[archagon]

One of the most enlightening things I learned while studying music in college was discovering why classical harmony ended up the way it did. What makes a V7 chord work? Where did augmented 6th chords come from? How did the Neapolitan chord fit into these systems? By looking at the progression of music history from one-voice chants to counterpoint to harmony and then to the explosion of ideas in the Romantic era and beyond, you acquire the skills to know why music — any music — can sound good and express rhetorical ideas.

With a foundation in classical music theory, you can go beyond what anyone is doing in popular music today. I strongly believe that (for example) Beethoven's 5th, from a compositional perspective, has more rhetorical power than any music produced in the last century. I think this is largely due to popular music being very simple structurally. Where is the counterpoint? Where are the modulations? All we get is simple chord progressions repeated ad nauseum. Imagine how much farther we could go if we combined the lyrical and textural variety of popular music with the compositional depth of classical music! I salivate at the thought of an electronic or metal musician[1] delving into this territory...

[1]: Phish is one of the few bands I know of who actually focus on this stuff. Some of their pieces even include bona-fide fugues. I'm not the biggest fan, and it's a simple example, but I love listening to the motifs and variations in "Stash": https://www.youtube.com/watch?v=8OfQCAj2Ppg

[TheOtherHobbes]

>Where is the counterpoint? Where are the modulations?

In the sound design, the rhythms, and the production, where they never trouble the hearing of anyone who has been trained to believe that musical structures are defined almost entirely by pitch patterns.

Even the idea that music exists to 'express rhetorical ideas' is... actually quite odd, outside of classical training, anyway.

I happen to like fugues very, very much. (The fugue in BWV 542 is a favourite - http://www.youtube.com/watch?v=g6Kul3JzKI0.)

But the idea that music should aim for that always? Uh, nope.

[archagon]

I never said "always"! But it would be nice to have sometimes. It's an area that's almost completely unexplored in popular music.

[_deh]

So, doing things that don't scales?

[baddox]

Out of curiosity, have you studied just intonation? I'm currently reading the mostly excellent Haromonic Experience [0]. I'm reasonably well educated on music theory, but I had never looked into just intonation and the way frequency relates to our perception of pitch and harmony. I'm finding this stuff enlightening.

An ideal string (or any oscillator) when disturbed (e.g. plucked) will tend to vibrate at a fundamental frequency of x Hz as well as modes of 2x, 3x, 4x, etc. These higher frequencies at integer multiples of the fundamental frequency are called harmonic partials. This is a physical phenomena unrelated to music and human hearing.

But the basic elements of harmony come from the fact that our auditory system seems to be "tuned" to identify harmonic partials.

If we start with a fundamental frequency x Hz (let's call it C), the first partial is 2x Hz, and it is another C an octave above (multiplying or dividing a pitch by a power of 2 will give you the same pitch in another octave).

The next partial is 3x Hz, and it sounds like a G. This is the interval called a perfect fifth, and is the strongest, most stable sounding interval (other than the octave). The next partial is 4x Hz, which is just another C, two octaves above the C we started with.

The next partial is 5x Hz, which sounds like an E. This is a major third, which is another strong and stable interval which is ubiquitous in most music.

[0] http://www.amazon.com/gp/product/0892815604/ref=oh_aui_detai...

[archagon]

Yeah, a little bit! What's interesting is that we're so used to equal temperament (i.e. a bit of error added to most intervals in exchange for greater flexibility) that pieces played in just intonation sound "off" to us, even though they're more mathematically correct.

Also, I believe instruments with arbitrary pitch (violin, voice) tend to naturally drift closer to just intonation.

[baddox]

I've been trying to train myself to hear the JI resonances (Harmonic Experience has tons of exercises for this). I can hear the sharpness of the ET major third and the flatness of the ET minor third fairly easily.

Barbershop quartet music (and other a capella music) is a great place to hear just intonation. The consonant barbershop seventh chord was a relevation to me when I first learned of it. It's really close to the dissonant dominant 7th interval, but serves a very different purpose harmonically. The minor seventh is also a different interval. Thus there are actually 3 seventh intervals, all of which are approximated in ET by a single note. This blog post has a good summary:

http://www.garygarrett.me/?p=1575

[ambler0]

I feel the same way about gaining insight from studying the history of music theory, but I have to disagree with a couple of points, too:

1. Studying the history of Western music theory doesn't give you insight into any music, as you claim. It gives you insight into Western music. Check out music from another part of the world with a completely different notion of tuning, different scales, etc, and your music theory background isn't going to help very much. The only thing that is truly universal is the overtone series, because that's based on physics.

2. I think we could come up with plenty of structurally complex music from recent idioms, particularly jazz and jazz-influenced music. I would say that a bigger difference between something like, I dunno, Steely Dan, and Beethoven's Fifth, is length. Popular musicians don't seem to attempt such longer pieces. But for me personally, longer != more powerful. For that matter, more complex != more powerful, but I happen to share your desire for what we're calling "compositional depth", whatever that may be...

[archagon]

Classical music theory is a rigid, structural, almost mathematical system that emerged over several centuries. In those centuries, composers learned some very powerful techniques to express ideas in their music. Although the specifics of classical music — the rhythms, the chords, the tonalities — may be antiquated, I really do think that the forces that guided their development are just as relevant to modern music. For example: why is a V7 chord so powerful? It's because you have the interval of a 5th — a tense interval with almost universal meaning vis a vis the overtone series — combined with two minor 2nd intervals that are brimming with tension to resolve to the tonic and the third. The study of intervals and of tension in voice leading is, I think, absolutely essential in jazz as well, and can help explain some extremely confusing jazz chords in analysis as almost incidental results of voice leading. This is what I mean by classical music theory offering insight into any genre of music: classical music emerged out of the study of things like intervalic tension, and even though our own century's music has diverged from this origin, I think it's very important to study the lessons learned over those hundreds of years.

(EDIT: I just noticed that you said outside of Western music. Yes, that may be correct. Many systems of music in the world are very different from our own. But I think most people writing music today are writing with Western ears in mind. After all, we've been conditioned to understand this kind of music for hundreds of years!)

As for your second point, I think what I latch on to in classical music more than anything is the use of motif, and Beethoven's 5th of course epitomizes this. Don't get me wrong — I love popular music, and I listen to it more than anything — but most of the "top 100" songs in any popular music ranking feature wandering, improvised music more than any systemic use of motif to make a rhetorical point. And that's not a bad thing! I love Stairway to Heaven. But it just "sounds good" — it doesn't really develop its musical material.

Compare to something like this[1], where every single musical detail is repeated and developed across all the voices. It's so intricate. I've never heard this level of motivic development in popular music, and I've been looking for a few years now.

I am sorry if this is not making any sense, I am having beers.

[1]: https://www.youtube.com/watch?v=hWLotW5AKjg

[ambler0]

You're making plenty of sense, beers or no

I would say that the V7 gets it's power from the flatted fifth interval, aka the tritone, aka the most dissonant interval this side of a minor second. And like you say, it can be understood in terms of voice leading, e.g.the 7th (the "leading tone"!) "wants" to resolve up to the tonic.

It's interesting that you mentioned motif because I think that fits well with what I was saying about the length of the pieces. Seems to me that one isn't going to have much room to develop motifs unless writing in an extended form. But for me personally, this doesn't seem like a good requirement for a piece to be satisfying in the way that I think we are talking about. If you are seeking that kind of intricacy from modern music, have you checked out Bela Fleck & the Flecktones? Also, have you explored Zappa at all?

[archagon]

I mean, there are many ways to be satisfying in music. I am very satisfied by the exploration of texture and improvisation in modern music, for instance, and I am very grateful that we live in such an exciting time for musical experimentation. But at the same time, in a way that's hard to describe, the moment where the theme returns in the third movement in Beethoven's 5th[1] just absolutely trumps any musical moment I've heard in popular music. I'm talking Schindler's List level goosebumps. There are plenty of long pieces in popular music, too — prog is big on that. But the techniques of Beethoven and ilk just aren't getting used, which I think is a great shame. I don't think it's "magic" or "genius". I really do think it's a matter of harnessing the medium to its full potential, which might require more education in music theory than (in my experience) many musicians feel comfortable with.

I don't think you need a long piece to develop motif. Look at something like "Vocalise"[2], or, heck, any of Bach's Well-Tempered Klavier.

One of my teachers used to stress the original meaning of the word "sublime". I think that's what's missing in modern music. A feeling of awe that leaves you speechless.

Zappa's been on my to-do list for a while, I'll have to give him a listen soon!

[1]: https://www.youtube.com/watch?v=jdvsRJL4Mtw

[2]: https://www.youtube.com/watch?v=iBVkYGLEUpg