WARNING: This post contains music theory jargon and math. Therefore you should read it THE WHOLE WAY THROUGH because it is awesome!!!
I like to tell my students that in music there are no rules. Sure, there are traditions and conventions, but at the end of the day, you get to do what you like, and some people will like it and some people won't. End of story.
But of course studying music means absorbing and exploring those traditions and conventions, some of which are quite mind-boggling when first encountered. Kids are brilliant at asking, "Why?" In the beginning it's often musical notation and language that causes consternation. Why does an eighth note get half a beat while a half note gets two beats? Who thought that was a good idea? Why aren't the notes in the bass clef the same as the notes in the treble clef and where can I complain? Soon they are questioning the music itself. Why do the melodies of so many songs end on the tonic? Why do lots of songs in the key of C avoid the note F-sharp? Why don't we see any songs using a 25/4 time signature?
I adore these questions and try my best to give honest answers. A lot of times I say something like: "That's how many people have done it in the past because they liked it that way." From there we can try to guess at why they like it that way and also imagine alternative musical universes. Then the student goes on to compose a piece of music in 25/4 time rooted in C Major but with lots of F-sharps and we both come away feeling pretty good about ourselves.
I like to ask why too. For musical mores, I especially like to ask whether the phenomenon in question is more a cultural artifact or, instead, the reflection of something more universal. Did P.D.Q. Bach do it that way and now everyone does it that way to be like him? Or is the human brain actually wired so that doing things that way is more pleasant than some alternative? I usually wind up with more questions than answers, but it's a fun rabbit hole to go down.
I especially get to scratching my head this way as I read through "The Jazz Piano Book" by Mark Levine (mentioned here). He writes, for example, of the following convention: "The half-diminished mode, the sixth mode of the melodic minor scale, is played when improvising on half-diminished chords." And we raise our hands to the sky and ask, "Why, Lord?" I love this example. When a half-diminshed chord is the ii-chord in a minor mode ii-V-i progression, the result is such a classic minor mode progression - and yet playing what Levine suggests actually means that over the ii chord you'll be using the major third, not the minor third, of the tonic scale in your solo - woa! Just a tiny example of the complexity and beauty of jazz harmonies. Levine points out that this was not always done (nor is it always done today): In earlier times, it was standard for jazz musicians to employ the locrian mode on a half-diminished ii chord in a ii-V-i progression, a more conservative choice in some ways because you never have to leave your native minor mode. And then he makes his case for why he prefers the more modern sound.
Jargon aside, the point is that times and tastes change, and what was once bizarre and dissonant can seem charming or refreshing or pleasingly edgy only a decade later. This example is probably a case where cultural vogue explains a preference, but something more universal (a bias against dissonance) determines the direction of the evolution (simple stuff first - complexity is an acquired taste enjoyed by the more experienced palate). Maybe?
See, isn't this fun??
Now, get your pencils and envelope backs out for this next example.
I was thinking about seventh chords the other day. I think about them quite a lot, actually. I was marveling at how people - children, adults, anyone - who have never studied music can often consistently describe seventh chords: "That one sounds suspenseful and jazzy," they will agree of a dominant seventh chord, while, "That one sounds serene" (major seventh chord) "but that one sounds sad" (minor seventh chord). My favorite is the minor-major seventh chord: "That one sounds evil!" Sure, even at a young age our ears have had hecka-tera-gigabytes of cultural conditioning, and this would be an easy explanation (the cultural explanation) for the easy recognition. But I also wondered if our ears are cuing in to mathematical patterns that help us discern the "sweetness" of some chords and the "bitterness" of others (the universally human explanation).
Chords are made up of combinations of notes (pitches). Harmonious, "nice-sounding" chords traditionally have pitches whose sound waves fit together nicely and don't clash too much. Each pitch can be described by its frequency - a number that describes how fast its sound wave wiggles up and down, and if you think for a little bit you might (like I did) decide that a good way to measure the "nice-sounding-ness" of a chord is to take the least common multiple of the frequencies in the chord. The lower the result, the less complex the chord, and (perhaps?) the more naturally pleasing to the human ear.
With a little scratch work on my envelope, I figured out that indeed, the least common multiple measure for a major seventh chord (the serene chord) is ten times smaller than that for a minor-major seventh chord (the evil chord). So, yeah, on top of all of that cultural filtering I would guess our ears are doing some fast math! Tell me that doesn't make you grin ear to ear.
So you can see it's fun to fish for answers to the persistent "Why?" In this way we can visit places mysterious and wonderful (like pop music!), though often the actual answer eludes us. In the meantime, I say, do what you like and like what you do. Convention can catch up later.