The music is made up of distorted single-line electric guitar improvisations over a clean chorus/delay backing track. Although the improvisations themselves do not repeat, there is a distinct melody containing 14 notes that repeats twice.

The musical key of the melody is the first letter (only one valid possibility) of
one of the directional headings North, East, South, West. (E??)

There are 9th notes in the secret melody. Treat these as a major second off
the root note one octave up.

They are the highest notes in the scale and should be easy to discern.

The scale used in the secret melody is the major scale (in the key discussed above) also known as Ionian mode.

but you never refer to an 8th note or a 10th note. I've never heard of anyone referring to anything but a 9th and 11th above 7th.

Right, but most of the time I see them it's as a Eadd9 or Esus2. The difference between those two chords is whether or not the 3rd exists, but they still always use the different terminology for the 2nd. I don't know why.

Here is the link for the Ionian Tusk of the Daywalker geocache itself.

How about this, though. What other places in the world can we find interesting musical cyphers, or other stuff where the notes come from something patterned or numerical (rather than straight from a musician's imagination)?

I can't think of many. There's a Bela Fleck piece called "UFO Tofu" where he tries to do some musical palindrones (the title of the piece is a palindrone). Anyone else?

Oh, and Bach did write a piece with a melody based on his name (using "Bb" for H), which is no simple feat being as that puts all four notes as half steps from one another.

s it just me, or is Gustav Holst's Mars : The Bringer of War the music in world 8 of Super Mario 3?

Ah, ok, I only took beginner's music theory at Penn State, so I didn't know "H" was typically used to indicate Bb. I was just thinking like a comp. sci. guy, as in "the letter G plus one letter is H, so the note H should equivalent be G plus a half step."