From earliest times, composers of Byzantine chant have identified each musical mode by a characteristic intonation formula (ajphvchma), a phrase normally sung in its entirety by the protopsaltis (the lead chanter of the right choir) alone, without the ison. Its function is to help the chanters recall the ethos of a given mode before beginning the chant. Moreover, it also provides the choir with the pitch required for the first note of the piece.
In Byzantine music, there are eight modes and three modal genres: the diatonic, the enharmonic, and the chromatic.2 Furthermore, each of the eight modes is broken down into three species, characterized by the number of notes typically attached to a syllable. A melody with one or two notes above a syllable is called “heirmologikon”; one carrying approximately three or four is called “sticherarikon”; and that having a dozen or more notes is called “papadikon.” In the first and third modes, the musical patterns are identical for each of these three species.For the others, however, the musical gestures differ significantly; hence the need for more than one intonation formula for each mode.
Taken from "The Intonations of the Eight Modes" compiled by Saint Anthony's Monastery.
Ρόδον τό Ἀμάραντον