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.
Music To My Ears 
There are a lot of songs in this raga as listed below:
Adiyali smaripe shri gananathana K/Chapu Bangalore S.Mukund
Airavatam tanin arumai undan adiyenai paninden Adi C.V.Padmanabhan
Ambikaiyai panivome Rupaka K.Hariharan
Annapurni vishalakshi adhikarini akhila loka janan Adi D.Pattammal
Apasvaramai padade avalamadai Adi T.A.Sambandamurti
Appa nan vendudal kettarul puridal vendum (a) Adi Ramalingasvami
Bhaja manasa ramam bhujagadhipati Adi C.Rangiah
Bhavaja janakure (lng) Triputa Govindacharya
Bhogachaya natakapriye bodham dehi brihadishajaye Adi Muttusvami Dikshitar
Daya judu ?
Deva nayaki Adi Chitravina N.Ravikiran
Dinam oru kana neram Rupaka K.S.Krishnamurti
Izhatturaviyin yazh nalum tamizh Adi Abhayambika
Jnana murti Adi Dokka Sriramamurti
Kaladu ledanagalare daivamu ilanu kalaya juchuvaro Rupaka R.Venugopal
Kamala nayana Adi Svati Tirunal
Karunarasa sagara ni dasuda haridasuda Sriramachandra Murti Sistla
Maha ganapatim manasa smarami matangi Adi Kadalur Subramaniam
Maha tripurasundari Rupaka K.Ramaraj
Nadanusantana nanmargame sanmarga Adi Kotishvara Iyer
Nagapattadharam Bangalore S.Mukund
Namostute sarasvati Rupaka R.Vishveshvaran
Nave nikka sol (tv) Adi Rukmini Sivakumar
Navinikka sol tiruvachakam Adi Rukmini Sivakumar
Ni pada nirajamule Sriramachandra Murti Sistla
Ni sharanu jochchi ni namamu japinchutakanna Sriramachandra Murti Sistla
Nila varnaya (p) Sriramachandra Murti Sistla
Nilavarnude nikhileshvarude shrihari Sriramachandra Murti Sistla
Padu paraman pugazh Adi Nagpur Srinivasan
Parama purushaparandama vega ravayya nanu Sriramachandra Murti Sistla
Paramatmudu velagu muchchata baga delusukore Adi Tyagaraja
Pattune paratatva bhavampu ninu mari mari Sriramachandra Murti Sistla
Pranamamyaham shri pankeruhasanam panchanana K/Eka Balamuralikrishna
Pusanaikkiniya tiruvenkatamuraiyan C/Triputa V.Ramachandra Naidu
Ruchirambaradhara guna (lkg) Eka Venkatamakhi
Sada ninna smarisuvanta Adi R.K.Padmanabha
Sharadendimukhi Adi Bangalore S.Mukund
Shri janaki manohara Adi Mysore Venkatagiriappa
Sundaram bhaja sundram bhaja bhaje shri ? V.Chandrasekharan
Tarunam ide devi dayai puri indire (tv) Adi Radha Hari
Tillai vilakkattil Ambujam Krishna
Vagadishvareni Adi A.V.Krishnamachar
Vagadishvari devi vara muni gana vandite Rupaka Ashok R.Madhav
Vagadishvari raga sudeyolu (tv) Adi C.Honnappa Bhagavatar
Vagadishvari varakavi yogigal Jhampa Shuddhananda Bharati
Vagadishvarimm ashrayeham (tv) Adi Madokaram Prashanth Iyengar
Vagadishvarim vagishvarim gandharva Adi R.K.Suryanarayana
Vama devam bhavayeham C/Triputa Jayachamaraja Odeyar
Vani vagadishvari sarasvatiye amba gana kalavatiye Rupaka Lakshmi Krishna
Vani vagadishvari varam arulvai isai kalai arul Rupaka Mysore Chikka Rama Rao?
Thank you Sir for writing out such a comprehensive list! I am sure my readers will appreciate this very much. I will try and hunt out as many as I can to listen to.
cheers. Suja
Brilliant write up on one my favrt raagams – Vaagadeeswari – Can you please share the Audio clips – am yearning to listen to the varieties- Many thanks and have a wonderful year ahead
Thank you Archana. I do not upload music for the sake of downloading. I suggest joining a site such as Sangeethamshare (free membership) for access to many excellent recordings.
Cheers. Suja
Vagadeeshwari is N3. Nattai is N2.
Its the other way around..vagadeeshwari has a kaishiki nishadam, N2 and Nattai has N3..
Yes! Forgive me! I forget about Nattai and my ignorance took the best of me! I was explaining to my appa about nattai and we were debating scales only to realize that Nattai was N3 and D3.
My apologies!
Rishi Manoharan