First, I'd like to say something about St. Ephraim using the music of Bardesan. As far as we know at the time of St. Ephraim the music of the whole region - from contemporary Syria to Iran used the same principle - there were several modes and 360 classical melodies that the musicians had to know by hearth. Every musical performance was improvisation using musical fragments from these classical melodies. This can explain why the Byzantine music is also based on using formulae (this is not entirely true for the contemporary Byzantine music but it was true for the classical Byzantine music, 12th century and earlyer). This means that we can not say that the heretics were using music that was different from the music of the whole region.
However, if we compare the Byzantine Octoechos and the Octoechos of the Syriac Church (Nestorian) we will see that two of the Syriac modes are not used in the Byzantine Octoechos. Considering that the Syriac Octoechos predates the Byzantine Octoechos we can ask about the reason for this change. In think that if we look at the ethos of these unused modes the reason becomes clear. The first unused mode is maqam Huzam which expresses acute/violent passion and/or love and the second unused mode is maqam Saba and it expresses weeping, agony, repentance or extreme joy for something. This means that discernment is required when using non-Orthodox music in the Church.
Regarding the polyphony in the Church. It is not difficult to find on the Russian web-phorums several discussions about the polyphony - several of the people in Russia feel that the polyphonic music does not serve the pray well. And there is one rather interesting comment by one Russian saint (St. Ignatius Brianchaninov) who says that this new polyphonic music is foreign to the spirit of the Church. St. Ignatius doesn't speak against the polyphony in general but only to this particular form of the polyphony that was used in the Russian Church in his time. He says that the music of the church has to be made by saints and he gives the following verse from the Bible as argumentation: "How shall we sing the LORD's song in a strange land?" (Ps 136:6). The song of the Lord can not be sung in the "strange lang" (by people who are not saints, having the Holy Spirit). According to the saint to modernize the old Russian Znamenny chant it is the same as if someone who knows perfectly some foreign language but doesn't know mathematics tries to translate a mathematical book. Unfortunately it is too difficult for me to translate from Russian to English (neither of these languages I know well) but here is one quotation:
On the other hand it is simply not true that the Orthodox Church doesn't accept the polyphonic music in any form and a good example for this is the Georgian Church. The Georgian polyphony is very old (maybe even the oldest in the world). Several saints participated in the creation of the Georgian Chant and there were some saints who made analogy between the three singing voices in the Georgian Orthodox chant and the three hypostases of the Holy Trinity. After all it is all matter of holy tradition - the polyphony is not accepted in the Greek Churches but at the same time a decision of the Holy Synodos of the Georgian Church forbids any chant (Russian, European or Byzantine) other than the traditional Georgian chant.
However, if we compare the Byzantine Octoechos and the Octoechos of the Syriac Church (Nestorian) we will see that two of the Syriac modes are not used in the Byzantine Octoechos. Considering that the Syriac Octoechos predates the Byzantine Octoechos we can ask about the reason for this change. In think that if we look at the ethos of these unused modes the reason becomes clear. The first unused mode is maqam Huzam which expresses acute/violent passion and/or love and the second unused mode is maqam Saba and it expresses weeping, agony, repentance or extreme joy for something. This means that discernment is required when using non-Orthodox music in the Church.
Regarding the polyphony in the Church. It is not difficult to find on the Russian web-phorums several discussions about the polyphony - several of the people in Russia feel that the polyphonic music does not serve the pray well. And there is one rather interesting comment by one Russian saint (St. Ignatius Brianchaninov) who says that this new polyphonic music is foreign to the spirit of the Church. St. Ignatius doesn't speak against the polyphony in general but only to this particular form of the polyphony that was used in the Russian Church in his time. He says that the music of the church has to be made by saints and he gives the following verse from the Bible as argumentation: "How shall we sing the LORD's song in a strange land?" (Ps 136:6). The song of the Lord can not be sung in the "strange lang" (by people who are not saints, having the Holy Spirit). According to the saint to modernize the old Russian Znamenny chant it is the same as if someone who knows perfectly some foreign language but doesn't know mathematics tries to translate a mathematical book. Unfortunately it is too difficult for me to translate from Russian to English (neither of these languages I know well) but here is one quotation:
Not only the son of this world in incapable to sing this song [the song of the Lord], but even the very pious christian who is not yet free from the slavery of the lust in his heart. His heart doesn't belong to him because it is enslaved by the sin. Also even if someone walks on the path of feat for the Christ and goes mourning all day long (Ps 37:7), i.e. who is still always contemplating his sin and weeping about it, who still doesn't hear inside the joyful voice which is heard in the spiritual dwelling-places of the righteous men - even he is unable to sing the song of the Lord. Then who can sing it? Whose soul can give birth to this song for comfort and enjoyment of the whole Orthodox Church?
On the other hand it is simply not true that the Orthodox Church doesn't accept the polyphonic music in any form and a good example for this is the Georgian Church. The Georgian polyphony is very old (maybe even the oldest in the world). Several saints participated in the creation of the Georgian Chant and there were some saints who made analogy between the three singing voices in the Georgian Orthodox chant and the three hypostases of the Holy Trinity. After all it is all matter of holy tradition - the polyphony is not accepted in the Greek Churches but at the same time a decision of the Holy Synodos of the Georgian Church forbids any chant (Russian, European or Byzantine) other than the traditional Georgian chant.