Greenlandic Eskimo (Eskimo-Aleut) (before the dual became obsolete) and Nama (Khoisan) limit their nominal dual to nouns other than those denoting natural pairs (Plank 1989: 309).
The reverse formulation: “If there is a Dual with nouns denoting natural pairs, there will be one with non-natural-pair nouns as well” does not hold. Plank (1989: 309-10) mentions as counterexamples: Maidu (Maiduan), Kâte (Huon, Trans-New Guinea, Papuan), Ngiyambaa (Pama-Nyungan) and Tunica (isolate possibly remotely related to Algonquian). Plank proposes a less restrictive implication: “If in any language some nouns are eligible for dual marking while others are not (or less readily), the criterion is whether or not they denote natural pairs.”Refining this implication, Plank (1996) suggests that two further dual preferences need to be added to the implicatum: animate rather than inanimate, frequently-counted objects rather than other objects.
The reverse formulation: “If there is a Dual with nouns denoting natural pairs, there will be one with non-natural-pair nouns as well” does not hold. Plank (1989: 309-10) mentions as counterexamples: Maidu (Maiduan), Kâte (Huon, Trans-New Guinea, Papuan), Ngiyambaa (Pama-Nyungan) and Tunica (isolate possibly remotely related to Algonquian). Plank proposes a less restrictive implication: “If in any language some nouns are eligible for dual marking while others are not (or less readily), the criterion is whether or not they denote natural pairs.”Refining this implication, Plank (1996) suggests that two further dual preferences need to be added to the implicatum: animate rather than inanimate, frequently-counted objects rather than other objects.