My favorite early Orthodox hymn is the fifth century hymn Ho Monogenes, which in our Eastern Orthodox liturgy and by our Oriental Orthodox friends in the Armenian liturgy is part of the second Antiphon (or rather follows it), and which is also used on Great and Holy Friday by the Coptic Orthodox, and the Syriac Orthodox actually use the hymn as the first hymn in their liturgy, in the same location in the liturgy where we use the Litany of Peace.
What I love about Ho Monogenes is the elegant manner in which it rejects Nestorianism and teaches us correct Christology:
Only-Begotten Son and Immortal Word of God,
Who for our salvation didst will to be incarnate of the holy Theotokos and Ever-Virgin Mary;
Who without change didst become man and was crucified;
Who art one of the Holy Trinity, glorified with the Father and the Holy Spirit:
O Christ our God, trampling down death by death, save us!
The hymn has a sort of supplemental creedal quality, like Te Deum Laudamus and the Orthodox version of Quincunque Vult, which I don’t think we actually sing, but one can find it in various Orthodox liturgical books - for example, A Psalter for Prayer, which is the corrected version of the Coverdale Psalter published by Holy Trinity Monastery in Jordanville, and also Metropolitan Kallistos Ware, memory eternal, reported that the Orthodox version (which lacks the filioque) could be found in some Greek editions of the
Horologion.*
*This book, for the benefit of members such as our friend
@David Lamb who might not be aware of the different Orthodox service books, hymnals and their function, contains the invariant portions of the daily services such as Matins, Vespers, Compline and the Hours of Prime (the first hour after dawn), Terce (the third hour), Sext (noon), and Noone (the ninth hour - roughly 3 PM). Terce, Sext and Noone are important because it was at the third hour when the Holy Spirit descended on Pentecost, it was at the sixth hour, or noon, when Christ our True God was crucified, and it was at the ninth hour when He died on the cross. The Unabbreviated Horologion published by the same monastery that publishes the aforementioned A Psalter for Prayer also contains most of the Divine Liturgy, and also some propers for major feasts, making it quite a useful book.
The main hymnals in Orthodoxy are the Octoechos, from which the normal daily prayers are populated with hymns according to one of the eight tones, which are musically and lyrically distinct, and there is a tone of the week, so the Octoechos is used on a continual eight week cycle, and the Menaion, which contains the hymns for fixed feasts such as the Nativity (Christmas), the Baptism of our Lord (Theophany, or Epiphany), the Meeting of our Lord (Candlemas as it is known in the West, on February 2nd) the Annunciation, the Transfiguration, the Dormition of the Theotokos, the Beheading of St. John the Baptist, the Nativity of the Theotokos, the Exaltation of the Cross, the Holy Apostles, and so on. Then, those hymns that are connected to the date of Pascha (Easter, the Feast of the Resurrection) are compiled into the Triodion, which contains those hymns for Lent and Holy Week, and the Pentecostarion (also known as the Flowery Triodion) which contains those hymns starting with Paschal Matins and continuing all the way through Pentecost to the Feast of All Saints (the first Sunday after Pentecost).
There are also other hymn books, for example, books containing the hymns sung during the divine liturgy, and also the Euchologion, which contains services for Baptism, Chrismation, Holy Matrimony, Holy Unction (annointing the sick with oil), Holy Orders, and other services such as the
Pannikhida (the memorial service), the Great Blessing of Water and so on, will often contain the appropriate hymns for those services.
These books usually do not contain the music, but rather there are separate books which do contain the words and music. The music will vary depending on the particular jurisdiction - for example, the Greeks tend to use Byzantine Chant, while the OCA, ROCOR and, for historical reasons, many Antiochian Orthodox churches, will use hymns which are based on Church Slavonic melodies (many Antiochian churches will use a mix of Slavonic music and Syro-Byzantine chant, translated into English in all cases of course). One example is St. Philip’s Antiochian Orthodox Church in Souderton, Pennsylvania, which streams their services online:
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One can find English translations of many of these here:
Ponomar Project :: Liturgical Texts in English