In their singing, Copts make an excessive use of cymbals and generate inebriating rhythms and sounds of percussion. I also have once seen a video of a Greek Orthodox liturgy in the US where an organ played: but it was only used to support the singing choir, not to play anything unrelated to the chants. Finally, there is the jingling of the twelve bells attached to the thurible: a metaphorical interpretation says that this reminds of the presence of the Apostles.
Apart from exceptions like these, Eastern liturgies generally do not use instrumental music. The only meaningful sound is that of the human voice. In large communities, there is a tendency to professionalize the singing: Very skilled choirs perform all the chants, while the other people focus on listening and on gestures like the sign of the cross or several bows. In small communities you can sometimes find the opposite tendency: The chants are easy to learn and easy to adopt, and everyone is invited to join in whenever the cantor intones a well-known chant. All this also depends on the national customs: Greeks do it different from Russians, Serbians do it different from Romanians etc. Anyway, there are no instruments.
There are several historical and biblical reasons for that practice. According to the Book of Genesis, the ability to speak in words is something that defines the human being in his or her unique relation to the Creator (Gen 2:19) as his image or icon (Gen 1:27): The Creator creates by speaking words (Gen 1:3). If liturgy is an expression of the unique relationship between humans and God, then it is appropriate to express faith by words and make no use of other sounds as a substitution for or as an addition to human words.
In ancient Roman times, Christians were tortured and murdered under instrumental accompaniment to entertain Roman citizens. An important current interpretation says that it would be disrespectful to the ancient martyrs if we enjoyed instrumental music during our services.
I also see practical advantages of singing a cappella:
It makes cantors – male and female – essential for the liturgy, and everybody knows that. A priest alone is not enough, and even when parishioners are not used to sing themselves, at least they know that they have to find skilled singers among themselves. Cantors are no luxury feature, they are indispensable. While a Western liturgy works with one priest and one organist alone and nobody even misses singers, Eastern liturgies lose almost everything of their beauty and atmosphere when there is no cantor. So, this uncontroversial tradition prevents from some sort of clericalism. It gives the human voice an essential place in the liturgical culture that cannot be replaced by anything else.
Secondly, I know many good Catholic organists and other musicians, but I also experience instrumental music that puts the community somehow under tutelage: People do not feel responsible for the liturgical aesthetics any longer because they only rely on the instrumentalists. Some instrumentalists have a bad approach to the rhythm of the human breath. Singing hymns under their guidance can be physically exhausting instead of lifting up my heart. In singing a cappella the human breath always and automatically obtains priority. This is even a spiritual experience that leads back to the Book of Genesis where the Lord breathed into the human’s nostrils the breath of life and such made him a living being (Gen 2:7).
Of course, I am thankful for the great tradition and permanent development of liturgical instrumental music that we have in the West, but sometimes I wish we would give the human voice the same dignity that the strict Eastern tradition of singing a cappella does.