In GnuEmacs prior to 23, you could not open frames on other ttys. You could, however, use the same Emacs from different Linux consoles by using screen(1) to do this.
The preferred approach would be to use EmacsClient.
In 22 or if you do not wish to use features like EmacsAsDaemon.
Note that “another tty” may also be remote. Just ssh to the account where you have your screen session running and start screen -x.
You can also easily connect tty frames and X frames to a single instance of Emacs easily in [[emacs23?]] same time. This is possible with XEmacs. Or with older versions of GnuEmacs using the MultiTTYSupport that has now been integrated into Emacs23.