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This article introduces two new mathematical formulas designed to describe, compare, and contrast languages in terms of the overall markedness and complexity of their phonological rule components. The Transparency Index evaluates the four classical types of ordering relationships which obtain between individual pairs of rules, building on Kiparsky's (Linguistic universals and linguistic change, Holt, Rinehart & Winston, 1968, Historical linguistics, University of Maryland Linguistics Program, 1971) classification of these as either feeding, bleeding, counterfeeding, or counterbleeding. Among these, feeding and bleeding orders are transparent in that they result in surface-true generalizations and are therefore natural and preferred, whereas counterbleeding and counterfeeding relationships lead to opaque (non-transparent) phonetic outcomes since the final surface representation appears to be a counterexample to one of the rules. For each language that we wish to analyze, the Transparency Index calculates the attested frequency of both types of transparent interactions grouped together (feeding and bleeding), and divides this sum by the total number of tokens of all four rule ordering types combined. The Density Index, on the other hand, computes the total number of crucial rule orderings (regardless of which kind) among each exhaustive, language-specific inventory of processes. These two statistical proposals are applied to a sample of seven genetically and areally diverse languages to illustrate their usefulness and rank each language along a continuum of relative typological markedness and simplicity. This study constitutes the first rigorous attempt to quantify the occurrence of different types of phonological rule relationships – including their degree of interaction and inherent rate of opacity – both within and across languages. It thus represents a step forward in extending an old line of inquiry into a topic which has recently spawned a renewed wave of interest, partly due to the problems it raises for standard Optimality Theory.

An underdescribed sound change in Germanic is the shift of initial kl and gl to tl and dl respectively. Though not widely known, KL > TL has occurred more than once in the history of Germanic. Relevant phonetic factors include coarticulation and perceptual similarity. A third structural factor in Germanic and elsewhere is a pre-existing TL gap. KL > TL gives rise to common TL clusters, though, under many phonological analyses, TL clusters are disfavored or marked. Typological comparison suggests that TL clusters are not marked, but that contrasts between KL and TL are disfavored.

Base-6-36 numeral systems, a typological rarity, are found in Kanum languages of New Guinea as testified by Donohue (Linguistic Typology 12: 423–429, 2008). We look at the probable relatives of the Kanum languages and show that the base-6 system must have emerged in the Tonda group specifically. Since there is no evidence of body-part terms in the base-6 forms attested, we speculate that these systems have a different origin. Specifically, we suggest that the base-6 systems arose for counting yams. The ethnographic data for Kanum and other relevant languages are in concord with such a scenario. Whether there is a historical connection with base-6 systems of the Kolopom languages, near, but not adjacent, to the west, remains an open question. If there is a connection, it is areal rather than genetic, but sufficient evidence for a pre-historic areal connection remains to be collected. Equally, if not more, puzzling would be the conclusion that there is no historical connection, given the rarity of base-6 in the world as a whole.

Southern New Guinea languages possess unusual senary systems, used for yam-counting. This article demonstrates the common presence of cognate base-6 numeral systems with monomorphemic power terms up to 6 6 , with attestation across the major branches of the Morehead-Upper Maro group. Kanum, related to the Morehead-Upper Maro family, has cognate forms but with ambiguity between the readings 6n and ‘numeral in nth senary cycle’, while Agöb in the neighbouring Pahoturi family has recently borrowed the senary power numerals. Evidence is presented for convergent cultural factors that would have selected for the emergence of a base-6 numeral system, including the six-petal arrangement in which they are laid out in piles and other aspects of ceremonial counting routines.

This paper attempts to summarise the discussion of senary, or base-6, numeral systems in this and the preceding issue of LT and to place the results for New Guinea in a wider typological perspective. In light of current crosslinguistic evidence about numeral bases, to be distinguished into construction-bases and cycle-bases, some universals on record need to be adjusted, while a couple of new universals can be suggested specifically for base-6 systems.