There are several speculations that the words Adem and Edema Ruh are similar enough to be connected. This is my version of the theory in a wider context plus some further speculations:
We learn in TWMF (Chapter 128) from Shehyn that the Adem are descendants from people living in Ergen "before the land has broken and the sky changed" which most probably can be translated to "before the land was devastated by war and the moon was stolen". They "sang songs of power and fought as well as Ademre do." Skarpis story of Ergen and the creation war (TNOTW Ch 28) tells that some Ruach also sang songs of power after they were transformed to ethereal beings (angels). A second group of Ruach joined Selitos and became Amyr. Some other Ruach did not join either group.
Skarpis story seem to describe a scene directly after the creation war was ended and it was to decide how to proceed. Therefore, the participants are most likely groups of warriors and their leaders. Since songs of power were known at the time before the war, they may have been used in the war also. The Ruach could sing songs of power after the transformation but they might have been able to do so before. Thus, Ruach may be a word for those who can sing songs of power and the Adem would be descendants of such people. Since singing is considered to be a very private thing not to be done in public in the Adem culture, they seem to have forsworn that ability and concentrate on fighting (with sword, bow and without weapons). Contrary, the Ruh (which is a word close to Ruach) love to sing but are not much into fighting. A similarity is their names Adem/Edema. Maybe there was a common original word like Aedem and since the Adem developed from fighting Singers to pure fighters it might translate as warrior. This would make Aedem Ruach the warriors which can sing songs of power. After the end of the war the troops were disbanded but those without home left to go to (e.g. the Ruach that did not join neither Selitos nor Thelu) probably have formed groups to live together and eventually settle down in a place not claimed by anybody (like Ademre). Since it is told that Lanre and his wife Lyra both fought in the war, it is probable that the army consisted of men and women and could be therefore an origin for tribes/cultures. Thus, the Adema Ruh descend from Aedem Ruach and could sing songs of power once. Probably Arliden remembered/found such a song and sang this "wrong sort of songs" (TNOTW Ch 16) before the Chandrian attacked. This would lead to a direct connection between the songs of power and the Chandrian. Since the Chandrian can be harmed by "the singers" they might try to destroy any knowledge about songs of power. If this is one of their goals (maybe even Lanres original goal to prevent wars like the creation war), they were very successful since songs of power are basically a distant myth by the time of Kvothes story. The killing of the wedding party could be due to the writing on the pot (TNOTW Ch 82) tells about songs of power.
Being successful in one of their goals could motivate the Chandrian to follow other goals. One obvious goal would be to break the curse which defines their existence. The curse is told to be done by "I bind you ... by your own name" (TNOTW Ch 26) which suggests that the curse might be broken if Haliax is able to change his name. This would fit to the picture since the Chandrian seem to destroy also any knowledge about them and thus could be remembered/named differently e.g. by Dennas song about Lanre as a hero and not a traitor. This would put Denna or more specifically her patron connected to the Chandrian. The speculations that Bredon might be Dennas patron would fit since he would me most probably fascinated/drawn to such a "beautiful game". It would be beautiful in even broader context if Haliax tries to become good Lanre again. This would put Dennas song/activities in a good light but Kvothes fight against anything connected with the Chandrian would not be helpful for a "greater good" with Lanre back again as the good guy.
It is my impression that Patrick Rothfuss does not tend to black and white descriptions of good and evil. The Japanese tales approach of levels of gray instead of black and white seem to fit better. Even the bad characters could have an understandable reason (not a justification) for their actions.
For example: Assuming that Iax became the Cthaeh, the story could be like that:
Iax was the first and most powerful shaper and perfected the art of seeing to the highest level where he could see the connection of everything (found the deep name of Temerant). Such an insight was too complex to bear so he got insane and teared at the world to simplify things by decimating its population and make people behave in more similar ways. Thus he would force wars and corrupt organizations like the Tehlu church to make people act to a simple script (do your prayers and behave this and that way or we punish you). This would not please everyone for sure. Since the enemy ( = the Cthaeh plus the Fean?) was shut beyond the doors of stone (sealed in the Fae realm), the Cthaeh could easy influence the Faen which put the Sithe into action to limit the Cthaeh's influence on the Faen as a self defense (they let Kvothe pass because they do not care about the Cthaeh's influence on the world of men). This way the simple search for greater knowledge led to global disaster. A different result of a similar path could be Auri. She might have found the deep name of Temerant also, but managed to "be small" not to get overwhelmed by the insights. Nevertheless she can seen the future (e.g. knows when Kvothe will visit her) uses small actions/details to correct turnings of the world and is able to perform world shaking magic (e.g. when she made the candle for Kvothe). This would make her the most effective antagonist to the Cthaeh. Unfortunately she might be tempted to sacrifice parts of the world to make Kvothe the hero she sees in him - thus the ongoing war at the time of Kvothes story. Hopefully Auri will end the war by giving Kvothe the new name she planned to give him (as described at the end of The Slow Regard of Silent Things) when he is "all eggshell hollow empty in the dark" (which would fit to Kote) enabling him to make an important move in the grand scheme.
An influence of Asian philosophy would also fit to the description of Denna/Kvothe since they seem to have a rather Yin/Yang kind of relation circling each other. She is the more passive/evasive part mastering the art of listening (to people [seven words again], to unspoken questions and maybe even stones (TWMF Ch 148)) and the quite art of Yillish knot magic. Kvothe in contrary is the active/aggressive part, does not do listening but naming, always acting for great effect, channeling energy and being generally headstrong (alar of Ramston steel).