This piece is an etude by Stephen Heller, and J. T. says its purpose is to help students work on velocity. In keeping with this, the song isn't very hard to learn or to execute. I have problems with a couple sections, but in general the whole is designed to be easy enough to play so that one can focus on the speed of the fingers. (Coming up in the Fourth Grade Book is Il Penderoso, which also provides a velocity workout using modified arpeggios, so I think J. T. finds Heller's studies in general to be useful.) I'm thinking of learning Curious Story really well and keeping it in my repertoire precisely for practising speed. I know I need to work on my arpeggios, and there is a section of this text (we'll see) that contains them and would give me that needed practice. 
I notice that J.T.'s own composition Tarantella is similar in sound to this piece, and I think it helped prepare me in such a way that learning this song seemed a lot easier. This opening (right) shows the triplets that are characteristic of the text, and Tarantella was similarly based on triplets. Here, however, the triplets give way far more frequently to quaver-semiquaver beams. This (for me) always begs the question of the difference between the triplet with the missing middle note and those (semi)quaver complexes. I believe I raised this question in Serenade as well. Every time I think I have it figured out, something comes along to make the distinction murky again. The math makes the difference clear, of course: one's divided into thirds, the other into fourths. But that difference of 1/12 is so elusive! [da-(u)-di vs da~ah-(u)-di?] Anyway, this is the main theme of the song and it's got some variations, which I will presently discuss.
Top left we have a denser harmonic accompaniment added to the main melody, but this does more than just add harmonies. It also modifies the text by raising some of the pitches along the way. B-flat is naturalized and G is sharpened, for instance. I'm not sure if these and other changes add up to an expression of D-minor in one of its forms. Melodic, probably. Looks more like an implied E major or G#m. But it could also be some exotic scale that I haven't learned yet, like Dorian or Phrygian (or some other term that sounds like it belongs in Aristotle's Poetics.) Below that is a neat thirds section that I've already begun to be able to play pretty fast. Oh for the day my speed on the rest of the sections finally catch up! 
The text pictured right is a strange, slowing and dissonant section, which provides another good velocity workout because the semiquaver thirds double the already significant speed. It also provides a good exercise in finger control, because the second and third fingers, used to playing trills or fully consecutive passages in both directions, tend to want to play another C after that final B-flat (right hand). I have to force my fingers not to do that, and it's good for them. The C actually does get played, but not for another two beats, and the B is held for the duration. 
Pictured top left is a slightly chromatic section that begins with the right hand leaping over an octave and then ends with both hands playing a dissonant melody in unison. This repeats again in C. The second is another triplet section that requires some fast hopping down the keyboard. These triplet groups are consecutive, but the next two following have a larger gap between the groups as this pattern simply repeats in a lower octave. A similar thing happens at the end of the song (bottom right pic), where two arpeggios (in F and C) are played in a specific pattern and then repeated twice in lower octaves. I've been working to get that part especially even and fluid, and its been improving so far. This is a song I'd definitely like to keep working on until I can play all the sections as fast as J. T. and Heller intended. 
Alan Chan's rendition
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