Ensure tune graphic is confined to a single page. Set a maximum height for the graphic of 0.9 text area as well as the current target width of the text width. And also keep the aspect ratio. So if the height is small enough, you get full width. Otherwise the graphic is shrunk enough to keep it all on one page. Perhaps one can then go back and edit the tune to fit it into fewer lines.

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\newpage
\section{List of tune first lines}

You know the feeling. Everyone has just launched into a well-loved tune.
You've heard it before, but don't remember the name. So here's a list of
tune first lines to help you figure out what it is in time to join in.

\setlength\LTleft{0pt}
\setlength\LTright{0pt}
\begin{longtable}{lr}