Mooi ben je, mijn vriendin 4:1-7

1. There are those that claim talpiyot comes from the Greek telopos - and means "seen from afar" (tele, meaning "far" and opsis, "view, appearance"). We've discussed here some reasons to question Greek words in Shir HaShirim (although the Septuagint didn't translate this word at all but rather transliterated it, so not all the points in the previous post are relevant.)
   
2. Perhaps it is a place name - this could explain why the Septuagint transliterated it as Tel Pivoth.
3. The Daat Mikra suggest that talpiyot may mean "complete, flawless" from "connected, joined." Onkelos translates מחברת "connected" as lofei לופי in Shmot 26:4.
4. Another opinion mentioned in the Daat Mikra is that the root אלף means "to study" (as in ulpan, which we talked about here.) So the phrase could mean "worthy of gazing and examining".
5. Steinberg explains this in a slightly different way, by saying that the tower was where they taught the warriors archery - a sort of military academy.
   
6. Of course there is the well known Talmudic explanation from Brachot 31a: תל שכל פיות פונים אליו - "the mountain (tel) that all mouths (piyot) turn to" - Jerusalem in prayer. A nice drasha, but I haven't seen anyone claim that it is meant as a real etymology of the word.
7. A lesser known midrash is from Shir HaShirim Rabba, where it says מהו תלפיות - טטרגון - "What is talpiyot? A tetragon". Kraus writes here that this four-sided tower would have been like a ziggurat (also four-sided).
8. This site writes that:
   

   Honeyman suggests that תַלְפִּיּוֹת is a feminine plural noun with a standard nominative prefix ת and is derived from the verbal root לפא ("to arrange in stones"). Probably, the best solution is to relate this Hebrew root to Akkadian lapu ("to surround, enclose"), Arabic laffa or lifafah ("to envelope"), and Aramaic lpp and lp' ("to interlace, entwine, plait"). This is the simplest solution and does not demand emending the text. The preposition לְ (lÿ) could denote "in respect to" and the colon בָּנוּי לְתַלְפִּיּוֹת could be translated "built in rows (of stones)" or "built in terraces." Thus, the phrase "built in rows of stones" refers to the outer walls of a tower built in spiraling rows of stones or built in terraces. This is a comparison of sight: (1) her neck was long and symmetrical or (2) she was wearing a strand of beads or necklaces wrapped around her neck like a tower built in spiraling rows of stones.
   

9. As the same site above mentions: Ibn Ezra redivided לתלפיות as ל תל פיות "for suspending weapons" by taking פֵּיוֹת ("mouths" = edge of swords) as a reference to weaponry.
10. And again from the same site: Perles connects תַלְפִּיּוֹת to Akkadian tilpanu ("bow")