How to send a command to all panes in tmux?

Question

I like to call :clear-history on panes with a huge scrollback. However, I want to script a way to send this command to all the panes in the various windows.

Answer 1

Update June 2019

Quick illustration on how to configure your own binding for synchronize panes.

Added the following into my tmux.conf (the comments certainly apply to my overall configuration):

# synchronize all panes in a window
# don't use control S, too easily confused
# with navigation key sequences in tmux (show sessions)
unbind C-S
bind C-Y set-window-option synchronize-panes

Now, I can toggle the ability to synchronize commands across multiple panes with .

(Yes, I remapped the bind key to Ctrl a).