In Otzrot Hayyim, Sha'ar Tant"a (Ta'amim Nekudot Tagin Otiyot), in a description of Adam Kadmon, the first form taken by the line of light of the Infinite that enters the vacated space, it says that there are four aspects to the internal being of Adam Kadmon, refered to as 72/Av, 63/Sag, 45/Mah, and 52/Ban, or as Ta'amim, Nekudot, Tagin, Otiyot. It seems that each of the four is again divided into four sub-divisions to make 16 aspects. These are not fleshed out. But in the case of the one level (Sag/Nekudot) that is described in further detail, it is a sub-division into three that is described, with the three aspects referred to as ta'amim elyonim, emtsa'iyim, and tahtonim, i.e, the cantillation marks in a text of the Bible that have their place above the line, those that have their place in the middle of a line, and those that have their place below the line. Why the sub-division into three rather than four, when it seemed like the principle was that the structure would sub-divide into components that mirrored the whole? If there's no room for a fourth level in the representation based on the types of ta'amei ha-mikra then why is that representation used?
I do not have expertise in this area, but the following is my understanding of the topic as discussed in אוצרות חיים:
This seems to refer to the munach l'garmeih (as well as the shalsheles) and the sof pasuk (where the word carries a makaf), respectively. In both cases the words are followed by symbols that are neither above nor below the letters, unlike all other ta'amim.
After reading the section more carefully, it seems that the three divisions (upper, middle, and lower) of ע"ב and ס"ג are unrelated to what you call "the four sub-divisions" of each of the four expansions of HaShem's name. The three divisions of both ע"ב and ס"ג are mechanisms for filtering the Divine light, corresponding to figurative body parts of Adam Kadmon. The three divisions of ע"ב correspond to the ta'amim. At this level, the Divine light is so sublime that it is impossible to discuss it or even conceive of it.
Therefore, R' Chaim Vital begins with a discussion of the three elements of the filtering process of the Divine light at the level of ס"ג, corresponding to the three categories of ta'amim (even though overall it corresponds to the n'kudos) as well as the figurative ears, nose, and mouth of Adam Kadmon. R' Chaim Vital describes how the light is filtered through these elements and becomes progressively less intangible.
The comparison of the ס"ג expansion to the categorization of the ta'amim into upper, middle, and lower, is a means of characterizing the filtration of the light at that level. The fact that there are three categories seems to be incidental. By contrast, R' Chaim Vital mentions that each of the four expansions of HaShem's name contain elements of all four. The four aspects contained in each of the four expansions are ways of referring to different incarnations of the light at different levels, as opposed to the means by which the light is filtered.
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