The association of music and mathematics is unusual in the context of orally transmitted musical traditions. But in such traditions, there exist some structures that are comparable with mathematical constructions. In this article, we present a case study of an elaborated musical structure, which can be analyzed into two different ways which are logically equivalent. Our main problem is to select the logical explanation which is the most relevant from the musicians point of view, or in other words, to describe the cognitive process which gave birth to these constructions in the native peoples mind. This article introduces a psychological framework adapted to this situation, and then, presents an overview of a classical ethnomathematical example dealing with sand drawings from Vanuatu, in order to give some methodological backgrounds. Finally, we turn to the harp repertoire of the Nzakara people from Central African Republic, and we show how it contains an interesting case of a musical structure which is ambiguous according to the mental representations associated with it.