How to get 640x400 out of an ATI HD5670?

Question

I am trying to get 640x400 out of an ATI HD5670, the card is connected via VGA to an old ~1996 TuTCybermax VR headset. Goggling around tells me something like this should work:

$ gtf 640 400 60

  # 640x400 @ 60.00 Hz (GTF) hsync: 24.90 kHz; pclk: 19.52 MHz
  Modeline "640x400_60.00"  19.52  640 648 712 784  400 401 404 415  -HSync +Vsync

$ xrandr --newmode "640x400_60.00"  19.52  640 648 712 784  400 401 404 415  -HSync +Vsync
$ xrandr --addmode CRT1 640x400_60.00
$ xrandr --output CRT1 --mode 640x400_60.00

However, it fails at:

$ xrandr --addmode CRT1 640x400_60.00
X Error of failed request:  BadMatch (invalid parameter attributes)
  Major opcode of failed request:  141 (RANDR)
  Minor opcode of failed request:  18 (RRAddOutputMode)
  Serial number of failed request:  37
  Current serial number in output stream:  38

What is going wrong and how can I fix it?