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I know that placing the mouse cursor over the horizontal scroll bar makes turning the wheel scroll horizontally, but it would be handy to be able to use tilting the wheel to scroll horizontally while the mouse cursor is over the text being edited, as one can do in Excel.

I agree, with a rapid advancement option. I recently found crtl-right/left Arrow. Faster than most approaches but still not what we really need. Scrollbar will run fast enough, but my machine I use most of the time is a department store machine which came installed with shell hooks that will put the mouse anywhere other than where you are trying to go. You have to do a fast approach and stop within a few pixels.

A fast tabbing across a line with operator selection of stop char ( pause char ) would alleviate some of the carpal tunnel.