This is the 29th Melakarta raga in the Carnatic music system, with 'Dheera' added to the beginning to follow the Katapayaadi nomenclature system. The equivalent in Hindustani music is raga Bilawal.
Raga Shankarabharanam has the same notes as the diatonic major scale in Western notation. It is also the most universal of all scales, with the notes being the most natural ratios. Through graha bhedam, Shankarabharanam also produces Kalyani, Todi, Harikamboji, Natabhairavi and Kharaharapriya. And because these ragas also share the same intervals between notes, though at different points,
Shankarabharanam is one of the weighty and important ragas, and is often referred to as the king of ragas. It has dozens of compositions, each of which explores different aspects of the raga. Of course, in Carnatic music, a raga is more than just the scale that represents it in notation, and Shankarabharanam, like all the major ragas, goes way beyond the scale. Which is also why even though Kalyani and Shankarabharanam differ only in one note, 'ma', there is a world of difference between the ragas, and one can't at all be mistaken for the other even when only the common notes are being played or sung.
Just as one talks about the Varali 'ma' or the Gaula 'ri', Shankarabharanam can be said to have the 'ga'. Not that other ragas don't have that note, but people tend to automatically identify the steadily held 'ga' with Shankarabharanam.
Shankarabharanam has a bright feel to it without any undertones. This, along with the even spacing of notes and the sharp notes, makes it ideal for any kind of composition, whether it is a heavy kriti or a simple song.
Some of the well known compositions in the raga are Swara Raga Sudha, Enduku Peddalavale, Manasu Swadeena (Tyagaraja), Sarojadala Netri (Syama Sastri), and Akshaya Linga Vibho (Muthuswami Dikshitar). Everyone who has had even a year or two of training in Carnatic music is likely to know Veena Kuppier's elegant varnam, Sami Ninne.
Other popular compositions are Annamacharya's Alarulu Kuriyaga, Papanasam Sivan's Mahalakshmi Jaganmata and Harikesanallur Muthiah Bhagavatar's Manadhirkkisaindha Manaalan. Swati Tirunal has two ata tala varnams in Shankarabharanam - Chalamela and Indumukhi, which explore the lower and upper sthayis of the raga respectively.
Apart from the regulars, there is also a significant body of work by Muthuswami Dikshitar, Tyagaraja and others - the nottuswaras - which are exclusively in the scale of Shankarabharanam. Dikshitar's Shakti Sahita Ganapatim (among his 39 known nottuswara sahityas), Tyagaraja's Vara Leela Gaana Lola, and Muthiah Bhagavatar's unforgettable English Note are popular examples of this sub-genre that exists in Carnatic music.