Kurdish music is distinct from the Arabic and Iranian traditions, although both borrow the Kurd mode (in modified form in Iran) among their modal possibilities. The Kurd mode is basically the Dorian mode, and is named "Kurd" in both Arabic and Iranian music. The Kurdish tradition remains unique, and appears to be rather immune from external influence.
An older recording of largely soloistic conception, one which served to captivate me with the expressive possibilities of this music:
This disc is one of the most affecting recordings on these lists. The strength of expression is almost unparalleled, and makes a great comparison to Spanish Flamenco guitar. The main instruments are plucked strings, but there is also one vocal piece and a couple of short wind pieces.
While that older recording is more of the manner of an anthology, several newer recitals have appeared. While most seem to lack the same level of passion, one notable recent example is:
This disc emphasizes the voice & tanbur combination to good effect. The history of the tanbur has been identified for at least five thousand years, making it one of the world's oldest instruments. Some of these melodies are said to date to antiquity as well.
Several recordings concentrating on more amiable folksy music have also appeared. There is no doubt that Kurdish music should be essentially defined as a folk music, but its forcefulness of expression is its most captivating trait, and so these largely politically-motivated issues often fall flat. However, interest in Kurdish music does seem to be spreading, as various ensembles are touring with it.
There are also various fusion-type records of Kurdish music with the adjacent cultures of Iran, Turkey or Iraq. The second citation above is connected to Iran, for instance, and indeed there is definite regional variety in Kurdish culture. The boundaries of this writeup remains fluid, as do those for many of the middle eastern discussions.