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Can emacs running under urxvt be made to recognize Hyper? From what I can tell, it doesn't distinguish hyper+something from just plain unmodified something. urxvt itself does recognize the modifier, I am told. But I cannot work out whether emacs in turn can, and if so how to configure this.

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Yes, you may not even need to play with xmodmap, nor modifiers, just bind them in your ~/.Xdefaults like this:

URxvt.keysym.XF86AudioPlay: string:\030@m
URxvt.keysym.Menu: string:\030@s
URxvt.keysym.Muhenkan: string:\030@h

How it works

To get a good explanation on how key events are handled, see How do keyboard input and text output work? first.

TL;DR: Let's take "C-a" as an example, emacs won't receive "Ctrl down, a down, a up, ctrl up", urxvt does, and convert it to \1 (yes, ctrl- sequences are short, C-a maps to \1, C-b maps to \2, C-c maps to \3 and so on).

Here my modification happen very late in the process, when urxvt send the escape sequences. I'm asking urxvt to send \030@m to emacs, which is C-x @ m (look at man ascii, 030 on the left column is conveniently aligned with X on the right column). C-x @ m adds the meta modifier, C-x @ s adds the super modifier, and C-x @ h adds the hyper modifier (see https://www.gnu.org/software/emacs/manual/html_node/emacs/Modifier-Keys.html).

Happen on my keyboard I have XF86AudioPlay, Menu, and Muhenkan keys conveniently placed near to my Ctrl key, so I bound meta, super, and hyper to them.

There may be a better solution, we'd have to learn how emacs expects to receive meta and hyper escape sequences, to send directly the right one instead of using the C-x @ s workaround, intended to be used when one does not have said keys.

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