Intonation idioms (?)

John Wells (= JW) in his two blog entries of the 6th and 7th of October writes about what he terms "intonation idioms". To give some examples (all taken from JW's blog):

credit: www.canaryzoo.com

    What’s ˈthat supposed to mean?
    You can say \that again!
    \There’s a clever dog!
    Now \there’s a  thought!

 JW then continues: "My ideal is to supply EFL learners with an algorithm that enables them to predict with confidence an appropriate spoken intonation pattern for any written fragment of dialogue. Where I fail in this ambition, I may need to refine my rules. Failing that, I call the pattern idiomatic."

Any advanced EFL learner and certainly an EFL teacher should be able to use the appropriate prosodic pattern for, say, "Now there's a thought!" as a response to someone else suggesting "Let's have another drink." What kind of construction is this sentence? Taken literally "now there's a thought" means something like "at the time of speaking a thought exists" or "at the time of speaking some thought is over there". Both readings do not make sense as a comment on or reply to the preceding suggestion of having another drink. Since the sole application of morphosyntactic and semantic rules does not lead to the proper meaning, the sentence is called an idiom. The borderline between an idiom and a non-idiomatic expression is fuzzy, of course.

Applying the rules for nucleus placement gives "Now there’s a \thought!", which is not what native speakers say. Since the application of nucleus placement rules does not lead to the proper prosodic pattern, the sentence is an idiom -  now in a double sense: semantically and prosodically.

What term should we use to express this duality of idiomaticity? When we call an expression 'idiomatic', most of us, I guess, automatically think of its grammatical and semantic irregularity. I was tempted to name them 'idioms squared', but refrained from doing so. I chose the (probably not very felicitous) term 'abnormal idioms' (see my blog entry of the 27th of September); on second thought 'double idioms' may be a more apposite term. JW uses 'intonation idioms'. I'm not very happy with this coinage, because it's not the choice of the intonation contour which is idiomatic but rather the choice of the word within the phrase/sentence to which the nucleus is assigned. Jack Windsor Lewis dislikes the coinage as well (see his blog #288) and proposes 'accentuation idioms', 'stress idioms' or 'tonicity idioms', which are much more appropriate. But ... when I read 'accentuation/stress/tonicity idiom' it seems to me that a phrase classified as such is an idiom due to its irregular accentuation only. My impression may be wrong, but there it \is.