Indian classical music has its origins in the pre-historic Vedic age. The date for this age is said to be around 1,500 B.C., and by some scholars it is set as far back as 3,000 B.C, The Rig veda used a form of chanting first with a monotone (Archika), then with 2 tones (Gathika) and yet later with 3 notes (Samika). The Samika scale later developed into the Sama Saptaka of 7 notes. During the Vedic age the concept of raga was not developed. However, the idea of using vowel sounds like Stobha aksharas and the pulling of the words of the mantras to set them into music are forerunners of the idea of raga. The ucchara vikara (shaping of notes) included Vikara (distortion), Vislesa (splitting up a word) Vikarsana (stretch the vowels) Abhyasa (modulation) Virama (silence) and Stobha (filling up with syllables). There were 13 stobhaksharas like Aaa, See, Uuu, Hai, Hau, Ham, and so on. The using of meaningless syllables in music is the precursor of the raga alapana. In Vedic music, there was Sama gana and Sametara gana - ie.. Religious music and other types of music. This is the beginning of the Margi and Desi classification. Margi music was part of religious ritual and it was rigid, rule bound and practised seriously by a few who were initiated into it. Marga ragas had names like Vajpeyika, Agneshtika etc. Desi music was the music of the masses. All regional melodies, folk songs etc. were grouped under this category.

By the time of the Ramayana (the epic age around 500 B.C.) there were well defined Jaathis, Jaathi is the original name for Raga. Valmiki is said to have set the music of the Ramayana in 7 jaathis using 3 octaves and 3 layas. These suddha jaatis belonged to Marga music. In Bharata's Natya Sastra (200 A.D.) he has described the Shadja grama and the Madhyama Grama, and he has also given 10 Lakshanas for Jaathis (this is similar to the Raga lakshana).
Shadja Grama - Kharaharapriya scale 
Madhyama Grama - Kharaharapriya with Suddha Ma and Prati Ma, No Pa
Gandhara Grama - Todi scale with Suddha Ma and Prati Madhyama, no Pa. 
Grama means 'scale' (arohana and avarohama swaras of a jaathi) Bharata, mentions 84 jaatis out of which 18 are important. There were 7 suddha jaatis derived from the Sa Grama scale. For each jaati the following 10 lakshanas were specified; Graha (starting note), Amsa (Jeeva swara) Nyasa (staying note), Mandara, Tara, Apanyasa, Sanyasa, Vinyasa, Bahutwa and. Alpatwa. Here we can see the grammar of classical ragas developing. A jaati had to be elaborated in sections in which certain swaras would be prominent. Only certain sthayas could be handled in certain jaatis.

By the time of Matanga, the raga idea developed further. Matanga mentions the word Raga for the first time. In his Brhaddesi, Matanga brought many folk melodies like Ananda bhairavi and Nadanamakriya into the classical system. The distinction between Marga and Desi was removed because Matanga gave many Desi or folk tunes a classical status and enunciated raga lakshanas for these. The original division of Margi music as religious music bound by rules and as Desi music having no particular grammar was not relevant now. However musicologists still classified some ragas as suddha (the original) ragas. Matanga gave a classification of Suddha,Chhayalaga (ragas that had a shade of other ragas) and Sankeerna (Ragas that are a mixture of many ragas). He mentions 6 Marga Ragas that came from the 5 faces of Siva plus one from Parvati's face - Takka, Hindolak, etc.

In the Tamil tradition, ragas were called Panns. Some of the very old panns were known as Adi Isai. Many panns carried regional names like Kurinji and Gandharam. Slowly these regional melodies were also included into the classical system. 

With the evolution of raga, the idea of Margi Music that was meant strictly for religious purpose and which was rigid because of too many rules, lost ground. We can say that after Matanga, the Desi and Margi blended into one system which is the classical system of today. Parswa deva who wrote the Sangita Samaya Sara (1300 A.D.) mentions the Raganga, Bhasanga, Upanga and Kriyanga ragas. Of these the Raganga was considered the original and pure type. In the 13th C, Sarnga Deva in his Sangita Ratnakara mentions the Marga ragas that became obsolete after the 400 A.D. These were Grama ragas, Upa ragas and Suddha ragas. However by the time of Sarnga Deva only Desi ragas were in vogue. Among the Desi ragas the Raganga ragas were mentioned as close to the original Marga ragas. Bhasanga had chaaya of other ragas. Upanga ragas were edited forms of the ragas. The Kriyanga ragas were mood setting ragas which would evoke rasas like Soka, Roudra etc.

Marga ragas were sung to the accompaniment of music. Today the Suprabhatam and other ritual Vedic chants can be called Marga music. The Bhagavata Mela also has traces of the Margi tradition.

According to Sarnga Deva the 6 Suddha melas were the Marga ragas, Of these, Bhairavi, Sri, Vasanta, Megha and Panchama are said to have emanated from the 5 faces of Siva and Natta Narayani from the face of Parvati.

After the 13th C, the idea of Marga ragas is mentioned less until it eventually disappeared. The scale of Marga music was the Gandhara grama which was extinct even before Bharata's time. The 6 Marga ragas mentioned in the Brhaddesi are : Malava Kaisiki, Kakubha, Hindolaka, Takka, Bhinna Shadja, and Bhinna Panchama.

All the ragas that we sing today have developed in the Desi tradition. Raga alapana developed in a major way after the 18-c A.D.

Marga and Desi in the sphere of Talam

In Sama gana from whicn our classical music is derived, there is a mention of Hasta Vidya which is a method of reckoning time. In order to establish the duration of the notes the marks on the fingers were counted with the thumb. There were movements of the head neck and arms also to maintain the rhythm.
Later when the 108 talas were codified, the first 3 talas in this list were called the Marga talas. These 5 talas were said to have originated from five faces of Lord Siva: From

Varna deva - Chach chatputa tala
Sadyojata - Chaa cha puta tala
Aghora - Shatpita putrika tala
Tatpurusha - Sampadveshtakaa tala
I sana - Udghatta tala

In these 5 talas the Laghu duration is equal to 5 akshara kalas. In the rest of the 108 talas the laghu is equal to 4 akshara kala. The rest of the 108 talas are called Desi and they are said to be derived from the 5 Margi talas. Till the Suladi Sapta Talas were established and popularised by Purandara Dasa in the late 15th C , the system of 108 talas was followed and the distinction between Marga tala and Desi tala was recognised.
The tala kriyas (method of reckoning with the hand) were different for Marga and Desi.

Marga Kriyas:

Nissabda Kriyas : - Avapa (lift hand and fold fingers) Vikshepa (unfold fingers), Nishkrama ( move arm to right ) Pravesa ( bring arm down anti clockwise) Sashabda Kriyas - Dhruva (snap finger), Samya (strike right hand with left hand ) Taala (strike left with right hand) Sannipate (clap with 2 hands ).

Desi Kriyas:

Nissabda - Sarpini (arm moves to left), krushya (arm moves to right) Patakam (lift right arm), Patita (put down right arm) Visarjita (wave), Vikshipta (close fingers), Dhruvaka (snap fingers without sound ) Padmini (bring arm down with palms stretched out), Sasabda - Beat for Drutam , Laghu and Anudrutam.
Arunagirinathar in his Tirupugazh in Bhuta Vetala vaguppu mentions the 5 Margi talas as having emanated from the 5 faces of Siva.
The Sangita Ratnakara mentions the 5 Margi talas as well as 120 Desi talas like Saraswati tala , Gouri tala , Nissanka tala etc.
The distinction between Margi and Desi talas disappeared when the Suladi Sapta talas come into vogue. The earlier tala systems included the 108 tala system, the Navasandhi tala which were used for the 9 directions in religious rituals and talas in the Tamil tradition mentioned in works like Tala Samuthirtham, and Bharata Sastiram. The Margi talas used the angas Laghu, Guru and Plutam. In the Suladi sapta talas the angas used are Anudrutam , Drutam and Laghu. The old Desi talas like Ara Jampa and Erukula Jampa figured in Yaksha gana. In the present day Tala system , there is no classification such as Desi and Margi.
Marga and Desi in the sphere of Prabandhas
Prabandha was the name for all compositions in the classical style in ancient music. The Prabandha evolved from the Gitis or short songs. In the Natya Sastra 4 Gitis are mentioned - Magadhi , Ardha Magadhi, Sambhavita and Prithula. The Prabandhas evolved from these Gitis. By about the 4th C the various types of Margi music, Margi Ragas, Margi talas, and Margi Prabandhas became slowly extinct. Margi music was too rigid and serious and thus did not enjoy much popularity. The prabandhas of the margi type were in use only in Ritual worship as in vedic Saman recitation and in some hymns and other sacred musical forms used specifically for temple ritualistic worship which can be found even now in the form of Suprabhatam in some temples. Some Bhagavata melas done during temple festivals also use the Margi Prabandhas. Since even in the Brhaddesi there is only a mention of 49 types of Desi Prabandhas, we can guess that the Margi type was not popularly known. The Lakshana Geetas that figure in the Sangeeta Sampradaya Pradarsini and the Moorchanakara Mela Gitas can be classed as Margi music These forms are not meant for enjoyment of aesthetic values , but are composed to preserve the grammar. They are not attractive enough to be sung by people at large. The Gita Govinda is the last Prabhanda available with Raga and tala. The Margi type of Prabandha existed in a minor way in the form of the Lakshana Gitas and some other types of Prabandha because they were useful in preserving the grammar and other rules of various subjects. We must remember that in an age when there was no print, the only way a subject could be memorized was by putting information in a verse form and setting it to music. Subjects like astrology, maths and Ayurveda were preserved in verse and either chanted or sung. These were a type of Margi Prabandha . Even as late as the 17th C , Venkatamakhi composed Lakshana gitas along with his father Govinda Dikshitar. In the early 18th C, Shahji Maharaj of Tanjore composed a raga-tala-malika Suladi with 7 sections in the order of the Suladi Sapta talas in the Gaulantya Ragas. Later in the 19th c we have the 72 Melakarta Ragamalika composed by Maha Vaidyanatha Sivan which is also primarily meant as a grammar of music. The Sangraha Choodamani of Govindacharya gives Lakshana Gitas for all the 72 Melakartas. These are in 3 sections - the Sutra Khanda, the Upanga Khanda and the Bhasanga Khanda. The first section gives the Swarams, the Chakra and the placement of the Mela within the Chakra . The next 2 sections give the Upanga and the Bhasanga ragas derived from it.

The Desi Prabandhas were quite popular till the 15th C after which the kriti form discovered by Annamacharya and later established by Purandaradasa displaced the Prabandha form. The Prabandha was found too restrictive by the 18th C composers and Tygaraja did a great service to classical music by developing the more elastic kriti form. The Musical forms that are popular now like the Varnam, Kriti , Padam, Javali, Tillana etc all belong to the Desi type. Though they are bound by rules, the main aim of these musical forms is to give artistic pleasure and to express the beauties of raga and rhythm. Desi music has always been geared to Jana Ranjakatwa and tries to give a refined type of enjoynent. Desi music is different to light music and folk music because Desi music is fully classical. Now the term Desi and Margi are not relevant, because we refer to classical music and light music which are 2 different types of music. The Margi music of earlier days has become so outdated that it is not considered as part of music. The big divisions now are the Classical, the Light and Film music. The earlier classification is not applicable any more in today's music.