Matangi is dark, green or black, holds a vina, and is associated with speech, music, learning and the arts, which is why she is routinely described as the tantric Sarasvati. The comparison is useful up to the point where it breaks, and where it breaks is the whole of her.
Sarasvati is the goddess of purity in its intellectual form: white, seated on a white lotus, approached by the clean and the well-spoken. Matangi is approached with ucchishta, food already tasted, left over, in contact with saliva and therefore polluted beyond any possibility of use in an orthodox offering. Worshippers are directed to offer her leftovers and to come without the ritual purifications that precede other rites, and one of her standard names is Ucchishta Matangini. The prescription is not a relaxation of a rule. It is the deliberate reversal of the rule, and the reversal is the practice rather than a defect in it.
Her name is traced to the sage Matanga, whose austerities are given as the occasion of her appearance in several accounts, and the word matanga also carries associations with the elephant and, in ordinary usage, with people held to stand outside the caste order. Descriptions of her retinue and her setting place her at the edge of the settlement rather than at its centre, which is consistent with everything else about her.