That’s a good question. Something I’d like to get out of the way first, is that it’s often tricky to speak of “influence” as a causal process in the development of religion. People wishing to give a concrete face to relationships often go for the simple answer, “x taught/influenced y” — this is the easy response which made 19th century enthusiasts, seeing immense similarities between the theologies and mystic exercises of different religions, to conclude that “it was all passed down from Atlantis, which had the philosophia perennis (original philosophy).”
But it’s really not that simple. Often there is no such substantial, historical link: very distant systems of mysticism and philosophy, even cultural movements, show similar traits because they capture identical aspects of thought and nature, not because they were comparing notes. I’m not saying this to rule out mutual concrete influence, but to point out that’s not the only option.
In any case, there is good reason to think - or at least so it seems to me - there was a great historical convergence between (a) the synthesis of legalist Sunnism and Sufi mysticism formulated by Al Ghazali in the 11th c., which formed historical Islamic orthodoxy until the modern period, and (b) the school of traditionalist Christian mysticism, centred on hesychasm, outlined by Gregory Palamas in the 14th century, which has remained the core of Greek Orthodoxy.
The main similarities I am thinking of are:
- The systematic ‘cardiac’ or Jesus prayer, consisting of the statement “Jesus Christ, Son of God, have mercy on me”, constantly remembered. This has often been paralleled with dhikr or remembrance of the name of God.
- The division between the energies/actions and the ousia/essence of God, the former perceptible, the latter inexpressible and incognizable. Similar ideas were expressed by the Moslem philosophers, and later integrated into Sufism, as the essence-being or wahiyya-wujud distinction.
- The aktiston phos, or Uncreated Light revealed at Christ’s Transfiguration, and forming part of the experiences of Christian mystics, and the nur or light that is central to many Sufi schools.
Equally pertinently, the school of Palamas emerged as the anti-Latin and anti-rationalist school - comparable to how Ghazali’s dogmatic-mystical synthesis was set against the rationalists and the philosophers - during the 14th century controversy between Palamas and his Italiote Greek rival, Varlaam (who, after Constantinople sanctioned Palamas’ view, converted to Catholicism).
This was the same cultural rift exploited by the Ottoman state - of which the Sufis were, at the time, the strong right arm - to rally the anti-Latin elements within the Greek Church to sanction their rule. Greek scholars who favoured Hellenistic philosophy and Union with Rome generally fled to Italy, and the writings of their most prominent scholar (who was revealed to have covertly believed the “equality” of Christianity with Hellenic paganism) were burnt.
Culturally, this signalled the end of the period (13th-15th c.) in which the Greek literary culture had especially accepted classical, pagan, Latin and archaizing elements - including the Hellenic identity - and a resurgence of a more dogmatic, anti-rationalist Christianity institutionally supportive of Turkish rule to drive away Western influence (not just intellectually, but materially; medieval Greeks hated the profiteering and religiously aggressive Crusaders far more than they disliked the comparatively enlightened Turkish rule, which viewed the natural ‘order of the world’ - i.e. the tax-payer’s way of life and existing sense of community - as sacrosanct, indeed the justification for the existence of the state).
Whether the link between Palamism and Sufism was somehow causal, the two schools ended up on what was definitely the same political and social boat.
Over time, aesthetic similarities became established. The Ottoman harem was the nerve center of funding for the arts, including both secular and devotional music as well as dancing and the distinctive cultural life of Constantinople, which was in turn exported to the general Ottoman urban world. That life was disproportionately reliant on Greeks, Armenians and gypsies - who especially engaged in art, trade, music, banking and prostitution, all more vital to cultural life than farming, herding, and war, the official business of the Moslem millet. As a result, the music of the Church and the Sufis was often written by the same artistic people.
Modern Orthodox ecclesiastical music long, long ago became inseparable from this continuum with Sufi music; today, reconstructions of “original” sounds are speculative and the province of secular musicians, not the Church.
Christians freely engaged in Sufi activities, and the defining characteristic of the Sufi lodges established all over the Balkans was openness to Christians. It’s worth noting that this openness of Sufi lodges extended to men of the sword as much as to cultured associates of the harem; the Sufi lodge or tekke was so vital to the Ottoman society because it opened a free space for all communities. After the end of Ottoman rule, the Greek word for Sufi lodge or tekke was seamlessly extended to the gathering places of the criminal, impoverished and generally fringe elements of society, where they were free to continue the Ottoman musical tradition (sometimes banned by Greek dictatorships as both criminal and culturally suspect as non-Western) or rembetiko music, fraternize, drink, smoke, fight and be passionate romantics. The word that’s now used to characterize the Greek soul par excellence - the “meraki” - is a Turkish loan for suppressed passion and the romantic’s search for the weird, that was generally used in these circles.
This folk musical tradition continues what used to be secular Byzantine and later Ottoman music. Here’s a song that caused quite a bit of shock when it was released in the early 20th century, by publicly broaching the (actually very wide-spread) feeling of loss at the forced population exchange of Moslem communities in Greece with the Christians of Turkey. The singer, Stella Haskel, was Jewish, indicative of the social fringe this music developed in:
When the Hoca comes out on the mosque
at the turn of evening
When he says the Bir Allah (Tur. ‘God is One’)
my heart bloodies
On a moment like this I met you
in a far land
and whenever I hear the Bir Allah
my mind goes to you
in the depths of the east
in my black exile
when I hear the Bir Allah
my heart bloodies
The song nods to a common experience - that is, observation of the other community’s prayers, and the call to prayer in the local language - from the perspective of an ‘exchanged’ Moslem, who had first met their Christian lover when kneeling at prayers. Calling the exchange exile or xenitia to the East - exile being considered a terrible burden in Greek culture - completes the picture of a suppressed passion that cannot be fulfilled, i.e. the suffering artist’s meraki and desire for union with the Beloved. And true to Sufi form, the boundary between the earthly lover in a ‘far land’ (the original homeland) and the spiritual lover is blurred by the song making a formulaic prayer its crie de cœur to the One God.