These Are Not Cryptograms
Answer: WOODWIND INSTRUMENT
Summit Wei

This puzzle has nothing to do with cryptograms. Rather, the key words in the flavortext are "keyboard" and "composer" of the New World Symphony. The composer is Dvorak, and there is a Dvorak keyboard layout, so we should consider that layout.
Upon mapping the Dvorak keyboard layout and seeing what these keys are, there is confirmation we're on the right track because the keys pressed are very close together. In each of the lines, at most two rows of keys are pressed. This helps lead to the aha: The Dvorak keyboard is being treated like a piano keyboard. For instance, if the key I were middle C, then F would be C#, D would be D, G would be D#, and so on.
However, we still don't know what song is being played, and there is no good way to determine the offset of each piece. However, since the flavortext mentions the New World Symphony, we should probably look into that. It turns out that each line of ciphertext plays a theme within one of the four movements of the New World Symphony. Each word represents a measure within the movement. This lets us determine the keyboard offset of each movement, and which movement each ciphertext line refers to:

Movement Ciphertext Notes
I HDHU IUIO EOEUI U EDEB CBCG AGABC B
II MNNMDI DMNMD MNNMDI DMDII FBbBbFEbDb EbFAbFEb FBbBbFEbDb EbFEbDbDb
III HHH EEHHH EEYD IYEIH IYE BBB EEBBB EEF#A GF#EGB GF#E
IV DCT CDD DIEI DD DCT CDD DTDTSE D EF#G F#EE EDBD EE EF#G F#EE EGEGBB E
Note that for Movement II, the theme is played by an English horn which must be transposed to the five-flat key signature of concert pitch. This was not an issue for the data source I was using in construction, but during testing some solvers used data sources where it was presented with four flats. I apologize if this happened to you :c
Also, in Movement III, some notes that are played at the same time are separated.
Now that we have these, we can look at the final extraction. We are given notes, so it makes sense to go in reverse and see what Dvorak keyboard keys are associated with those notes. We want to do this for the given offsets for the first, second, third, and fourth movements in order. The options are sometimes ambiguous since there can be a high and low octave note, but they resolve cleanly to words: FLUTE or OBOE (EIGHT TEN), a crossword clue that clues the final answer, WOODWIND INSTRUMENT.


Author's Notes

The original idea for this puzzle was called These Are Not Namystics, and the puzzle was a bunch of musical namystics (over a chromatic octave) that played pop songs. I scrapped it because 1) I don't know pop music, 2) songs repeat the same notes too often, and 3) I think this would be even less fun to solve than regular namystics.
Afterwards, the final extraction to the puzzle involved a musical cryptogram, which was a nice tie-in to the name of the puzzle, but had to get dropped because it seemed too hard to find.