When "Singularity Complex" first starts it has an introduction type of track called "Peace Before Disruption" and then it really starts off on the second song which is called "Room 208, Part 1". If I was going to suggest one song from this album for you to listen to for that complete vibe of The Amatory Murder, it would be "Room 208, Part 1" but that also feels a bit incomplete because you would want to also hear "Room 208, Part 2", as I feel like the songs work best together over the broader spectrum of the album.
The Amatory Murder has a gothic sound. It's full of guitars and other instruments such as keys and through all of the spooky groove on "My Love" there is also a sax. But at its heart, it is a rock album, perhaps even a rock opera of sorts. At first, during "The Illusion Of Time", I heard that great guitar drive like you might hear on that one U2 song which was on a Batman soundtrack. But as I listened to this more and more, those ideas began to fade and I found the music to be a combination of three artists: Panic! At The Disco (mostly in the way the vocals are delivered and it can feel like a dance at times), My Chemical Romance (because of the dark energy) and Escape the Fate (because the way the vocals sound plus the underlying themes)
Now, I could probably be more specific in the sense that the only Escape the Fate albums I've really listened to are "Dying Is Your Latest Fashion" and the EP which came before it. And as for Panic! At The Disco I've mostly only heard "A Fever You Can't Sweat Out" so the music of The Amatory Murder might not be as pop as you're thinking. I've listened to My Chemical Romance since they were first a band but the sounds I most hear from them within these songs would be on "Three Cheers For Sweet Revenge". It is strange for me to not only be able to place this based on artists I hear within it but also these three specific albums, but there is also more to this sound.
The general mood of the music makes it feel like we're in a haunted house or "Repo: A Genetic Rock Opera". There are metal undertones and just killer guitar riffs, which are also in the form of the rhythm on a song such as "Master". "Cruelty And A Second Death" opens with dark keys and then there is this sound of doors opening and closing, laser blasts and la-la-la type of vocals which make it all feel quite disturbing before we go into the second part of "Room 208", which can be described as a heavily distorted guitar anthem. There is static inside the melody on "Part Of Everything" and I really think that just describes how the entire album feels conflicted within itself- there is beauty within the music and it can feel pure, but there can also be chaos and destruction.
Lyrically, this album reminds me of something out of a Philip K. Dick novel. It's part of the larger idea of feeling like we're machines and not really human, but also just those small day-to-day routines which can make life feel so mundane. Many people probably go through life as part of the system and don't even realize it or give it a second thought, but we all have those thoughts at times of how every day can begin to seem like it's the same actions: get up, go to work, come home, sleep, repeat. I definitely enjoy lyrics which go against social norms and this completely lives up to that.
In many ways I feel like music is rebellion- that's why it exists- because I don't really hear songs which are about being happy being abused by the corporate machine. Maybe they do exist and I just don't listen to them. But the general vibe on "Singularity Complex" is of music which is rock laced with metal and Queen. That just feels like it wouldn't be true to itself if it wasn't rebelling against something. But the fact that it does- and even the idea of the title "Singularity Complex" feels like a struggle within oneself- makes this an album you really need to listen to not just for the unique music which The Amatory Murder has created here but also because it should leave you doing some searching within yourself.