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

  • Laura McPherson (a1) and Bruce Hayes (a2)

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.

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We would like to thank Robert Daland, Abbie Hantgan, Jeffrey Heath, Kie Zuraw, audiences at the Linguistic Society of America, the Manchester Phonology Meeting, Academia Sinica, Dartmouth College and UCLA, and the anonymous reviewers and editors for Phonology for their help with this article; all remaining defects are the authors’ responsibility. We are also indebted to the Tommo So language consultants, who provided all of the data. We would also like to thank Joni Ricks and her colleagues at the Statistical Consulting Group of the UCLA Institute for Digital Research and Education for their guidance in preparing and interpreting the statistical tests reported here.

The materials used for all the tests (including the program code for the Monte Carlo simulation) are available as online supplementary materials at This research was supported by a grant from the Fulbright Foundation and by grants BCS-0537435 and BCS-0853364 from the U.S. National Science Foundation.

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Albright, Adam (2012). Additive markedness interactions in phonology. Ms, MIT. Available (January 2016) at
Baković, Eric (2000). Harmony, dominance, and control. PhD dissertation, Rutgers University.
Bermúdez-Otero, Ricardo (1999). Constraint interaction in language change: quantity in English and Germanic. PhD dissertation, University of Manchester & University of Santiago de Compostela.
Boersma, Paul (1998). Functional phonology: formalizing the interactions between articulatory and perceptual drives. PhD dissertation, University of Amsterdam.
Boersma, Paul & Hayes, Bruce (2001). Empirical tests of the Gradual Learning Algorithm. LI 32. 4586.
Boersma, Paul & Pater, Joe (2016). Convergence properties of a Gradual Learning Algorithm for Harmonic Grammar. In McCarthy & Pater (2016). 389434.
Chomsky, Noam & Halle, Morris (1968). The sound pattern of English. New York: Harper & Row.
Clements, G. N. (1985). The geometry of phonological features. Phonology Yearbook 2. 225252.
Clements, G. N. & Sezer, Engin (1982). Vowel and consonant disharmony in Turkish. In van der Hulst, Harry & Smith, Norval (eds.) The structure of phonological representations. Part 2. Dordrecht: Foris. 213255.
Cole, Jennifer & Kisseberth, Charles (1994). An optimal domains theory of harmony. Studies in the Linguistic Sciences 24. 101114.
de Lacy, Paul (2004). Markedness conflation in Optimality Theory. Phonology 21. 145199.
Della Pietra, Stephen, Pietra, Vincent Della & Lafferty, John (1997). Inducing features of random fields. IEEE Transactions: Pattern Analysis and Machine Intelligence 19. 380393.
Fasold, Ralph W. (1972). Tense marking in Black English: a linguistic and social analysis. Arlington: Center for Applied Linguistics.
Flack, Kathryn (2007). Templatic morphology and indexed markedness constraints. LI 38. 749758.
Flemming, Edward (2001). Scalar and categorical phenomena in a unified model of phonetics and phonology. Phonology 18. 744.
Frisch, Stefan A., Broe, Michael B. & Pierrehumbert, Janet B. (1997). Similarity and phonotactics in Arabic. Available as ROA-223 from the Rutgers Optimality Archive.
Frisch, Stefan A., Pierrehumbert, Janet B. & Broe, Michael B. (2004). Similarity avoidance and the OCP. NLLT 22. 179228.
Fruehwald, Josef T. (2012). Redevelopment of a morphological class. University of Pennsylvania Working Papers in Linguistics 18:1. 7786. Available at
Goldrick, Matthew (2000). Turbid output representations and the unity of opacity. NELS 30. 231245.
Goldwater, Sharon & Johnson, Mark (2003). Learning OT constraint rankings using a Maximum Entropy model. In Spenador, Jennifer, Eriksson, Anders & Dahl, Östen (eds.) Proceedings of the Stockholm Workshop on Variation within Optimality Theory. Stockholm: Stockholm University. 111120.
Gouskova, Maria (2007). The reduplicative template in Tonkawa. Phonology 24. 367396.
Guy, Gregory R. (1980). Variation in the group and the individual: the case of final stop deletion. In Labov (1980). 136.
Guy, Gregory R. (1991). Explanation in variable phonology: an exponential model of morphological constraints. Language Variation and Change 3. 122.
Hantgan, Abbie & Davis, Stuart (2012). Bondu-so vowel harmony: a descriptive analysis with theoretical implications. Studies in African Linguistics 41. 187212.
Hargus, Sharon (1988). The lexical phonology of Sekani. New York: Garland.
Hayes, Bruce & Wilson, Colin (2008). A maximum entropy model of phonotactics and phonotactic learning. LI 39. 379440.
Hochstetler, J. Lee, Durieux, J. A. & Durieux-Boon, E. I. K. (2004). Sociolinguistic survey of the Dogon language area. SIL International. Available (January 2016) at
Inkelas, Sharon (1993). Nimboran position class morphology. NLLT 11. 559624.
Jesney, Karen (2011). Licensing in multiple contexts: an argument for Harmonic Grammar. CLS 45:1. 287301.
Jesney, Karen & Tessier, Anne-Michelle (2011). Biases in Harmonic Grammar: the road to restrictive learning. NLLT 29. 251290.
Jurgec, Peter (2010). Disjunctive lexical stratification. LI 41. 149161.
Katamba, Francis (2004). Morphology: critical concepts in linguistics. London & New York: Routledge.
Kaun, Abigail R. (1995). The typology of rounding harmony: an optimality theoretic approach. PhD dissertation, University of California, Los Angeles.
Kimper, Wendell (2011). Competing triggers: transparency and opacity in vowel harmony. PhD dissertation, University of Massachusetts Amherst.
Kiparsky, Paul (1973). Phonological representations. In Fujimura, Osamu (ed.) Three dimensions of linguistic theory. Tokyo: TEC. 3135.
Kiparsky, Paul (1977). The rhythmic structure of English verse. LI 8. 189247.
Kiparsky, Paul (1982). Lexical phonology and morphology. In The Linguistic Society of Korea (ed.) Linguistics in the morning calm. Seoul: Hanshin. 391.
Kiparsky, Paul (1984). On the lexical phonology of Icelandic. In Elert, Claes-Christian, Johansson, Iréne & Strangert, Eva (eds.) Nordic Prosody III. Stockholm: Almqvist & Wiksell. 135164.
Kiparsky, Paul (1994). An OT perspective on phonological variation. Handout from Rutgers Optimality Workshop 1993 and New Ways of Analyzing Variation 1994, Stanford University. Available (January 2016) at
Kiparsky, Paul (2000). Opacity and cyclicity. The Linguistic Review 17. 351365.
Kiparsky, Paul (2003). Syllables and moras in Arabic. In Féry, Caroline & van de Vijver, Ruben (eds.) The syllable in Optimality Theory. Cambridge: Cambridge University Press. 147182.
Kirchner, Robert (1993). Turkish vowel disharmony in Optimality Theory. Paper presented at the Rutgers Optimality Workshop, Rutgers University.
Kroch, Anthony S. (1989). Reflexes of grammar in patterns of language change. Language Variation and Change 1. 199244.
Labov, William (ed.) (1980). Locating language in time and space. New York: Academic Press.
Legendre, Géraldine, Miyata, Yoshiro & Smolensky, Paul (1990). Harmonic Grammar: a formal multi-level connectionist theory of linguistic well-formedness: theoretical foundations. In Proceedings of the 12th Annual Conference of the Cognitive Science Society. Hillsdale: Erlbaum. 388395.
Linzen, Tal, Kasyanenko, Sofya & Gouskova, Maria (2013). Lexical and phonological variation in Russian prepositions. Phonology 30. 453515.
Lombardi, Linda (1999). Positional faithfulness and voicing assimilation in Optimality Theory. NLLT 17. 267302.
McCarthy, John J. (1999). Sympathy and phonological opacity. Phonology 16. 331399.
McCarthy, John J. (2004). Headed spans and autosegmental spreading. Ms, University of Massachusetts, Amherst. Available as ROA-685 from the Rutgers Optimality Archive.
McCarthy, John J. (2007). Hidden generalizations: phonological opacity in Optimality Theory. Sheffield & Bristol, Conn.: Equinox.
McCarthy, John J. & Pater, Joe (eds.) (2016). Harmonic Grammar and Harmonic Serialism. London: Equinox.
McCarthy, John J. & Prince, Alan (1995). Faithfulness and reduplicative identity. In Beckman, Jill N., Dickey, Laura Walsh & Urbanczyk, Suzanne (eds.) Papers in Optimality Theory. Amherst: GLSA. 249384.
McClelland, James & Vander Wyk, Brent C. (2006). Graded constraints on English word forms. Ms, Carnegie Mellon University. Available (January 2016) at
McPherson, Laura (2013). A grammar of Tommo So. Berlin & Boston: De Gruyter Mouton.
Mooney, Christopher Z. (1997). Monte Carlo simulation. Thousand Oaks, CA: Sage.
Mosteller, Frederick, Rourke, Robert E. K. & Thomas, George B. (1970). Probability with statistical applications. 2nd edn. Reading, Mass.: Addison-Wesley.
Myers, Scott (1991). Structure Preservation and the Strong Domain Hypothesis. LI 22. 379385.
Nesbitt, C. F. (1984). The linguistic constraints on a variable process: /t,d/ deletion in Sydney speech. BA thesis, University of Sydney.
Neu, Helene (1980). Ranking on constraints on /t,d/ deletion in American English: a statistical analysis. In Labov (1980). 3754.
Nida, Eugene (1949). Morphology: the descriptive analysis of words. 2nd edn. Ann Arbor: University of Michigan Press.
Pater, Joe (2000). Non-uniformity in English secondary stress: the role of ranked and lexically specific constraints. Phonology 17. 237274.
Pater, Joe (2008). Gradual learning and convergence. LI 39. 334345.
Pater, Joe (2009a). Weighted constraints in generative linguistics. Cognitive Science 33. 9991035.
Pater, Joe (2009b). Morpheme-specific phonology: constraint indexation and inconsistency resolution. In Parker, Steve (ed.) Phonological argumentation: essays on evidence and motivation. London: Equinox. 123154.
Pater, Joe (2016). Universal Grammar with weighted constraints. In McCarthy & Pater (2016). 146.
Potts, Christopher, Pater, Joe, Jesney, Karen, Bhatt, Rajesh & Becker, Michael (2010). Harmonic Grammar with linear programming: from linear systems to linguistic typology. Phonology 27. 77117.
Prince, Alan (1997). Paninian hierarchies. Ms, Rutgers University.
Prince, Alan & Smolensky, Paul (1993). Optimality Theory: constraint interaction in generative grammar. Ms, Rutgers University & University of Colorado, Boulder. Published 2004, Malden, Mass. & Oxford: Blackwell.
Rhodes, Russell (2012). Vowel harmony as Agreement by Correspondence. Annual Report of the UC Berkeley Phonology Laboratory. 138168.
Ringen, Catherine O. & Heinämäki, Orvokki (1999). Variation in Finnish vowel harmony: an OT account. NLLT 17. 303337.
Ringen, Catherine O. & Vago, Robert M. (1998). Hungarian vowel harmony in Optimality Theory. Phonology 15. 393416.
Rose, Sharon & Walker, Rachel (2004). A typology of consonant agreement as correspondence. Lg 80. 475531.
Ryan, Kevin M. (2010). Variable affix order: grammar and learning. Lg 86. 758791.
Santa Ana, Otto (1991). Phonetic simplification processes in the English of the barrio: a cross-generational sociolinguistic study of the Chicanos of Los Angeles. PhD dissertation, University of Pennsylvania.
Smolensky, Paul (1986). Information processing in dynamical systems: foundations of Harmony Theory. In Rumelhart, D. E., McClelland, J. L. & the PDP Research Group (eds.) Parallel Distributed Processing: explorations in the micro-structure of cognition. Vol. 1: Foundations. Cambridge, Mass.: MIT Press. 194281.
Smolensky, Paul & Legendre, Géraldine (eds.) (2006). The harmonic mind: from neural computation to optimality-theoretic grammar. 2 vols. Cambridge, Mass.: MIT Press.
Steriade, Donca (2008). A pseudo-cyclic effect in Romanian morphophonology. In Bachrach, Asaf & Nevins, Andrew (eds.) Inflectional identity. Oxford: Oxford University Press. 313359.
Sussman, Harvey M., Hoemeke, Kathryn A. & Ahmed, Farhan S. (1993). A cross-linguistic investigation of locus equations as a phonetic descriptor for place of articulation. JASA 94. 12561268.
Tagliamonte, Sali & Temple, Rosalind (2005). New perspectives on an ol’ variable: (t,d) deletion in British English. Language Variation and Change 17. 281302.
Tesar, Bruce & Smolensky, Paul (2000). Learnability in Optimality Theory. Cambridge, Mass.: MIT Press.
Walker, Rachel (1998). Nasalization, neutral segments and opacity effects. PhD dissertation, University of California, Santa Cruz.
Wilson, Colin (2006). Learning phonology with substantive bias: an experimental and computational study of velar palatalization. Cognitive Science 30. 945982.
Wilson, Colin & George, Benjamin (2009). Maxent grammar tool. Software package. Available at
Zuraw, Kie (2003). Probability in language change. In Bod, Rens, Hay, Jennifer & Jannedy, Stefanie (eds.) Probabilistic linguistics. Cambridge, Mass.: MIT Press. 139176.
Zuraw, Kie (2012). Quantitative patterns of constraint interaction. Paper presented at the 30th West Coast Conference on Formal Linguistics, University of California, Santa Cruz.
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