When churches last used metrical psalms, there were two different sorts of tunes to which they sang them. Although most of the time congregations sang them to the sort of four line tunes we still know in CM, LM or SM, there was also a lively tradition of singing them to what are often referred to as ‘fuguing tunes’, with multiple repeats. We still sing a few of these. Lyngham, “O for a thousand tongues” is one. Cranbrook, “On Ilkley Moor Baht ‘at” is another.
There are some wonderful examples in Praise and Glory and on the Francis Roads and Sue Glover Websites on the link page.
The compilers of the first edition of Ancient and Modern really hated these sort of tunes, and the bands that played them. So they have tended only to survive for certain special examples, and some Christmas music. There are a few in this collection. For those that can get access to them (see below) there are many more that are well worth trying.