An Ancient Egyptian Story

Question

Deep under the sands of Ancient Egypt, a dusty chamber lies undisturbed. It is not a tomb, no - but it tells a story nevertheless. Despite the walls being ruined by time, an inscription is visible on the coarse sandstone walls - one that tells the tale of a girl and her animal:

And this leaves us with two simple questions:

What was her name, and what animal did she have?

Hint:

You consult your smartphone. You know from experience that these symbols are purely mathematical in nature.

Hint II:

You wonder why this has a music tag....

Answer 1

It is indeed Mary Had A Little Lamb. The lines correspond to the notes C, D, E and G (as per the C major scale in this link from hint 2) and if you play them in the positions indicated by the tick marks in the long horizontal lines you get the familiar tune. Like so:

                                      (Its)
C ----|-------------------------|-------------------------|--
      had                       had                      snow
D --|---|------|||------------|---|----------||-------|-------
    ry   a   little lamb      ry   a     fleece was   as
E |-------|||--------|------|-------|||----------|-----------
  Ma-   little lamb  li-    Ma-   little lamb   white
G ---------------------||------------------------------------
                     -ttle lamb

Answer 2

Her name was Def and she had a sea snail.

The notes on the Pythagorean scale are: D E F# and A, or DEFsharpA - Def's Harpa

Answer 3

According to the sign list:

• the single bar stands for "it has", "singular", or "one"
• the symbol that looks like a capital lambda stands for "approach, enterprise, do not move, stop, injure, leg, thigh"
• the symbol that looks like a horizontal grain of rice stands for "mouth"
• the symbol that looks like a horizontal knife blade stands for "side area" or "side"
• the vertical ticks stand for 1's (as in unary digits) and the bumps stand for 10's

I also believe the Egyptians used top-to-bottom reading order as in English, hence free from interpretation, the story is

(one)
(one) (approaches, does, stops, is injured, does not move, leg, thigh) (mouth) (eight)
(one) (approaches, does, stops, is injured, does not move, leg, thigh) (mouth) (four) (approaches, does, stops, is injured, does not move, leg, thigh) (mouth) (sixty-four)
(one) (approaches, does, stops, is injured, does not move, leg, thigh) (side area, side)

The numbers four, eight, and sixty-four, and their relationship to "mouth" is obviously significant, but I have no idea how they would imply the identity of the girl or her animal. My three guesses are:

1. She had a pet rabbit that multiplied for two generations, until she got fed up and let them die off ("side" in the final sentence).

2. She had a pet she taught to first obey eight vocal commands, then sixty-four vocal commands. The pet had borne offspring, and the younger animal (perhaps a pup) could obey four vocal commands. Eventually both the older animal and its offspring died.

3. She had a pet parrot that initially could say 8 things. Eventually it could say 64 different things and understand four different things. Ultimately it died.

I gather from the Wiki article that reading ancient Egyptian is significantly more complicated that just chaining together base word meanings, but if this problem requires some degree of proficiency in interpreting ancient Egyptian, you should probably indicate that in the OP.