Analysis of Sajou no Roukaku
English translation used from the fandom wiki (no credit provided)
To start out, big premise here is that this song had to have been written and practiced by exvalk before they fell apart, otherwise Nazuna couldn't have joined so easily during StarFes. It also has to have been the intended song for Valkyrie in StarFes, even without Nazuna joining them, which is a good signal to Shu's mental health at the time given that he couldn't even create a new song for them.
As for the title, Castle built on the Sand, this is a phrase meaning something grand that wasn't built on something stable. It can easily collapse. The song itself also references that sand being the sand of an hourglass, signifying that it will be swallowed up by time itself. Slightly irrelevant, but I'd also like to mention that in Antique Legend, Madara says he doesn't want to attack Valkyrie like him and Kohaku did because it feels like kicking over a child's castle made of sand, another signal towards Valkyrie's naivete.
Moving on to lyric breakdown:
A doll, adorned with the threads of time, dwells
In a beautiful museum that lies on the sand of an hourglass
Alright this song starts out strong (terribly awfully brutally depressingly). Obviously Mika and Nazuna having these lines is painful itself as they were both the "dolls" for exvalk. Museums is also a pretty common motif with Valkyrie. In fact, there is a reference in the second epilogue of Marionette to Shu wanting to place Nazuna in a museum to protect him. Lots of references to time are in these lines as well, which is a theme throughout the song.
And to even the fact that it has broken
The way these lines are split apart is of note. In a lot of depictions of exvalk, Mika is commonly called the broken or useless doll, which aligns with the "covered in rust" phrase, Nazuna is the one who broke before any of them realized it, and Shu is the one who refuses to acknowledge the problems arising that threatened and eventually tore them apart.
The time that had been frozen in place falls away, like sand
And the memories that had been sealed away in its grains,
slowly melt away into the sunset
If I had a nickel for every time Valkyrie discusses memory and nostalgia... This line is notable in that Shu's ideal Valkyrie ought to remain perfect and immoveable, as if frozen in time. Time doesn't really freeze though, and it was the movement of time that destroyed them.
Likening the movement of time to grains of sand plays into the theme of being a castle built upon sand. The sand is time, and their downfall was Shu's naive expectation that it would not move.
When the fleeting perfection that had been constructed disappeared
A melody overflowed from within the glass
Shu's line here adds to the idea that his ideal Valkyrie was a brief dream, something easily destroyed. Mika's addition seems to reference the doll locked in a display case mentioned at the start, and that despite the destruction of Shu's ideal Valkyrie, Nazuna and Mika managed to find a way to continue on. For Nazuna, it was the formation of Ra*bits, and for Mika, it was helping Shu return and creating a new Valkyrie where they could be equals.
And though not a single trace of its former self remains
Sings of all its feelings
And resonates through the silence
If you haven't, I highly suggest you read my analysis of Memoire Antique, as that ties a lot into these references to a nostalgia and singing their feelings:
https://www.tumblr.com/tanyth-overanalyzing-shit/810005812219117568?source=share
So for these lines, I wanna focus on Nazuna's part. When Nazuna formed Ra*bits, it was vastly different from any of his prior experience. Not only was he now the unit leader, but the theme and music style was different from both Valkyrie and his experience in a church choir. He changed completely from his former self, and did everything he could to avoid his past with Valkyrie, at least for a while. He also finally began singing and speaking again, breaking his own silence, and I won't lie, those lines make me wanna cry every time I read them.
If the light of the setting sun can allow your glass eyes to shine
Then I shall bid farewell
... To my dream of eternity
In my understanding of the lore, though these lines are shared, I think they pertain particularly to Shu. In Cloth Waltz, he also references glass eyes of a doll. I believe that the setting sun is meant to stand in for Valkyrie's end, and the shining eyes are Nazuna's and Mika's. He loves them irrevocably, and to him, perfection and eternity was how to express that love. However, he has also learned to accept leaving things in the past if it makes those he loves happy. You can see this in Human Comedy as well, where he believes that pushing Mika away is how to make him happy (everybody say thank you Naru-chan for talking some sense into Shu).
Aah... though everything has been shattered to pieces,
Mika & Nazuna: These engravings are not wounds
But all of the feelings that we carried in our hearts
Again building on the doll imagery here, porcelain shatters when put under stress. The idea is that even despite everything falling apart, shattering into pieces, the marks they bear are proof of their humanity, not of becoming a broken doll. Here is the beginning of the real transition into the idea that things have fallen apart, but Mika and Nazuna are shedding the idea of being dolls.
The time that had been frozen in place falls away, like sand
And the memories that had been sealed away in its grains,
These lines build on the idea that not only was exvalk formed on flawed reasoning (sand), but that the flaw itself was time and time had swallowed their past whole. However, despite all their efforts to move on, they will always remember those times, both the good and the bad.
In the beautiful museum that lies atop the illusion of sand,
The singing voice of a doll without strings
Resonates through the silence
The final lyrics in the song. I like to interpret this as them realizing that their past is not something to feel shame for or to try and bury, but instead remember and learn from. They accept that there were bad times, but they try to remember the good times, the times where their Valkyrie was beautiful. As this at StarFes is the last time exvalk truly performs together, it also implies that this is the exvalk they want to remember, not the pain of their past.
The doll also no longer has its strings, and there's a repetition of "resonates through the silence", this time coming from all three of them, which furthers the idea that Shu has released Mika and Nazuna, and they are adapting to their own humanity and expressing themselves.
In Elio's words, Sajou no Roukaku is my Nebula (double face song). It makes me want to sob violently, and I've wanted to write about it for a while. Hope you enjoyed this breakdown because I cried in public for this.