We had a chat about these the other evening, and I'm just getting around to reading the article myself and looking up the form in Temperley.
Chanting tunes are a way of singing prose psalms and canticles to metered music -- unlike Anglican chant, the words aren't sung in natural rhythm on a single reciting note. Instead, each word is assigned a note value within the melody. The tenor and alto alternate singing verses of the psalm, the basses sing throughout, and the sopranos tend not to have much to do until the doxology. Like other music of its period it would likely have been accompanied by whatever instruments were available. Having sung with musicians who are not singers or even wind players, I wonder whether the challenges of getting a number of amateur instrumentalists to accompany chanting with a freer rhythm was another factor contributing to the need for regular, metrical music. This would especially apply if there were few enough resources that the person directing the music also had to sing or play.
I think there are some advantages and disadvantages to this method of chanting psalms. The first thing is that it will require rather more paper than either Anglican prose chants pointed for singing, or metrical psalms in Common Metre. But there is an advantage too -- with flexibility of word placement but metrical music it should be possible to make sure the emphases stay on the right syllables, which is not easy in Anglican chant.
A second disadvantage is one that applies also to other chant forms: the longer psalms and canticles may get tedious with so much repetition of the same melodic material. In Anglican chant this is sometimes worked around by not only the alternation of the cantoris and decani sections (which is echoed in chanting tunes by the alternation of alto and tenor) but by dramatic treatment of the text, easier in a free rhythm, and by creative registration on the accompanying organ (if any). Having all the music written out without any specified variations might make people less likely to experiment with such variations; but in the hands of a sensitive and competent director, even a small group should be able to give an effective performance.
One of the things Francis mentioned was the adaptation of chanting tunes to the resources available today. This is definitely an area of interest for me -- this evening at St Andrew's I had three choir members turn up for rehearsal, and I consider myself fortunate on Sunday mornings when there are twice as many as that. With three, I would need to adapt the tenor and alto parts to be sung by all, and play the bassline on the organ; with six, if the two gentlemen turn up, it should be possible to alternate the ladies and mens voices. Since I'm using an organ all the possibilities for creative registration are there; and this style of chanting is going to be much easier to learn and to direct than the more fluid Anglican chant.
I guess my next steps in exploring the possibilities of chanting tunes for modern liturgy are to visit the British Library to look at some more examples, and to try my hand at writing some -- perhaps using the Common Worship psalter, which aims to retain some of the feel of the Coverdale psalter used in the 1662 Book of Common Prayer but uses somewhat less archaic language.