I have composed an exapostilarion available here in three different arrangements.
This is a special Sunday for me as it was the first Orthodox Divine Liturgy I attended as an inquirer. That day I obtained a book on the faith (The Orthodox Church by Kallistos Ware) and never looked back.
Exapostilarion of the Feast (the original melody)
Johann von Gardner was the Russian musician and musicologist who uncovered this Exapostilarion Special Melody and helped to revive its use. The origin is an old Russian ‘Put melody.
People sing this with variations in the rhythm. Gardner himself produced different versions of this melody, one more melodic and slow-moving, the other more syncopated.