Fraymotifs are special abilities or attacks that seem to be musically related. They have come up only a few times over the course of Homestuck. Fraymotifs are optional components to successful sessions, as indicated by Aradia. She also mentioned that the trolls had the strongest fraymotifs boondollars could buy, which was part of how they were able to defeat the Black King (who was much more powerful than he should have been due to the prototyping of Feferi's lusus).
They appear to be accessible through shops on the kids' planets. In the John: Enter Village Flash, a shop with fraymotifs can be accessed, but John cannot afford any of them, since he only has 9,413,612 boondollars, having given his first boonbuck to Dave. They seem to be based on the characters' titles, and all of them have musically-themed names.
Dave, after making a killing on the LOHAC Stock Exchange bought all of his fraymotifs and presumably used them to get to the top of his Echeladder. The names of these fraymotifs are mostly unknown, save for Adagio Redshift, a fraymotif Dave and Jade used against Bec Noir during their strife. As Jade and Dave's meeting took place entirely offscreen and the Strife mostly offscreen, the actual mechanics of equipping, learning and/or using the fraymotif remain unknown.
Though there is no particularly developed formula, it appears that each player has at least 3 personal fraymotifs, and each player has a fraymotif with another. For example, John has 6 fraymotifs: 3 of his own, and one with each of the other players in his session (Dave, Rose, and Jade). If this were true, then that would mean that the kids have 18 fraymotifs (4 × 3 individual and 6 in combination), while the trolls have 102 (12 × 3 individual and 66 possible combinations). It can be assumed that both players must have the fraymotif to use it in combat.