(How) can autosegmental theories of tone account for pitch contours with more changes of direction than there are segments?

Question

I had been interested in the idea that tone contours are due to practical limitations in following an underlying target path that is always a straight line, as proposed by Xu. However, this theory seems to me to imply that the citation forms will be the same or nearly the same as the underlying targets, which is demonstrably not the case. I posted about that here but didn’t get any response, so have put Xu's approach on one side for now.

As I understand autosegmental theories, each segment of the rime is supposed to carry a unitary instruction or gesture like ‘up’ or ‘down’.

I know that in Thai, there are some words whose rimes consist of a short vowel but which nevertheless have a falling tone. Examples would be ก็ or ค่ะ. This as I understand it requires two instructions (up then down), but as far as I can see there is only one segment. Can an autosegmental theory accommodate this, and if so how?

Similarly, in Vietnamese the hook tone would seem to have three changes of direction in its citation form (up, down, back up a bit). Does that mean that a vowel like the one in khoẻ has to be analysed as having three segments?

I believe the duration of a final sonorant will be greater when it follows a short vowel, as in phẩn, but on first impression it seems clunky to me to say that this difference in length is due to the final consonant having two segments rather than one. Would that be the autosegmental approach?

Answer 1

Autosegmental theory does not "say" as much as you seem to think. For example, the theory does not say that each segment of the rime carries a unitary instruction or gesture like up or down. What is says is that there are two representational levels, "tone" and "tone-bearing units", and they can have a relationship ("association"). Some earlier versions maintained principles involving universal or existential quantifiers ("all vowels must be associated with some tone"), but such statements have not been part of the theory since the mid 80's. The question of what thing constitutes the tone bearing unit is an unresolved controversy: could be "segment", "vowel", "mora", "syllable" or some syllabic sub-constituent. "Up and "down" are not part of the vocabulary of autosegmental phonology (they are part of Clark's dynamic theory). Instead, the featural units specify positions in tonal space (not direction of movement).

It is a fundamental premise of autosegmental theory that a TBU can bear more than one tone. This indeed characterizes the difference between ASP and Woo's SPE-style theory of tone. The number of segments or the length of vowels does not impose any general limit on how many tones may be present in a syllable. However, there are many languages which observe functionally-motivated limits, to the effect that two tones are possible within a syllable only if the syllable has a long vowel, or a vowel plus sonorant coda. In addition, there are languages which do not have a length contrast for vowels (Vietnamese, for instance) which nevertheless have tones which are phonetically defined by multiple target levels (as well as other properties). The theory does not have any problem with positing three of four tones on a single short vowel segment. If you can learn (hear) that a word in some language has a rise-fall-rise tone on a short vowel, the theory allows you to represent it.

As far as I know, the simplest account of Vietnamese tone just does not care about the number of segments in a syllable. You do not have to add extra segments to provide docking sights for tones.