Highlight the white text inside the block for hints ranging from vague to specific...
This is a pretty difficult logic puzzle - be prepared to take a lot of notes on scrap paper.
A big hint on how to get started...
The clues provided all give some info about consecutive quadrilles. However, they don't tell you which quadrilles they are. For instance, in clue #2, it mentions that the Oceanid dances, the Limnad dances, Greco dances, and Faunis dances. You know these are consecutive dances, but you don't know if the quadrilles described are the 1st - 4th, the 2nd - 5th, the 3rd - 6th, or the 4th - 7th. A lot of the meat of this puzzle comes from comparing different clues to figure out which quadrilles each clue is talking about.
For the following, to avoid writing all of the names, UPPERCASE stands for satyr, lowercase stands for nymph, italics stands for races, and bold stands for dances.
If we start comparing some of the clues (and writing them in short hand, we can figure out which quadrilles those clues refer to.
In clue 3, we see these four dances:
In clue 4, we see these four dances:
t / m
A / D
G / t
We know from the clues that each satyr dances twice, but cannot dance consecutively, so we know that Clue 3 dance 2 (with satyr A) isn't the same as Clue 4 dance 2 (with satyr A), because then satyr G will dance consecutive dances. We also know that Clue 3 dance 3 (with satyr G) isn't the same as Clue 4 dance 4, because then satyr A would have consecutive dances. That tells you that you have to fit clue 3 and clue 4 like puzzle pieces over the 7 quadrilles so that satyrs A and G aren't next to their pairs.
The next section contains the answer. Do not reveal unless you want to be spoiled
The complete solution:
1st quadrille: Eurymos & Nikola the Pleiad dance the Fandango / Faunis and Portia the Hesperid dance the Sarabande.
2nd quadrille: Attikus and Hyla the Limnad dance the Waltz / Calicos and Olympia the Naiad dance the Allemande
3rd quadrille: Greco and Olympia the Naiad dance the Hora / Eurymos and Portia the Hesperid dance the Jig
4th quadrille: Bacchanus and Talia the Oceanid dance the Mazurka / Faunis and Minerva the Themeid dance the Galop
5th quadrille: Attikus and Nikola the Pleiad dance the Leventikos / Dionos and Hyla the Limnad dance the Tarantella
6th quadrille: Bacchanus and Minerva the Themeid dance the Can-can / Calicos and Lyria the Maenad dance the Bolero
7th quadrille: Greco and Lyria the Maenad dance the Reel / Dionos and Talia the Oceanid dance the Polka