Man... we're getting deep!
First off: about skrillex, you agree with my point (the arrangement being "better" than the actual song) when you say this: "He's simply emphasizing it by making absent other elements."
Like i said on my first reply: Melody in this song comes from the voices in the different chords and how they link, the arrangement the pianist does makes a few choices that are great, he made focus in a few lines that work great, which are not so easy to listen in the actual song.
Skrillex could have worked the arpeggiator a bit better, and more in detail, but he didn't. The pianist did, and hence got a better result from the original chord progression... which, again, it's not the most original.
Now, with that out of the way let's go into deep!
you make a few broad statements, like: The entire history of music is based on pitches separated into 12 equal (on a logarithmic) intervals that scale between multiples of some frequencies.
I assume (reading what you write afterwards about other cultures and stuff) that you refer to what could be commonly known as "classical music". Even assuming that, this is still wrong, Pitagoras established the famous "pythagoream choma". Equal temperament (what you're referring to) was studied for years and years... The Well Tempered Clavier, by Bach, is a study on how to deal with that "distance" in frequencies, which is not always the same. A violinist won't use the same fifths as a pianist or a guitarist when playing on their own. Neither will a singer, or anyone who hasn't a mechanical system that makes them. Distances between intervals is not and has not been always the same.
If you were actually referring to "the whole music history" for real, get to youtube and search for proper hindu music, they split the octave in many more intervals than 12.
Jazz is a mixture of elements, a great one for that... BUT, it has some "classical" elements there, specially regarding form. Even if it doesn't, why does Caribbean or African music deny "classical" music? Classical music deals with dissonance in many many ways, depending on the period and the composer... and some of those ways of dealing with dissonance are common to many other cultures' music. In fact, the music that openly "opposed" every rule in the classical book was classical music itself, when Arnold and his friends started with the dodecaphonic system, etc.
Jazz opposed classical music from a more social point of view, yes, but from the musical point of view, they have many things in common.
Also: Debussy was writing in 5 and 6-tone scales before Jazz was in any scene. So was Satie.
And saving the best for last:
This usually happens, and it happened to me before that many people tend to associate good music with:
-music that is not very popular
-music that is difficult to listen to
-music that sounds plain awful
I haven't said it before, so i'll say it now: I DON'T THINK THAT WAY...
Yes, there are music of all those characteristics that is good, but there are also silly songs that are good, or extremely popular ones, or easy to listen to or written by a guy who can't read music... Good music is GOOD MUSIC, there are no stylistic characteristics that can make something be good... Style comes into play, tho. I wouldn't say that a gospel hymn and a traditional chinese song play in the same category, but they can both be good, potentially... get my point?
Repetition won't make something bad... but it won't make it good either.
In art, there's no formula to be successful. That doesn't mean there aren't good or bad pieces. The elements that define quality in music are many, most of which are objective, and all of them matter. This being said, that doesn't mean you'll be either successful, famous, rich or get to many people doing something good. You can do shit music and get to millions' soul. That won't make your music good tho.
I like what you say here:
I probably should clarify that this wasn't necessarily to discuss whether or not he is a good songwriter in any absolute sense, but rather, to look at elements of his songwriting that people might find surprising.
Yes! absolutely. Good music has that "surprise" element... Rules come into place here, then. If you disregard 100% of what's familiar to people's ear, how can you surprise them? They'll get bored 10" into the song if they can't relate to anything you're doing. Cultural knowledge goes deeper than we think. It is impossible, anyway (specially after what happened in art between the 50s and today), to do something that is completely the opposite of anything...
And i finish with this:
you say: Because music is just the expression of an idea, if the listener takes away very vivid and detailed idea, even if misinterpreted, the songwriter has achieved what he was supposed to. The more people the songwriter connects with on this level, the better his music is. People tend to connect with music they like exclusively, but not always.
and I ask: Is (the guy/girl who writes for) Justin Bieber a better songwriter than Miles Davis, or (the guy/girl who writes for) Lady Gaga a better songwriter than Peter Gabriel?