Armenia offers some definite points of contact with the better-known music of Europe, especially via sacred choral music for the Christian rite. Choral music of this sort is generally what is termed "classical" in that tradition, along with the medieval sacred lyric songs that have been preserved. However, much of the music called "folk" is analogous to the classical music of neighboring cultures, and forms the core of my interest. Some of these performers do regard themselves as forming the "real" classical tradition.
In that sense, Armenian music is one of the most unique in the region, with some characteristic instruments of its own, and often more formal variety. Nonetheless, many of the instruments are ubiquitous, and the general modal style fits in the niche between that of Iran & Turkey fairly clearly. The primary differences are that there is no musical establishment for these styles, and that the articulation is often more Western in vocal works.
The most exciting series at present is the 6-volume set on the Celestial Harmonies label. This gives us some brilliant interpretations in a strongly classical style, something that has been lacking on record. The most compelling introductory recording featuring vocal selections is certainly:
Although those performances sometimes use several instruments at once, the textures are always clear and lucid. The sonorities are generally softer than one hears in most Near-Eastern music, and the vocal styles show a good deal of variety.
The director of the first ensemble above is one of the leading players on the duduk (Armenian oboe), the most characteristic Armenian sonority heard here. A fine solo recording:
This is really an amazing recording, very different from any solo instrumental in the other nearby traditions. It made quite an impact on me, and was the first recording listed here that I heard.
For vocal music, the two volumes on Ocora are also worthwhile. Note that Volume 2 of the Celestial Harmonies series is somewhat of a disappointment, and the Ocora Ashugh disc is to be preferred for the sacred lyrics.
There is also a developing discography of Armenian instrumental music, many of whose recordings have some merit, but this list will be kept necessarily brief.