This beautiful raga is an import from Hindustani music, like Behag, Kapi, Desh and Yamuna Kalyani. And, as with most Hindustani ragas, it is phrase-based and very difficult to put into an arohana-avarohana framework, and the scale can work only as a basic indicator. Hamirkalyani is also a bhashanga raga, using both the shuddha and prati madhyama notes; generally, it uses the shuddha madhyama in returning phrases like ga-ma-ga.
With such a background to the raga, it is perhaps to be expected that Muthuswami Dikshitar would have composed in it - his Purahara Nandana begins with distinctive phrases and runs through the arohana and avarohana. Tyagaraja's Maanamu Ledaa is another song that often comes up when the raga does. The Andal Tiruppavai, Thoomani Maadaththu, tuned by Ariyakudi Ramanuja Iyengar in this raga, is another favourite. A lesser known but equally worthwhile part of the Hamirkalyani stack is Swati Tirunal's Gaangeya Vasana Dhara. Keeping with the lighter nature of the raga, there are quite a few tillanas in Hamirkalyani. Lalgudi Jayaraman has composed a varnam too (Innum Thaamadham Eno) in the raga.