Thanks for your help.
tune2fs ran without any complaints, but didn't add anything to the /dev/disk/by-uuid folder, or to fstab, and nothing shows up in the output of blkid.
gparted reports the uuid as
# tune2fs /dev/sda5 -U 'd6d454dd-fc37-4933-8c57-03220c459bd4'
tune2fs 1.42.4 (12-Jun-2012)
/dev/sda2: UUID="A840C2E340C2B77A" TYPE="ntfs"
/dev/sda6: UUID="6ddeda4a-9de6-420e-94f3-0c3c64a49c2b" TYPE="swap"
# ls /dev/disk/by-uuid
# cat /etc/fstab
<file system> <mount point> <type> <options> <dump> <pass>
/dev/sdh5 / ext4 errors=remount-ro 0 1
under the "information" tab, but that's the only place I've seen it.
I really don't understand how this works.
Maybe a stupid question, but do I have to run tune2fs with the partition unmounted, like from a live CD or initramfs, or something?