Southeast Solomonic (SES) languages have retained the Proto-Oceanic decimal system for general counting, and also show evidence of a supplementary specific counting system, based on the number ten. These languages have lexemes that refer, for example, to 'ten pigs' or 'ten coconuts' (numerically specific nouns), as well as lexemes that refer to 'pig' and 'coconut'. This paper describes the linguistic and cultural context of this counting system. It describes the syntactic behavior of numerically specific nouns and the cultural context in which they were used. This specific counting system is not widely used today, and in any individual language there may be only a small number of numerically specific nouns. However, by looking at the languages as a group, with shared cultural and trading practices, the specific counting system and its uses can be better understood. In the specific counting systems of the SES, speakers count edible and nonedible objects of value and exchange by tens to calculate and remember large numbers during times of feasting and exchange.