TriTone²
If the legends of his early travels are to be believed, then Pythagoras' time in Chaldea would have coincided with the captivity of the Jewish ruling class there. It was during that time the Hebrew alphabet took on the box script form familiar today and abandoned its' more explicitly pictographic letters derived from Egyptian hieroglyphics. Perhaps that which became known as the secret teachings of the Pythagorean brotherhood were the result of a cross-pollination between cultural traditions. Given the Chaldeans' grasp of mathematics and metrology, and the crypto-numerological underpinnings of the Greek & Hebrew alphabets (descended, like Phoenician, from the 'Proto-Canaanite' glyphs dating as far back as 1900 BC), it is feasible that various related, but otherwise divergent, alpha-numeric traditions were re-calibrated by the Babylonian Magi - adapting an ancient cipher to more current cultural idioms and imminent equinoctial thresholds.
The recursive features evident in the Book of Formation's 32 wondrous paths, illustrated by the various Tree of Life diagrams and in the iconography of the Tarot tradition, echo descriptions of Pythagoras' quadrivium of mathematics, geometry, harmonics, and astronomy. Just as the theorem which bears his name was known centuries earlier in Chaldea, Pythagoras likely absorbed much of his mystery teaching from older sources. Perhaps, then, the author of the Sepher Yetzirah drank from the same well.
Inasmuch as the puzzle-box of numbered Hebrew letter-symbols draws geometric parallels from the mathematics of music and applies them to the measure of time & space, the tetraktys is already an intrinsic facet of the Tree of Life. From a certain perspective, one might even say that the Tree is 'resolved' by seeing the fundamental difference between a Pythagorean music scale and a system of 12-tone equal temperament - like pinpointing the 'balance' betwixt ratio & irrational number.