Douglas Harper's Etymology Dictionary
Wiktionary
n. (context poetry English) A technique in drama or poetry, in which alternating lines, or half-lines, are given to alternating characters, voices, or entities.
Wikipedia
Stichomythia (Greek: Στιχομυθία) is a technique in verse drama in which sequences of single alternating lines, or half-lines (hemistichomythia) or two-line speeches (distichomythia) are given to alternating characters. It typically features repetition and antithesis. The term originated in the theatre of Ancient Greece, though many dramatists since have used the technique. Etymologically it derives from the Greek stikhos ("row, line of verse") + muthos ("speech, talk").
Stichomythia is particularly well suited to sections of dramatic dialogue where two characters are in violent dispute. The rhythmic intensity of the alternating lines combined with quick, biting ripostes in the dialogue can create a powerful effect.
Usage examples of "stichomythia".
In the interval he concentrated on perfecting the odes and the rhymed variety of stichomythia in which he often had his characters speak, parrying epigram with epigram.
The author was well acquainted with classical drama, as may be seen in his use of stichomythia, amongst other things, and possibly in his preference for a Grecian story.