In today’s world, New Mexico might be as good a base as any for a band exploring the profound links between the music of Eastern lands from the Balkans through the gates of India. That’s the mission of A Hawk and a Hacksaw, a group traveling the road of sonic authenticity without much reference to ethnic purity or nationalistic musicology. Most of the instrumental tracks could sound just right in a caravansary in the Caucasus or a Hasidic wedding. Occasionally, the focus becomes specific. “Mana Thelo Enan Andra,” featuring the bewitching voice of Stephanie Hladowski, closely replicates the sound of century-old recordings by the long-displaced Greeks of Asia Minor.