Edit: After a semester of thinking about music, I am still unsure as to what constitutes "good" or "bad" music. I am also still inclined to think about it teleologically. Our discussion on profundity seemed to me to be very similar to our discussion on good and bad music. Perhaps we are simply stating preferences... perhaps we are muddling our terms... perhaps there is an objective "good" for music. Although I don't have any new answers, I have added a few more "good" pieces for you all to enjoy.
I originally thought "oh good! choosing a bad piece will be so simple! there is so much bad music out there!", but the task of actually sitting down and finding one was rather difficult. As it turns out, I have either seriously over-estimated the amount of awful music or I have had to repress the horrible "pieces" I have heard.
But this piece- "Ade! Ich Muss Nun Gehen", by Friedrich Nietzsche- sprang to mind. On the surface, there isn't much to point to as to what makes the piece bad. Nothing sticks out as horribly offensive: no poorly-handled dissonances, no random fragments of melody, and no awkward rhythms. A casual listen-through might even spare the song some dignity. But something about the song is... annoying. While trying to put together my thoughts, I listened to the song on loop and wanted to pull my hair out. Nothing breaks any "rules", the form is predictable... too predictable. As Levitin points out, there is a sweet spot between too simple and too difficult. This song is much, much to simple. There is nothing surprising and unexpected to catch the listener and draw them in.
And there is also something vaguely comical about it. For example, the thumping, plodding descending bass line at around 11 seconds is reminiscent of a portly older man trying to make his way down the stairs- neither elegant nor subtle. The exclamation at 40 seconds makes sense musically, but seems forced.
Overall, the piece is technically "correct", but lacks grace, elegance, and subtle points of interest. As Berlioz so aptly termed it, this piece is "insipid" and "innocently stupid".
The good yielded a much larger crop, so I have posted many songs for your aural pleasure, which you may listen to should you feel so inclined.
In order to give a good piece the respect that it deserves, I chose a rather short piece, the Prologue from the Prophetiae Sibyllarum, by Orlando di Lasso, to play in class. This piece, unlike the last, seems to ignore a lot of rules- like, for instance, general tonality (his works were pre-tonal, but I speak of the "rules" of our modern, tonal ears). Yet, even in ignoring these rules, the piece presents a delightful challenge to the listener and can still sound beautiful to a less experienced music-lover. But the piece isn't just a jumble of rule-breaking tricks- it makes sense. The final cadence is wonderfully satisfying.
The di Lasso piece provides a challenge, it is interesting, and it musically satisfies. But beyond that, I am stumped as to how to explain why it's good.
I am tempted to think of good and bad music teleologically. To think that music has a purpose and that any music that fails to reach that goal is "bad" and any music that succeeds is "good" (and that there are varying degrees of goodness and badness depending on how close or far it is from that goal). For instance, a chair that has no sitting surface is a bad chair. But what would such a telos be for music? The best I can think of is that the telos is to unfold an experience of the beauty and/or the sublime. But then music seems to be just a tool and then I am left unsatisfied with such an approach.