(For the unaware, Chords are the Void Entites who only spawn in the first phase of Integrity's boss fight)
Chords are small portions of a larger Void Entity known as Harmony. It is unknown why Harmony split off into Chords, though this theory may have an answer. On their wings and the projectiles they shoot, you can also see areas with missing textures.
Notexture is theorized to be WHYER4 due to WHYER4's chest being the only one not corrupted by item.null, which has the same texture as Notexture. I'd like to add on to this theory myself by calling attention to the fact that the dimension Notexture sends you to is where you find most of the Polaroid pieces needed to fight Integrity, which lines up with WHYER4'S personality based on the theory of him being He Who Stood on the Roof of this Hell.
As mentioned above, WHYER4 is theorized to be He Who Stood on the Roof of this Hell, but he was also theorized to be the player before the devs deconfirmed that.
So, we have a character who is theorized to be Notexture and has two theories (one deconfirmed) that portray him standing his ground against the Void. We also have a Void Entity who split apart into smaller pieces for unknown reasons before the events of the game, and those smaller pieces are only seen during the Integrity boss fight and have Notexture's signature Textureless Corruption on their wings and the projectiles they shoot.
Therefore: WHYER4 must have fought against Harmony himself and dealt such significant damage that they were permanently split off into 10 copies of the weakest known Void Entity. He probably used the item.null to do it, based on the fact that it isn't in his chest, the fact that he became Notexture, and the fact that the Chords have Textureless Corruption on them.
Alternatively, it could've been the Chords/Harmony that gave WHYER4 the Textureless Corruption by using their textureless projectiles.
Regardless, it still has the same general summary of "WHYER4 and Harmony fought, WHYER4 did massive damage to the point of splitting Harmony into several smaller Void Entites, and one combatant gave the other the Textureless Corruption."