I've been doing more research on the Corsair Carbide 400R's fans.
The exhaust fan has just a normal 3-pin connector, but the two front fans have a strange 3-pin connector shaped like a buckle insert that plugs into something that leads into the 4-pin molex connector, which powers the front fans and their LEDs. Details from
The Tech Report (bottom of the page, emphasis added to make a TLDR version):
Under load, the Carbide is the loudest of the bunch, but not by a huge margin. At idle, however, the difference in noise levels is more prominent. Whereas the other cases use fan controllers or have system fans that plug directly into the motherboard, which can regulate fan speeds to some degree, the 400R's front fans are tied to four-pin Molex connectors that have to be plugged directly into the PSU. This connection provides the juice necessary to spin the fans and light the LEDs, but it also restricts the fans to a constant speed, regardless of the system load.
The front fans can be separated from their Molex wiring harness, but each one has a non-standard three-pin plug. This plug can be jammed into a motherboard connector, but it doesn't play nicely with the vertical tab that extends upward from a standard fan header. You'll probably want to shave off that tab to avoid stressing the header. Also, the wire that would typically report the fan's rotational speed has been repurposed as the LED on/off circuit. When plugged into a motherboard, the LEDs glow at about 10% of their normal brightness and can't be turned off--without snipping wires.
Replacing the front fans entirely or connecting them to a fan speed controller would be the best way to reduce the Carbide's noise output. Doing so will leave the case's LED switch hanging, but I'm sure modders and tinkerers will find creative ways to use it.
Guess I'm not the only one who finds the 400R a bit noisy.
A related Corsair support thread
here. Someone had to cut off the front fan connectors' extra tabs to plug them into a fan controller.
So time to look into a fan controller.

I was thinking of the
NZXT Sentry Mesh, which
got good reviews,
is compatible enough with the black mesh of the 400R, and is $25. The guy who had to break off the connector tabs had a 400R, though.