Disclaimer: I am not trained in Carnatic music and despite my best efforts, there can be errors in this material. Carnatic cannot be written accurately using notation so the timing of the tabs and music may be off. Best would be to use the notation as a guide and rely on the audio clips for timing.
Hamsadhwani is a symmetric pentatonic (audava-audava) ragam that uses the notes
Arohanam (ascent): S R2 G3 P N3 S’
Avarohanam (descent): S’ N3 P G3 R2 S
If G# were the root note (equivalent to Sa) the notes of this ragam are: G# A# C D# G G#’
Of course, one can play it with any other root note as long as the intervals are the same. But G# is a reasonable pitch that matches that of many singers (5.5 kattai) and practicing at this pitch will make transcribing from recordings easier. On the other hand playing at a higher pitch – the D above the G# (7th fret 3rd string) – sounds nicer because the lower three strings are not wound and so there is less finger noise when playing. However, that pitch is high (certainly for singing) and the thara sthayi will be even higher so it may not be appreciated by many.
In the Carnatic melakartha scheme Hamsadhwani is the janyam of Kalyani (66th melakartha). It is placed under Kalyani because in this ragam Ga may be played plain or with gamaka. Some others place it as a janyam of the Shankarabaranam (29th melakartha) – though Ga in Shankarabharanam is played plain. The discovery of this ragam is attributed to Ramaswamy Deekshitar, the father of Muthuswamy Deekshitar.
The plain notes (swara sthana) on the guitar for the ascent (arohanam) and descent(avarohanam) for three octaves (sthayi) – middle (madhya), low (mandara), and high (thara) – are shown below (Sa = G#)
The last three bars (above) shows how the arohanam and avarohanam of this ragam as played with gamakam. The gamakas for Ri and Ni are played as slides and slightly different in ascent and descent. Ri is played as Sa-Ga-Ri and Ni as Pa-Sa-Ni in the arohanam. During the descent Ni is played as Sa-Ni (sometimes Sa-Ni-Sa-Ni) and Ri as Ga-Ri-Ga-Ri. Also Ga is played as a slide or a double slide Pa-Ga or Pa-Ga-Pa-Ga.
Here are some Hamsadhwani phrases transcribed from vocal records.
The notation does not capture the timing of the slides accurately, here is an audio of what it should sound like.