Maimonides ranks the chashmalim fourth of ten in the Mishneh Torah, Hilchot Yesodei HaTorah 2:7, and the Golden Dawn table assigns them to Chesed, the fourth sephirah, the sphere of mercy and of expansive giving. The correspondence between a rank named for a hard gleaming substance in the middle of a fire and a sephirah of overflowing kindness is not one either tradition explains; it follows from the numbering, because the table was built by pairing two lists in their own order rather than by matching qualities.
That is worth saying plainly, because correspondence tables invite the opposite reading. Presented as a grid, ten ranks beside ten spheres, the arrangement looks as though each pairing carries a meaning of its own, and later commentators have supplied that meaning readily enough. The underlying operation is simpler and older: two ten-item lists from different centuries, laid side by side, each kept in its own sequence.
The Dionysian scheme has no equivalent rank at all. There is no Greek or Latin choir named from Ezekiel's chashmal, so the usual cross-system equations that pair the Hebrew orders with the nine choirs have nothing to work with here, and any match a table supplies is being made by position alone. The atlas records no such equation, because a shared place in two sequences is not a shared identity, and printing it as one would put a claim on the page that no source ever made.