Its ārohaṇa-avarohaṇa structure (ascending and descending scale) is as follows (see swaras in Carnatic music for details on below notation and terms): The swaras in this scale are Chathusruthi Rishabham, Sadharana Gandharam, Suddha Madhyamam, Chathusruthi Dhaivatham and Kaisiki Nishadham.
[1] A different view is that this raga is a janya of Natabhairavi (which has D1, suddha dhaivatham, in place of D2), with D2 being the anya swara (external note).
[2] The original Abheri had Shuddha Dhaivatam and not Chathushruthi Dhaivatham in the Avarohanam, making it a Janya of Natabhairavi and not Kharaharapriya but was changed due to influences of Hindustani Bhimpalasi into the present form.
Today only one Muthuswami Dikshitar Krithi called Veenabheri and Kandha Vandharul of Papanasam Sivan are sung in the original.
As of Muthuswami Dikshitar, he has composed Panchashatpeetha Roopini in modern Abheri which he calls Devagandharam, a separate Raga.
It makes sense to sing Nagumomu with D1 as Thyagarajaswami pleads to Rama to not torment him so it gives a more melancholic mood.
Abheri's notes when shifted using Graha bhedam, yields 3 other janya rāgams, namely, Mohanakalyani, Kedaragaula and Arabhi (if we consider the Kharaharapriya-based scale).