Pallavi is a form of singing in Carnatic music which allows the musicians to improvise to a great extent.  It is one of the most complete aspects of Indian classical music, demonstrating the entire gamut of talents and the depth of knowledge of the musician.  It incorporates "raga alapana", "tanam", "niraval", and "kalpanaswara".  In more elaborate ragam tanam pallavis, a "tani avartanam" may follow.

Annamacharya: Taḷḷapāka Annamācārya (or Annamayya) (Telugu: తాళ్ళపాక అన్నమాచార్య; 22 May 1408 – 4 April 1503) was a 15th-century Hindu saint and is the earliest known Indian musician to compose songs called "sankirtanas" in praise of the god Venkateswara, a form of Vishnu.  He is the first known composer in carnatic music.  Other composers like Purandaradasa came after him.  The musical form of the keertana songs that he composed, which are still popular among Carnatic music concert artists, have strongly influenced the structure of Carnatic music compositions.  Annamacharya is remembered for his saintly life, and is honoured as a great devotee of Vishnu by devotees and saintly singers.

Simhendramadhyamam: Simhendramadhyamam or Simmendramadhyamam is a rāgam in Carnatic music (musical scale of South Indian classical music).  It is the 57th "melakarta" rāgam in the 72 "melakarta" rāgam system of Carnatic music.  It is called Sumadyuti in Muthuswami Dikshitar school of Carnatic music.  It is said to be borrowed into Hindustani music from Carnatic music.

Trinity of Carnatic music: The Trinity of Carnatic music refer to the outstanding trio of composer-musicians of Carnatic music in the 18th century, being Tyagaraja, Muthuswami Dikshitar and Syama Sastri.  Prolific in composition, the Trinity of Carnatic music are known for creating a new era in the history of Carnatic music by bringing about a noticeable change in what was the existing Carnatic music tradition.  Compositions of the Trinity of Carnatic music are recognised as being distinct in style, and original in handling ragas.  All three composers were born at Thiruvarur formerly part of Thanjavur District.

Dr. Annavarapu Ramaswamy: Dr. Annavarapu Ramaswamy (born 23 March 1926) is an Indian Classical Carnatic Violin Vidwan and Guru, whose musical journey entered into 9th decade.  He is in the fourth line of direct disciples in Guru Shishya parampara of the Great Musician Saint Thyagaraja and is a disciple of Sri Parupalli Ramakrishnayya Pantulu.  Both, Dr.M.Balamuralikrishna and him are very close friends, companions, classmates, learned carnatic music under the same guru Sri Parupalli Ramakrishnayya Pantulu.  They performed many concerts together throughout the world.  Many stalwarts in carnatic music, wanted and appreciated him as an accompaniment in their concerts in yesteryears.  He accompanied top ranked legendary stalwart musicians of India, carnatic musicians such as his guru, Sri Parupalli Ramakrishnayya Pantulu,  Dr. Mangalampalli Balamurali Krishna, Sri Arayakudi Ramanuja Iyyengar, Sri Chembai Vaidyanatha Bhagavatar, Sri G. N. Balasubramaniam, Sri Semmamgudi Srinivasa Iyyer, T. R. Maralingam, Sri S.Balachandar etc.. . ; and Hindustani Musicians - Pandit Vinayakarao Pathvardhan, Pandit Bhimsen Joshi, Pandit Jasraj, etc., on many Prestigious National and International venues.  He came up with his own style of performing solo concerts on Violin & Viola.  He invented new Ragas & Talams such as Vandana Ragam, SriDurga Ragam and Tinetradi Tala and Vedadi Tala.  He had written and composed many Varnams and Kritis.  He is a notable guru, taught many students, who are in successful positions such as Violin Vasu, Flute Phani, V.L.Tulasi Viswanath (carnatic vocalist), Peravali Nanda Kumar (Violinist), etc., For the past 7 to 8 decades, he has been doing free service to the society such as teaching students at free of cost.  He propagated the magnificence of his performances, teachings, demonstrations and Lectures on Music in countries such as U. S. A, Canada, European Countries (U. K, France etc.) and Asian Countries (Muscat, Bahrain, Dubai, Singapore, Malaysia, Doha, Srilanka, etc.,)

Supporting paragraphs: Pallavi Seshayyar Ragam Thanam Pallavi
Answer: Ragam-Thanam-Pallavi