Formatting Lilypond Sheet Music for the Kindle

Tired of fumbling around with my collection of sheet music looking for a certain piece, I thought it would be great to have some sheet music on my third generation kindle (now called the Kindle Keyboard). I have always been a fan of the open source program Lilypond. Lilypond is a TeX-like system where sheet music is written to a text file and then compiled into the desired output.
Since Lilypond is similar to Tex, Lilypond files have incredible control of the output. No exception is adjusting paper dimensions, only a simple command is required:
\paper {
   paper-height = H\mm
   paper-width = W\mm
where H is the desired height in millimeters and W is the desired width in millimeters of the output paper. Since the kindle was a "fit-to-width" option for PDFs, the first step is to figure out the aspect ratio of the display. Once we have the aspect ratio, then we can configure the scaling to make the actual output legible from a reasonable distance. At first I thought that this would be easy. The Kindle has a resolution of 600x800, or an aspect ratio of 3:4 (the screen is taller than it is wide). However, when creating sheet music of this ratio and the display mode of the Kindle set to "fit-to-width", the pages spanned multiple virtual pages. This meant that the music was cut off between virtual pages. This makes playing the music impossible. From here I decided to figure out the ratio by creating a bunch of files of varying ratios and testing the output.

It turns out that the Kindle is doing a little fudging on the display and allows a range of display ratios that will appear as one virtual page. From what I observe, any ratio between .57-.61. I tried many variations and it also seems there is some other logic going on in the "fit-to-width" option and determining when to page, but this is a decent rule of thumb to work with. Now that we have a few aspect ratios to work with, I wanted to figure out some nice paper size in absolute terms such that Lilypond will output notes about the same size as normal sheet music.

At first I tried 100mm x 59mm. As you can see, the notes were extremely large and didn't allow many notes to displayed at once. This would making paging an annoying operation while trying to play the music.
Next I doubled everything. I found 200mm x 122mm appears nice.

Compared to actual sheet music, the font is a little small, but completely usable. If you want a bigger font and don't mind paging frequently, I tried the in the between, 150mm x 80mm.

This is the closest to actual size, but fine tuning could be done.

It is worth noting that while doing this, the "fudge" factor I mentioned earlier, or variability in determining the aspect ratio of the virtual page the Kindle will chose to display, is frustrating. These values I found through trial and error by generating many sheet music files, and looking at all of them.

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