Peter van Dijk The liturgical function of Buxtehude’s organ works
Het ORGEL 104 (2008), nr. 1, xx-xx [summary]

Many organists in large North-German city churches improvised in the services, but compositions were also written down for the use of organists who did not improvise. Little can be said with certainty about the relationship between Buxtehude’s improvisations and his written-out compositions. That Buxtehude’s organ works were intended for liturgical use, among other uses, is practically undisputed. But there is disagreement about how the compositions were used within the liturgy. Using information from church regulations and from two orders of service from Hamburg (1607) and Danzig (1705) we can presume that music not based on a chorale was used as a postlude to services. It is questionable whether Buxtehude’s chorale settings functioned as preludes; they may just as well have functioned as organ verses in alternatim use. The large chorale fantasies may have sounded between the reading of the gospel and the sermon. They may also have been used as musica sub communione, but the chorales on which they are based are seldom specific to communion. There are no sources indicating that the chorale fantasies were played in the Abendmusiken.