Karnataka Devagandhari of Muthuswami Dikshitar e.g PanchAshaTpITa RUini
This confusion is similar to the suddhasaveri/devakriya/ karnataka suddhasaveri of the two schools.
There is no karnATaka dEvagAndhAri in dIkSitar school. It is dEvagAndhAram as per muttusvAmi dIkSitar. Viz. "dEvagAndhAra rAga tOSiNi" in the charaNam. I think thats how most books quote. rAjeshnAt's post also mentions it. Interestingly I was going thro sangIta sampradAya pradarSiNi (SSP). I neither found this rAgA dEvagandhArA or the kRti panchASaT pITa rUpiNi. subbarAma dIkSitar, however, lists a rAga dEvagAndhAri in mElas 22 (SrI) and 28 (DhIraSankarAbharaNam).
mELA 22: ArO: S R S G G M P D P N N S; Ava: S N D P M M G G R S - Its an upAnga rAgam (So close to kharaharapriyA!)
mELA 28: ArO: S R M P D S; ava: S N D P M G R S R G R S (This is the dEvagandhari of the kSirasAgarasayanA and kSitijAramaNam type)
vEnkaTamahin's SlOkam also calls this rAgA dEvagAndhAri. There is no SlOkam for the rAgA from the mELa 28.
Also in the foot notes for the rAgA from mELa 28, subburAma dIkSitar calls this rAgA dESiya dEvagAndhAri.
That may be the reason why people identity the first gAndhAri with karnATaka sabhdhA. It may be better to call it dEvagAndhAra or bhImplas.
subburAma dIkSitar clearly lists AbhEri under the nArirItigouLa mELa (22) . ArO: S M G M P P S ava: S N D P M G R S
Clearly stated is an upAnga rAgam. Hence uses svarAs of nArirItigouLa/naTabhairavI and not SrI/kharaharapriya!
Same is the story with tarangini. One svara (Suddha deivatam to chatuStruti deivatam) change and it sounds like chenchuruTTi/jhanjhUTi.
Poor AbhEri along with tarangiNi and many other have been mutilated by our beloved musicians in the name of janaranjakatvam!
SuddhasAvEri may be compared to devakriyA. But the suddhasAvEri of asampUrNa mEla paddati is from a different mElakarta.
SuddhasAvEri: janyA of mElam 29, ArO: S R M P D S; ava: S D P M R S
According to SSP, dEvakriyA: janya of mElam 28, : S R M P D S; ava: S D P M R S
And (karNATaka) Suddha sAvEri, janyA of mELam 1, ArO: S R M P D S; ava: S D P P M R S
In his footnotes, subburAma dikSitar say this is the Suddha sAvEri which pUrvAchAryas like purandaradAsar have composed pillayAr gItam in. He then says, "Now-a-days the suddhasAveri is being sung like dEvakriyA (harikEdAragouLa janyam) with panchaSruti RSabha deivatams".