Thursday, July 1, 2010

Paradigm analysis

Hey readers! It's been a super-long time since I've updated, I know, but with a combination of being ridiculously busy and changing my mind on how best to do this post(and the one after it) as well as now-resolved technical difficulties with my MIDI keyboard, which made putting examples into Finale an exercise in frustration. Anyways, I'm now back-ish. I have an audition in a couple of weeks which will be super-important, so I'll be in and out practicing for that many hours a day, but after that I should be able to keep at least something approaching a regular schedule.

Now, last time I brought up the idea of Paradigms for chord progressions, which are interesting ways of thinking about progressions where you're not nailed down to a specific progression of chords, but rather you have a nice framework that you can play around with a little more. I've got today examples of the first two paradigms I mentioned, as well as a single variation on both. Without further delay, here's the first example, a very short piece for a string quartet.

I'd like to apologize again for the PDF handling.  If anyone can suggest a way to host PDFs, or any multi-page document, that'd be awesome, but for now we have to go through Wuala, which while not awful, I can't just have a hotlink or inline.  Or at least don't know how.

Anyways, that score is great, but since that's sort of useless without the corresponding sound...

Wonderful. Ok, this is fairly straightforwards as a piece, so let's do a quick and dirty analysis. The first thing to do is figure out what key we're in. After that, see if you can get the general idea of what the chord progression is. In this example, all of the chords are in root position, so that makes that part super easy. Also, the title happens to be the Paradigm I'm using, so that makes it even easier.

So we're dealing with a piece in F major, and the progression is I-vi-IV-V-I-vi-IV-I. Now we can notice that it sounds like we have two phrases in here, the I-vi-IV-V, and the I-vi-IV-I. So the first phrase ends with a Half-cadence, and the second ends with a Plagal Cadence.

Now, here we already are starting with playing around a bit. The Paradigm is I-vi-IV-V, right? But while the first phrase does that, the second one careens off the cliff at the end and doesn't go to V, instead opting for a Plagal Cadence. Well, we'd still call that the I-vi-IV-V Paradigm, probably, because the function of the chords is still about the same as though it were, and the first phrase does it exactly. The only difference is that to preserve having the phrases having equal lengths, we just chopped off the V and replaced it with a I.

Ok, now let's look at a slightly changed piece.

And it sounds like...

Bam. Ok, almost the same, right? In fact, I don't know how many of you are using Foxit Reader, but I've got them both open and can quickly change between them in tabs to see very clearly the difference. All I've done is altered the Viola line in measures 2 and 6 from alternating between F and A to alternating between F and Bb. So what does that mean? Well, a vi chord in F Major is D-F-A, right? A d minor triad. And a Bb chord, Bb-D-F, is a IV chord. Well what I've done is taken out the vi chord and replaced it with a IV6 chord, or a IV chord in 1st inversion.

Now let's think about that for a second. The vi chord is a minor chord, and was played in root position. This gives it that nice grounded sound of the root position, and it's the only minor chord in the progression, which gives that sort of more “sad” sound to it. Meanwhile, the IV6 chord is in first inversion and is a major chord. This means we have a much, what I would call softer texture to the whole thing. It gives us a nice “happier” sound, it makes the progression have less movement, since we're really now just going I-IV-IV-V in terms of the actual notes played... while we're only changing one note, it really gives a nice different feel to the progression.

However, calling that a I-IV-V progression wouldn't really give us the whole picture, because of the way it's voiced. This is what makes thinking in Paradigms so great. The variation still sounds like I-vi-IV-V, for the most part, but just subtly different. The bass line has the same contour and the same notes, and we could use this progression as we use I-vi-IV-V much more than we could use it as we use something like I-IV-V.

This is also great if we're listening to something, and we hear a I-vi-IV-V run in the bass, and when we play it it just sounds wrong. There's always the chance that they're doing a IV6 or some other variation somewhere that makes it sound a little different.

So, to expand on that, let's take a quick look at a second example, and then I have some tunes I cooked up in Reason that are a little more full, so we have the use of the paradigm in context and not just on paper in tiny examples.

Great, so here's one for brass, if you couldn't tell. Let's do the quick look here. We have two sharps, which puts us in D major, and the progression.. uh oh. This one is a little busier than the last one, which makes this a bit harder. Well, luckily, again the title is the progression, but also, just take a look at the beginning of each measure. That first beat is a really nice way to figure out where things are, because barring a suspension, it's really common to have things line up there. Also, the first thing I do is just look at the bass line for major changes, which in this case is the Tuba. Sometimes, as we saw in the variation back there, there are inversions, but the bass notes will very, very often be at least in the chord, if not on the root or outlining it entirely. Anyways, the progression is I-ii-IV-V for the first and second phrase, and then the 2nd page just finishes the whole thing off with I-V-I.

So this is pretty straightforwards again, it's the second paradigm I mentioned in the last post, and there are some more nonharmonic tones, but for the most part, there it is.

So let's fuck with it a bit, because we can.

Now this one is slightly more changed than the last one, but again it's that second chord that I changed up a bit. This time instead of a ii chord, which in D major is E-G-B, an e minor triad, I substitute in a V in 2nd inversion, with the notes E-A-C#. Now here's a huge example of how thinking in Paradigms is really, really, really awesome. The progression, were we to ignore inversions, would be I-V-IV-V. I-V-IV-V is another paradigm all together from I-ii-IV-V, and has its own very distinct sound. Even if we just add in the inversion, and say it's a I-V6/4-IV-V, it still would be super-easy to think about a I-V-IV-V thing if that's all we saw. However, having the bass line rise to the second scale degree makes the piece have a very clear sound that is characteristic of the I-ii-IV-V progression. The sound is a little different than I-ii-IV-V, but it's much, much closer to that than I-V-IV-V. So this is a great example of how thinking in terms of these big broad umbrellas that I call Paradigms and then whittling down to specific variations and progressions gives this really nice immediate recognition and classification that just looking at a billion progressions doesn't.  In fact, if someone were to talk to me about I-V-IV-V, the sound I would immediately go to would be Blink182s All the Small things.(There may be an ad with that link, sorry about that).  Now, that's not only a different sound from this Paradigm because of the style, but it just has a completely different harmonic sound in general.  Again, this is why Paradigms are awesome. All the Small Things could be I-iii6-ii6-V and would probably sound a shitton of a lot closer to the original song than doing a variation of I-ii-IV-V. 

If I had to pick one reason that I'm spending so much time on this subject, that would probably be it. Being able to look at a piece and just sort of give a nice broad classification, and understand how those broad classifications fit together will make doing any sort of deep, particular analysis faster and easier, and being able to hear in those giant brush strokes and then pick out the finer detail is also incredibly useful if you're trying to play by ear. Note that I've always said “think about” in terms of Paradigms, and not “analyze”. That's because if we were to write down the paradigm instead of the progression in an analysis... yeah that would be wrong. But if we recognize and think in the paradigm, and then whittle down into the progression, we'll be adding a tool to help us easily understand the larger picture.  I know personally if I'm sightreading, or improvising over a line, I think in terms of the paradigm a lot more than the progression.  In general, thinking in Paradigms is the practical way to go about things.  "Close enough" is, well, close enough 90% of the time.

Anyways, I know that we've basically just covered two pieces with variations, but I'm working on some more fun examples of the things we covered today, it'll be an enjoyable experience.  Also, I have super-awesome news, which is that Tindeck seems to have added an embedded player, which I'll probably start switching over to soon.