Relating application frequency to morphological structure: the case of Tommo So vowel harmony

We describe three vowel-harmony processes in Tommo So and their interaction with morphological structure. The verbal suffixes of Tommo So occur in a strict linear order, establishing a Kiparskian hierarchy of distance from the root. This distance is respected by all three harmony processes; they ‘peter out’, applying with lower frequency as distance from the root increases. The function relating application rate to distance is well fitted by families of sigmoid curves, declining in frequency from one to zero. We show that, assuming appropriate constraints, such functions are a direct consequence of Harmonic Grammar. The crucially conflicting constraints are Ident (violated just once by harmonised candidates) and a scalar version of Agree (violated one to seven times, based on closeness of the target to the root). We show that our model achieves a close fit to the data, while a variety of alternative models fail to do so.