“By the Waters of Babylon” is a text appointed to be sung at Matins on pre-Lenten Sundays, after the Polyeleos. Its text is taken from Psalm 136 (LXX) — the entire psalm is appointed to be sung in the sixth tone, with Alleluias after each verse.
The Znamenny chant melody for this setting is taken directly from the Обиход Церковный Нотнаго Пения published in Kievan square-note notation in 1860. Arkhangelsky wrote a four-part choral arrangement of this melody, but the edition with which I am familiar has the choir only singing the first verse and the Alelluia refrains; the second and subsequent verses are to be chanted by a soloist.
I completed my own harmonization before I ever heard the Arkhangelsky. While his remains in a minor key throughout, mine maintains a more modal flavor, and resolves to a major chord at the end of each stanza.