The scales of Raga Vagadeeshwari are as follows :
Aarohanam (Ascending) : S R3 G3 M1 P D2 N2 S’
Avarohanam (Descending) : S’ N2 D2 P M1 G3 R3 S
This raga is 34th on the Melakarta scale.
The mood of this raga ranges from philosophical and contemplative to deeply mystical. There are only a few compositions that I know of in this raga. Paramatmudu by Tyagaraja is the iconic song in this raga. I have also heard a rendition of Vani Vagadeeshwari by P.Chidambaranathan and Bhogachhaaya Naatakapriye by Muthuswami Dikshithar.
Note : The 12 notes in the octave are named as below. Please note that C is used as Sa for the sake of simplicity as the scale is relative in Carnatic Music. Also note that the scales paint only a superficial picture of the raga as the gamakas(ornamentations) are a very important part of a raga.