Lent began yesterday for us Byzantines, and Ash Wednesday is tomorrow. So it's an appropriate time to think about fasting.
On Sunday at coffee hour I learned about this article by Fr. Alexander Schmemann, "Fast and Liturgy." He argues, based on the typikon, that the length of the Eucharistic fast was intended to vary with the character of the occasion. The Divine Liturgy was to begin at the third hour on Sundays, the fourth hour on Saturdays, and the fifth hour on other days when it was celebrated. Given that the Eucharistic fast was to begin at midnight, it would be longer on days of a less festal character.
On a few particularly solemn days, the Liturgy was not to be celebrated until after Vespers - either a Vesperal Liturgy or a Presanctified Liturgy. On a day of strict fasting (such as the Beheading of St. John the Baptist or the Exaltation of the Holy Cross), there was to be no celebration of the Liturgy at all, and thus it would have to be postponed until the start of the next liturgical day, which began with Vespers. (My acquaintance at coffee hour said these would originally have been Presanctified Liturgies before such services were restricted to Lent.)
The Christian life is defined by the complementary poles of fasting and feasting. We pray and keep vigil, watching and waiting for our Lord's parousia. But we also experience a foretaste of the messianic banquet in the Eucharist. So we fast in preparation for feasting. We keep a Eucharistic fast before every Liturgy, and we keep a season of fasting before major feasts.
Of course Schmemann says it better. Read the article.