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Information provided by T.N.Chitra

The term denotes oscillation of swaras (notes0. Carnatic music is gamaka oriented. There are two opinions on the number of gamakas (10 and 15). Some accept the no. as 10 and some 15. Some opine that the number comes to 15 due to the subdivisions within the 10 gamakas. The 10 gamakas are called Dhasavidha Gamakas.

Dhasavidha Gamakas
Aarohanam : singing the swaras in the akara brigas according to the aarohna krama of the raga.

Avarohanam : singing the swaras in the akara brigas according to the avarohana krama of the raga.
The aarohana, avarohana are generally referred to as brigas.
    AROHANA : is a series of notes in the ascending order of pitch.
    AVAROHANA : is the descending scale of notes of a raga.
Dalu : Starting from the base Shadja and basing on the raga bhava jumping to the higher notes. e.g., sm, sp, sr

Spuritham : Repeating the same swara wice. While doing so, the second time the swara is said with force. e.g., sasariri

Kampitham : Oscillating the same swara without mixing with its preceding or succeeding note.

Aahatham : Singing the swaras in the aarohana krama, giving the stress on alternate swaras.

Prathyahatham : Singing the swaras in the avarohana krama while stressing the alternate swaras.

Thripuchcham : The swara above will join the two swaras below in the same sruthi. e.g., risasa - gariri

Aandholam : Generally associated with combination of swaras which produce swinging movement. It involves jumping in a swinging manner. e.g., Sarisapapa Sarisamama Sarisagaga

Murchchana : For delineating the character of a raga the arohana, avarohana are successively delineated in a regular ascent from a swara through seven notes and a descent back to the starting note. e.g., Sarigamapadani Rigamapadanisa Nidapamagarisa

The 15 gamakas according to the other school of thought :
Thripam, Spuritham, Kampitham, Leenam, Aandholitham, Vali, Thribinnam, Kurulam, Aahatham, Ullaasitham, Plavitham, Hoompitham, Mudhritham, Naamitham, Misritham.

Stages in Abhyasaganam - Swaravali, Jantai Varisai, Dhatu Varisai, Melsthayi Varisai
Stages in Abhyasaganam - Alankaram, Gitam and Swarajathis, Varnams
Tala - Structure of Talam
Tala - Angams and Jaathis
Tala - Maarga Thalams