What really sets a song track apart to me is if it paints an image in my mind as I listen or how well it goes with the moment. That's usually why boss themes, credits themes, and the Pursuit themes stick out so much. Case 1-5 makes a lot of references to "grey" as the characters involved all have gray morality. An Ashen Dance only plays at two points in the case: when Gina is recounting the events of the night Windibank was killed and during Graydon's confession.
Both instances, the characters are stating their situations and what they wanted or needed. What they want can be considered noble or respectable, however the methods they went to achieve them were not so, and cost an innocent person their life. The song starts basic enough reflecting the character giving the initial rundown of their situation. Then at around 24s, the song begins its first variation, the characters explain what their need is. 46s, the song begins to repeat but with greater emphasis, the characters explain the steps they started to take to achieve that need. 1m9s, the sound becomes dramatically sadder with the use of strings, the characters explain how they began to use an innocent person in their efforts. And while this is going, the characters also explain how they understood what they were doing was wrong or underhanded and taking advantage of their respective innocent person...but then at 1m32s the song makes a somewhat abrupt repeat almost as if to say "...but I did it anyway". From there until the song loops, the song compliments how the characters explain how the situation goes wrong and the person they got involved paid the price.
With Gina, she was worried that Holmes was lying to Iris and taking advantage of her trust. Gina wanted to prove that Holmes was lying so he can properly apologize to Iris or confirm that he was telling the truth to put Iris's fears at ease. It's a very kind and considerate motivation, if too cynical. However she chose to solve this by breaking into Windibank's shop and threatening him with a gun. Sadly she leaves the door to the shop unlocked, letting the robbers into the store while Gina and Windibank are literally backed into the corner of the shop. Windibank confronts the robbers and is killed in the scuffle, and Gina blames herself for getting him involved. Obviously, Gina's actions had very little influence on what was going to happen that night. The robbers were going to break in regardless and Windibank's determination to protect his clients' property was going to put them at odds and every party having a pistol. But this is a significant character moment for Gina. When confronted with this horrible turn of events, she shows regret and self-blame for Windibank's death. It shows Gina's humility and genuine compassion for the people around her, despite her harsh attitude.
Graydon not nearly so. Graydon recounts the days of poverty and growing up in a home of desperation and his parents constantly fighting with each other. Graydon wants to escape that life and secure stability in a society that clearly ignores the plights of the downtrodden social class. However the method he chooses is deception and abuse of his position to steal government intelligence and sell to the highest bidder. And to help him do this, he tricks his father into creating music boxes to replay the transmissions. His father grows wise that things are amiss with his son and demands to participate in the exchange, and is killed for his trouble. While what happened to Windibank could hardly be considered Gina's fault, what happened to Milverton is absolutely Graydon's fault. If it wasn't for Graydon deceiving his father, he never would've been involved with a murderous madman like McGilded. And as a further contrast to Gina's humble compassion and regret, Graydon responded with wrath and revenge blaming McGilded for what happened to his father. It isn't until the very end when Van Zieks tells Graydon that he became every bit as horrible and heartless as the man he despised that he finally began to realize the weight of what he had done to Windibank, to his father, and to himself.