This post is prompted by a comment from Andrea on a post I did in September 2011. You might like to read that before continuing here. My response is too long to do in a comment, so I’ve decided to make a separate post of it.
The comment is about a version of the fall-rise nuclear tone that doesn’t have a terminal rise. Before launching into the details of my response I’d like to make it clear exactly what I mean when I call something a fall-rise nuclear tone, or a high fall or a low rise etc. etc. For me these are names of functional categories, not attempts at detailed characterisation of pitch/F0 configurations. When we call /t/, for example, a voiceless alveolar plosive phoneme, we don’t mean that it is always realised as that particular sound. We have to call it something, so quite reasonably choose a label which fits many of the realisations of the phoneme. Similarly, when I call something a fall-rise I mean a tone category which is often, but not always, realised by a falling and then rising movement in the pitch contour.
The particular realisation that Andrea comments on is a pitch fall from high to mid. We could symbolise the full form of a fall-rise as HLM. The cut-down version is HM. This phenomenon is known as tonal compression, not truncation as Andrea suggests. A truncated HLM sequence would be HL. A discussion of both phenomena with examples from various languages can be found in Intonational Phonology by D. Robert Ladd (Cambridge University Press, 1996, especially pp. 132-136). Some languages prefer truncation, but others, including GB English, prefer compression. The motivation for both is similar, namely the lack of time at normal speech rates to realise the complete tonal contour. Both phenomena can be avoided by slowing down the speech.
Andrea asks whether the HM tone is common in English. I have no hard evidence to give a definite answer, but my hunch is that it is. I can’t comment on Andrea’s other “stylised tone that is clearly a fall to me, and this one also begins relatively high and is somewhat flattened at the end”, because I don’t know what that sounds like. All fall-to-baseline tones flatten out on post tonic syllables, but I don’t know if that is what Andrea means. I would add that I think attempts to characterise tones as “statement-like” or “question-like” are very dubious.