This paper is a companion paper to Scherbaum & Mzhavanadze (2020). Jointly, the papers describe the results of an interdisciplinary study on three-voiced Svan funeral dirges, known as zär in Svan and zari in Georgian. In the present paper, to which we refer as paper 2, we focus on the (structural) musicological aspects of zär. Bluntly speaking, we want to obtain a basic understanding of ‘how zärs work’. Based on the results of the acoustical analysis of a new collection of field recordings from eleven different performances described in paper 1, where we developed a phenomenological description of the general building blocks, here we try to derive a simple model for the syntaxes of zär. The complexity of the musical structure of the zär shows a very clear connection to the history of the Svans’ settlement along the Enguri River, which is obviously systematically reflected in the Svans’ music. Finally, we see the most interesting aspects of our entire study in the implications it has for the discourse on the historical dynamics of Georgian polyphony. Thus, the results of our study challenge the generally accepted view of the development of Georgian traditional music from monophony to polyphony.