Arabic music is among the most difficult topics to discuss here, primarily due to the large number of countries and musical styles which the term nominally covers. In this case, the "classical" label is helpful in a fairly specific way, as opposed to the rather more vague manner in which it is applied to other world listings. Classical Arab music was defined by theorists during the classical age of the Arab Empire, and that definition continues to play a role today. While such a pan-Arab intellectual style is not as strong today as it once was, the various modern regional traditions have arisen from similar roots.
Indeed, the idea of classical Arab music was culled from a variety of regional traditions in the first place. It is modal and monophonic. The modal system is sometimes based on theoretical octave scales of 17, 19 or 24 notes, although the temperament is not generally equal, and the practice is essentially diatonic (the infra-chromaticism expressed in "neutral thirds"). The favorite modes (maqamat) come from throughout the greater Arab world. Classical Arabic theory & practice can be seen as a great synthesis of both the earlier classical traditions as well as regional melodic forms. Those constituent melodies were united in a theoretical way, such that they could be combined fluidly in performance.
The most serious musical expression has historically been solo instrumental improvisation (taqsim), although there are related vocal forms (layali). Musicians modulate frequently, and indeed a performance which remained in a single mode would not be considered fully artistic in nature. Much of the art is in the way a performer will select and prepare his modulations, especially in terms of following a tangential train of thought and back again. There are a wide variety of instruments, although plucked strings are the most visible (including the 'ud, ancestor of the European lute).
Some significant recordings devoted to the solo instrumental art of taqsim:
While developing pan-Arab ideas on modal improvisation, these recordings also illustrate the regional variation of Arabic classical music. Ali Jihad Racy is an ethnomusicologist from Lebanon who teaches at UCLA, and his duo with the popular lute player Simon Shaheen makes a particularly forceful introduction. On the other hand, Munir Bachir (1930-1997) was an Iraqi 'ud player with a contemplative style, almost letting imagination hang in the air. Muhammad Qadri Dalal has produced a rather personal elaboration of the classical style in seldom-used modes, based upon his own systematic technique of modal relation.
Whereas improvisation was exalted in the classical period, and remains an important part of modern musicianship, classical & modern poetry set to song is an important part of the Arab tradition. The style typically involves suites of songs, connected by improvisation, both vocal & instrumental. Three recordings by a particularly fine singer & ensemble in this style:
Egypt produced some of the primary classical music treatises, and continues to have a strong music tradition. Egypt is arguably the leading country for classical vocal art, as interpreted by ensembles of this type, and these are some of the most compelling examples of the wasla suite on record. These performances show a real dynamism, and continue the synthetic thread of Arabic musical culture in their choice of program. The idea of a pan-Arab contemporary classical style is strong here, including in the more individual creation of the third item.
At this point, one could reasonably list dozens of interpretations of music from across the Arab world, but I will keep this survey brief. I have made a separate listing for the music of Yemen, a more conservative tradition which particularly appeals to me. Various older styles have played a role in the development of what eventually became Arab classical music, making the reconstruction of earlier Arab music a burgeoning academic topic, even if results are still rather preliminary.
This survey remains particularly brief, and of course there are also many recitals of popular or light classical music, which I have avoided. Even with the present focus, there are other rather obscure recordings which would help to flesh out such a listing, and at some point, time might allow the development of a more extensive survey.