The harmonic relationship between chords that this progression contains are rock-solid.

April 19, 2010 6:56 PM

I've been playing music all of my life, and I've never seen a better distillation of music theory than this comment. It's a full semester's worth of study in a few short paragraphs. I know it's been months since it appeared ... but this is truly worthy of a sidebar, or a book deal, whichever comes first.
posted by jbickers to MetaFilter-Related at 6:56 PM (72 comments total)

To hell with a book deal. Make the guy a moderator.
posted by Fiasco da Gama at 7:08 PM on April 19, 2010 [17 favorites]

In a really aggressively reductive sense you could look at western music composition as consisting of (1) the tonic, (2) the dominant, and (3) whatever else happens on the path from the one to the other.

It even hints at Schenker.
posted by invitapriore at 7:20 PM on April 19, 2010 [1 favorite]

It's good, but all of that is pretty much chapter 1 of any decent book of music theory.
posted by empath at 7:22 PM on April 19, 2010

His early stuff was better.
posted by ludwig_van at 7:42 PM on April 19, 2010 [6 favorites]

I would favorite it if I understood more than about six words in a row of it.
posted by adipocere at 7:45 PM on April 19, 2010 [16 favorites]

Pssssh, I have that comment on vinyl.
posted by komara at 7:47 PM on April 19, 2010 [5 favorites]

Fuck this "universal constants in music" shit; I need help building this mountain out of mashed potatoes!
posted by yhbc at 7:53 PM on April 19, 2010 [7 favorites]

it's the "relative minor" of the major tonic root of the key. They're very similarly harmonically—you change one note to transition between the two.

Hrm.
posted by fleacircus at 8:07 PM on April 19, 2010

Oh man, I saw a stray new favorite hit that comment earlier this afternoon and went back and re-read it and there's a bunch of typos and little things that I wasn't as clear as I'd like about.

I'm glad it's comprehensible to the folks its comprehensible to, I remember enjoying writing it and trying to distill a bunch of that stuff that's been rattling around in my head into a primer. But, as empath says and as I acknowledged in the comment itself, this is more a napkin-drawing take on some of the stuff in week one of a Theory 1 class than any sort of well-kept secret.

I grew up doing music by ear in a fairly musical family, and only got some proper theory grounding my freshman year of college, when I took two units of Music Theory and finally learned some formal vocabulary for all the stuff I'd been actively and passively learning by brute force as a kid tooling on the family piano and then as a budding guitarist/songwriter in high school, and it was a really revelatory process for me.

Theory can be kind of dry, mystifying stuff out of proportion with it's actual conceptual difficulty, I think—the ideas aren't necessarily hard but the presentation matters a lot. A bit like math, and the distinction between people who "aren't good at math" (true for some, maybe, but not as many who think so) and those who just hit the learning curve at a bad angle, possibly with very little help from their instructor, and so let it go as not worth the anguish.

I've known tons of really talented musicians who just never ever went there not because they lacked the capacity but because they tried once and it went badly or they never saw the attraction. And that's okay, you can totally get by without it and make fantastic music (or, as a listener, appreciate the hell out of music without having any formal notion of what's going on at a theoretical level), but it's a really nice tool to have if you can manage to get a toe-hold and start taking on the theory in an anguish-minimized fashion. If that comment helps some folks, that's awesome. I suspect there are some very good books out there by people who are both better writers and better music theorists than me, though I hadn't ever gone looking.
posted by cortex (staff) at 8:11 PM on April 19, 2010 [2 favorites]

I need help building this mountain out of mashed potatoes!

Well if it's gonna be that kind of party
posted by Fiasco da Gama at 8:37 PM on April 19, 2010 [7 favorites]

Well if it's gonna be that kind of party

It would be a party of this kind (in case anyone didn't get the reference).
posted by Burhanistan at 8:39 PM on April 19, 2010

Burhanistan: It would be a party of this kind (in case anyone didn't get the reference).

So, uh... not the kind of party where, eh, you stick your, um... y'know... in the mashed potatoes.

I don't suppose anyone's got a napkin? These are new pants, you see and... oh great, whoever took that picture, please don't upload them to Facebook! My mom is on my friendslist and... oh, that's a video camera isn't it... nothing's gonna stop that from getting on YouTube, huh? No? Didn't think so.

Don't mind me, I'll just be in the basement with a rope and the tatters of my dignity.
posted by Kattullus at 8:50 PM on April 19, 2010 [2 favorites]

this is more a napkin-drawing take on some of the stuff in week one of a Theory 1 class than any sort of well-kept secret.

I think the comment is a favorite of so many because of the way you said it, not because it contains magical new information.
posted by ericost at 9:01 PM on April 19, 2010

I would favorite it if I understood more than about six words in a row of it.

Yeah, he glossed over the math part of it which usually gets brought into the introduction.

A musical note in it's purest form can be represented by a sine wave This represents the change in air pressure over time, which your ear interprets as sound. Sine waves have 2 important properties that relate to music -- Amplitude (volume) and frequency, which corresponds to pitch. There is also a wavelength, which is related to the frequency (the longer the wave length the higher the frequency).

The frequency of 'middle A' is 220hz (220 sound waves a second). If you double the frequency, it is also an A, but an octave higher, if you double it again, it's the next octave higher, and so on. Same if you lower the frequency by half. If you play a 220 hz tone and a 440hz tone simultaneously, they will be perfectly in sync with each other. They don't drift so your ear doesn't really distinguish between the two tones, but they reinforce each other.

Now, most instruments don't produce pure sine waves. They produce something called overtones. What generally happens when you pluck a string of length 1 unit, it will create a wave in the string of 1 unit length, but also a slightly smaller wave of 1/2 length, another of 1/3, another of 1/4th, and so on to a limit that depends on the material, but always in whole ratios (see the illustration in the wiki article).

A wave of 1/2 length will have double the frequency, 1/3rd will have triple and so on. So, let's assume you have a string that produces a middle A at 220hz. It will also produce sine waves of 440 hz, 660 hz, and so on. 440 is the next higher A, 660 is the next higher E, 880 is A again, 1100 is C#, 1320 is E again, etc.. you can keep going up, but as you go higher, the contribution gets lower and lower from each additional overtone.

But I'm sure you're already thinking, what happens if I play A, C# and E together? That should reinforce all those overtones and sound interesting.

Congrats, you've just discovered the A-major chord. If you're going to write a song around A, then that is going to be called your Tonic, or the 'I' Chord. You can just play around on the piano with those three notes and get a fairly pleasing sound, but you'll quickly find it's boring.

So what you do is look for other related notes to play around with. You probably noticed that E key mentioned twice in the overtones. Why don't we look at the overtones for E and make a new chord out of that? Well, if you do that, you end up with the 'V' chord or dominant. There's tension between the two of them because E's overtones aren't the same as A, but transitioning from E to A resolves it and sounds pleasing.

That's why cortex said "In a really aggressively reductive sense you could look at western music composition as consisting of (1) the tonic, (2) the dominant, and (3) whatever else happens on the path from the one to the other."

The tonic and it's 'perfect fifth' have a unique, mathematical relationship to each other that isn't really a matter of taste. They just sound nice played together. Musicians and music listeners can and do make music that doesn't involve the I-V progression, but when they do it, they're using dissonance and tension to get an effect. If you just want something that sounds 'pretty', I-V is pretty much the only game in town.

(Obviously I've simplified things a great deal, but hopefully I at least explained what chords are and why they sound nice).
posted by empath at 9:10 PM on April 19, 2010 [29 favorites]

(ahhh-- i meant to say 'the longer the wave length, the LOWER the frequency' above)
posted by empath at 9:11 PM on April 19, 2010

Hmm, I took music theory 101 once, but I think I forgot most of it.
posted by delmoi at 9:37 PM on April 19, 2010

empath, I think you've made a few assumptions that don't always hold.

What generally happens when you pluck a string of length 1 unit, it will create a wave in the string of 1 unit length, but also a slightly smaller wave of 1/2 length, another of 1/3, another of 1/4th, and so on to a limit that depends on the material, but always in whole ratios (see the illustration in the wiki article).

Well, kind of. Inharmonic overtones are a big part of why instruments sound the way they do, and why they're so hard to model.

Also, I lean on this example a lot, but a universal human predilection for low-denominator harmonic ratios in music is hard to assert in the face of the existence of gamelan. There might be a neurological bias towards those harmonic ratios as some of the cites in that link suggest, but it's evident that, if so, we're capable of overriding that bias and extracting musical information from non-harmonic tunings too.

In general, though (as in, this isn't really directed at you, more at pedagogical practice as it stands), I'm not sure the acoustics behind the theory really need to be brought in until you start learning orchestration. The note as it figures in western music is a pretty well-encapsulated abstraction -- I tend to think that the average person is sufficiently musically conditioned to the point that notes as syntactic entities have a similar cognitive relationship to their acoustic profile as a phoneme in speech does.
posted by invitapriore at 9:43 PM on April 19, 2010 [3 favorites]

Well, kind of. Inharmonic overtones are a big part of why instruments sound the way they do, and why they're so hard to model.

I did say I simplified things a great deal. Point being that there is a mathematical basis for constructing chords and that it is not arbitrary. And both Cortex and I were talking about 'western music', and the initial question was specifically asking about why one particular chord progression was popular.
posted by empath at 9:55 PM on April 19, 2010

Speaking as someone who picks up the guitar every few months and soon gets frustrated, that's probably the most grokkable bit of theory stuff I've encountered.
posted by Alvy Ampersand at 9:59 PM on April 19, 2010

Uh, that's cortex's AskMe response, not empath's comment. No offense.
posted by Alvy Ampersand at 10:00 PM on April 19, 2010

Yeah, you're right, sorry for derailing a bit. I do think it's misleading to say that there's a mathematical basis for chord construction. Realistically, those structures were arrived at by intuition and experimentation, and the theory came afterwards. To assume that the math explains why we find those structures to be pleasing is assuming too much, I think, and I think there's a certain hegemonic strain of thought involved in assuming that the basic principles of western music, principles that not all musics share, are directly founded on basic natural laws.
posted by invitapriore at 10:05 PM on April 19, 2010 [5 favorites]

To assume that the math explains why we find those structures to be pleasing is assuming too much, I think, and I think there's a certain hegemonic strain of thought involved in assuming that the basic principles of western music, principles that not all musics share, are directly founded on basic natural laws.

I assume that similar math is behind Gamelan music. The instruments don't produce harmonics, so there's no point in creating chords out of intervals, because they'll still be dissonant.

As far as I know, all experiments with children, even babies, show a preference for harmony.
posted by empath at 10:14 PM on April 19, 2010

Regarding the relationship between mathematics and music, this book is worth noting.
posted by HP LaserJet P10006 at 10:54 PM on April 19, 2010 [1 favorite]

Hah I think that "stray new favorite" was mine. I came across it from the Axis of Awesome thread, as I suspect jbickers did.

A nice little "behind the favorites" thread this is here.
posted by zachlipton at 10:57 PM on April 19, 2010

You should see the guy's drum solo.
posted by qvantamon at 1:08 AM on April 20, 2010

You should see the guy's drum solo.

You can't handle that on strong acid, man.
posted by chillmost at 5:02 AM on April 20, 2010

Fill Clip, do you want to mess with this? Gang Starr: one of the best.
posted by chunking express at 5:07 AM on April 20, 2010

Yet.
posted by chunking express at 5:07 AM on April 20, 2010

Ooh, cool, glad this made it into MeTa because now I can trot out my geekiest music joke without this being a derail.

Q. How many bassists does it take to change a lightbulb?
A. One. Five. One. Five. One. Five...
posted by ZsigE at 5:31 AM on April 20, 2010 [10 favorites]

To assume that the math explains why we find those structures to be pleasing is assuming too much, I think, and I think there's a certain hegemonic strain of thought involved in assuming that the basic principles of western music, principles that not all musics share, are directly founded on basic natural laws.

I don't think it's assuming too much to say that Western music is a complex as it is (at least classically) because of centuries of experimentation by composers like Bach experimenting with the latest mathematical theory of music. The power of that specific progression of chords on a major tonic discussed in that post are the result of writers using these theories to make plain chant into polyphony and symphony, distilling and refining what is compelling in sonic forms into their components and then seeing how far and in which directions one can push the boundaries of the simple relationships between tones.

It was as ingenious and as inevitable as the development from machine code to basic to pearl to ruby. It's no more hegemonic than penicillin, or more appropriately some bio-engineered virus that can infect any homo sapien from anywhere. Pop music isn't just popular because of imperialism--like fast food, it's been genetically perfected to hit some very basic needs in human sensory organs.
posted by Potomac Avenue at 5:32 AM on April 20, 2010 [1 favorite]

Also, I lean on this example a lot, but a universal human predilection for low-denominator harmonic ratios in music is hard to assert in the face of the existence of gamelan.

But gamelan is based around percussion instruments, which produce a very different series of overtones from a vibrating string or column of air. It makes sense to me to say that the major scale arises naturally from the overtone series produced by certain types of instruments. See: relating tuning and timbre.
posted by ludwig_van at 5:33 AM on April 20, 2010

The power of that specific progression of chords on a major tonic discussed in that post are the result of writers using these theories to make plain chant into polyphony and symphony, distilling and refining what is compelling in sonic forms into their components and then seeing how far and in which directions one can push the boundaries of the simple relationships between tones.

Weeeeell, I don't know about all of that. I think if you're going to use jargon it's important to do it carefully. "Plainchant," "polyphony," and "symphony" do not belong to the same category of things, for one.
posted by ludwig_van at 5:42 AM on April 20, 2010

To which exclusive catagories would you assign them? They were all developments in the history of Western music, invented and perfected by people and groups engaged in the active study of math-based music theory.
posted by Potomac Avenue at 6:06 AM on April 20, 2010

Sorry I was unclear I think! I was using symphony to simply mean "a sounding together"...in the way that 16th century composers used it to indicate a large orchestra accompanying a choral work--a form that developed into classical Symphonies in the baroque period. Pretentiousness is a dangerous meme, my bad.
posted by Potomac Avenue at 6:13 AM on April 20, 2010

There's tension between the two of them because E's overtones aren't the same as A, but transitioning from E to A resolves it and sounds pleasing.

Everything until this sentence sounded like science. Please define "tension" and especially "resolve". What does it mean to "resolve" a sine wave?
posted by DU at 6:22 AM on April 20, 2010

cortex, empath, and other music theoreticians: Can you suggest a good intro to music theory book? This thread that ReadMe links to doesn't really get a great answer. Or is a class the best bet for people who want to learn more about this stuff?
posted by Plutor at 6:22 AM on April 20, 2010

It would be a party of this kind (in case anyone didn't get the reference).

I was thinking of "Waiting...", myself.
posted by Pope Guilty at 6:51 AM on April 20, 2010

My problem is I can't make a recommendation because I haven't gone looking. The theory courses I took were great for me because a lot of it was essentially providing some grounding for the basic ideas I'd already developed and showing me a bit about how those ideas developed and some of the things I could do to extend them. I don't even know if they were particularly good courses in the general sense; the prof was an eccentric, impish loon who I liked a fair bit but possibly I'd have found his instructional style frustrating as hell if I wasn't getting along pretty naturally with the material.

Linking more as an example than as a suggestion, this is the text we used in college. It covers the traditional ground fairly thoroughly with lots of examples from western classical music, but is dry and doesn't try very hard to make things accessible if you aren't already naturally inclined to decoding musical notation and thinking in terms of that. I would not suggest it for anyone who wasn't specifically looking to sort of refresh or expand some existing grasp of traditional western theory.

So I'd love to see suggestions as well, really. It'd be fun to read a text that really tackled theory but in maybe more of a contemporary context—use pop music as the grounding for by-example explanations of some of these things instead of expecting someone new to the subject to immediately buy into piles of Bach and so forth. Bach's lovely and all but not exactly the at-the-fingertips material for the average reader compared with pop from the last fifty years or so.
posted by cortex (staff) at 7:04 AM on April 20, 2010

Your favorite comment sucks.

In all seriousness, thanks for pointing this out, I'd've missed it otherwise.
posted by nevercalm at 7:10 AM on April 20, 2010

I took guitar lesson in high school from a guy who loved jazz, so while my peers were noodling around with power chords, I was modifying diminished chords into half diminished. I'd get the tabs from Guitar World and couldn't figure out what the hell a "C5" chord was - and when I looked it up, it just didn't make any sense to me. Why would you use two strings when you have all six?
posted by yeti at 7:15 AM on April 20, 2010 [1 favorite]

(Of course, the girls in my class didn't appreciate the many versions of Cm7b5 I had at my disposal as they did covers of Bush.)
posted by yeti at 7:17 AM on April 20, 2010

To which exclusive catagories would you assign them? They were all developments in the history of Western music, invented and perfected by people and groups engaged in the active study of math-based music theory.

Well, polyphony is a type of texture, and a symphony is basically a form. A symphony can contain polyphonic textures. And I can't really agree with casting the history of western music as a journey from simplicity towards complexity based on composers experimenting with the "latest mathematical theory of music." I mean, after the height of polyphonic music in the Baroque period came the Classical period which was dominated by comparatively-simple homophonic textures. And while some composers were very engaged with music theory in a technical way (Schoenberg being another prominent example), in many (or even most) cases I think the theory came about after the practice, as a means of describing and codifying what had already become convention.

So I'd love to see suggestions as well, really. It'd be fun to read a text that really tackled theory but in maybe more of a contemporary context—use pop music as the grounding for by-example explanations of some of these things instead of expecting someone new to the subject to immediately buy into piles of Bach and so forth.

I don't think you can do much better than Alan W. Pollack's Notes On The Beatles.
posted by ludwig_van at 7:28 AM on April 20, 2010 [7 favorites]

But gamelan is based around percussion instruments, which produce a very different series of overtones from a vibrating string or column of air. It makes sense to me to say that the major scale arises naturally from the overtone series produced by certain types of instruments.

Absolutely, I don't think we disagree. It seems improbable that a lot of our notions of consonance coincide with the overtone series entirely by chance. The fact that the musical materials of gamelan seem to derive from the overtone properties of its instruments is in line with my point that, when circumstances dictate, the human mind is capable of arranging notes related by high-denominator frequency ratios into musically meaningful patterns. If the power of low-order consonances were as overwhelming as it is sometimes made out to be, it would follow that gamelan as a musical system is either immature or just wrong. You see a lot of that in Schoenberg's Harmonielehre, for example. I don't have the book on me right now, but he does his best to explain most every harmonic trope he covers in terms of overtones, and subsequently refers to unspecified foreign musics as imperfect.

I don't think it's assuming too much to say that Western music is a complex as it is (at least classically) because of centuries of experimentation by composers like Bach experimenting with the latest mathematical theory of music.

Sure, I think a two-way dialog between theorists and creators is inevitable in a culture that emphasizes theory, but your example is a perfect example of the sort of intuitive experimentation that I mentioned. Bach wasn't directly experimenting with math, he was probing the acoustic possibilities that well temperament allowed for. If they didn't sound good (i.e., if well temperament did not provide a close-enough approximation to just intonation in any given key), then the Well-tempered Clavier probably wouldn't have been published.

Pop music isn't just popular because of imperialism--like fast food, it's been genetically perfected to hit some very basic needs in human sensory organs.

This is really what I'm not on board with. Pop music, and music in general, is a hugely complex phenomenon. To treat it as if it's deterministic and entirely derivable from acoustical first principles is to ignore the fact that there are a lot of cultural artifacts in music that can't be explained that way. Music that sounds very different from Western pop music can be equally addictive. I have no doubt that all of those musics satisfy some basic rubric that the human brain requires to perceive and interact with a sound as music, but there's a whole lot of nurture piled on top that has very little to do with acoustics.

Plutor: I'd start out reading the Dolmetsch online series of theory articles, and then check out Salzer and Schachter's Harmony & Voice Leading, which is best approached with a little knowledge of basic structures like key already under your belt.
posted by invitapriore at 7:33 AM on April 20, 2010 [3 favorites]

Kattullus: Don't mind me, I'll just be in the basement with a rope and the taters of my dignity.

Hurm.
posted by shakespeherian at 7:38 AM on April 20, 2010

It covers the traditional ground fairly thoroughly with lots of examples from western classical music, but is dry and doesn't try very hard to make things accessible if you aren't already naturally inclined to decoding musical notation and thinking in terms of that. I would not suggest it for anyone who wasn't specifically looking to sort of refresh or expand some existing grasp of traditional western theory.

Yeah, admittedly, that's a problem with Harmony & Voice Leading too. A side benefit of a theory course based on roughly contemporary music is that it would discourage the sort of prescriptive thinking that a lot of people come out of Theory I with.
posted by invitapriore at 7:41 AM on April 20, 2010

I don't think you can do much better than Alan W. Pollack's Notes On The Beatles.

I don't think anyone can do much of anything better than that.
posted by SpiffyRob at 7:57 AM on April 20, 2010

Why would you use two strings when you have all six?

Sometimes, all you need are two, or maybe, just one. Sometimes, you need all six. Sometimes, all you need is love. It all depends on the moment.
posted by belvidere at 8:02 AM on April 20, 2010

I don't think you can do much better than Alan W. Pollack's Notes On The Beatles.

Ooh. Poking into a couple writeups, that looks like a lot of fun, yeah. Bookmarked.

My dream reference/course would cover a lot more ground than the Beatles, in part because as fascinating and varied as they were as songwriters they still only covered so much ground and so I think seeing a greater variety of artists studied together would offer a more complete picture of what has gone on and is going on in applied (intentionally or not) theory, and in part just because I think it might get a bit dry for any but the dedicated Beatle superfan to listen to nothing but. Also, I think there's a lot of value in hearing how two or six very different artists manage to use the same core ideas to different purposes, something that you could only go so far with using just the one band.

But if you had to pick one band to cover a lot of ground with they're definitely a great way to go. Prolific, varied, deeply accessible.

A side benefit of a theory course based on roughly contemporary music is that it would discourage the sort of prescriptive thinking that a lot of people come out of Theory I with.

Yeah, thinking back on both my textbook and the shape of the classes I took, I think what I see as being most usefully different as an approach would be something more willfully descriptivist as a contemporary introduction to the ideas. Show someone what is going on in music they're familiar with or which they will find immediately accessible, and work from there down to the basic theoretical components of the examples. Don't try to lecture someone on first principles before you tell them how to derive a pop song from it; show them what the pop songs are actually doing and then tell them how to think of that in terms of theory.

The Axis of Awesome song is a great funny joke that I think for a lot of people may feel like a "gotcha" moment—ha ha, you lazy songwriters, we caught you! or something like that—but it's actually a really great little example of I think a positive sort of miniature study in theory. Here are a lot of songs that while different from one another in lots of details (melody, harmonic nuances, rhythm, pacing, mood) have this thing in common, this underlying skeleton that the casual listener may never have noticed before. It's a way to talk about that structural similarity and to talk about the power of those other variables to distinguish one composition from another despite it.

So it's funny to see the songs all stacked together and conceive of that structural debt they're all collectively shouldering, but it doesn't have to stop at being funny. It can be educational as well. Framed not as a gotcha but as an exciting proof-in-practice, it makes a great way to start a conversation about how there's this whole school of thought lurking underneath the seemingly miles-from-academic, too-cool-for-school world of pop/rock music. And I think my desire to turn that conversation around a little was really why I left that askme comment in the first place; I think this stuff is wonderfully fun and exciting, and I hate to see it misunderstood and dismissed.
posted by cortex (staff) at 8:09 AM on April 20, 2010 [4 favorites]

Q: Why would you use two strings when you all six?
A: Seasick Steve.
posted by Kskomsvold at 8:14 AM on April 20, 2010

There's tension between the two of them because E's overtones aren't the same as A, but transitioning from E to A resolves it and sounds pleasing.

Everything until this sentence sounded like science. Please define "tension" and especially "resolve". What does it mean to "resolve" a sine wave?
posted by DU at 8:22 AM on April 20 [+] [!]

Self link to the rescue!
posted by Jpfed at 8:16 AM on April 20, 2010 [2 favorites]

Everything until this sentence sounded like science. Please define "tension" and especially "resolve". What does it mean to "resolve" a sine wave?

Songs that are based around a tonic condition your brain to expect certain frequencies (ie, AC#E in the case of a-major). When you play The E major chord (E, G#, B), the chord sounds good on it's own, and re-inforces the dominant E overtone of A, but the G# and B overtones clash somewhat with the overtones you hear in memory. That's what causes the tension, which is resolved by playing the tonic again.

It's psychological tension, not physical tension.
posted by empath at 8:46 AM on April 20, 2010

DU: "Everything until this sentence sounded like science. Please define "tension" and especially "resolve". What does it mean to "resolve" a sine wave?"

It is folk psychology. Also, technically, sine waves are infinite in duration, so they are only approximate sine waves at best if you can talk about switching from one to another.
posted by idiopath at 8:50 AM on April 20, 2010

So I'm still up for that.
posted by tellurian at 9:08 AM on April 20, 2010

Yeah, I personally feel like the idea of tension and resolution is kind of complicated and gets a little handwavey when you try and get away from examples (where you can really hear and feel what's going on) and down to some perfect abstract model.

One very simplified way to look at the idea of tension and resolution is to think of the root chord of a key, the tonic chord, as being a set of markers in the sonic landscape. You have your three notes in a major chord, say C and E and G as the root and third and fifth of a C Major chord.

So you open up a song by laying down a C chord, and those markers are firmly planted, and psychoacoustically we just instinctively make ourselves comfortable there as listeners. That's home base, we can come back there and everything feels okay.

And all three of those markers are important and have some function of making us feel comfortable and on familiar ground, but none of them is more important than the root. That C note is the biggie. The E and the G are playing second fiddle (or, really, third and second fiddle respectively, the G is a bit more important than the E for making us feel comfy).

And so everything else that happens in a song can be seen as a series of steps away from and back toward these familiar markers. How we react to any given harmonic change—any movement from one chord to another—can be seen as having a lot to do with how movement to and from each of those markers is happening. And the most fundamental effect there is what happens when we move away from that root marker. If the root note sudden disappears, nothing is going to feel entirely stable until we get back to it. Movement away: tension. Return to the marker: resolution.

That's a very simplified example, and in practice it gets complicated pretty quickly—if a song can be seen as the story of how we move away from and then back to the three markers of the tonic chord and particularly away from and back too that root marker, then harmonically complex songs can be seen almost as a series of little stories within stories, a series of moves away from and back to new temporary root markers, or of the establishing of some new root marker as our permanent home base and leaving the old one behind.
posted by cortex (staff) at 9:23 AM on April 20, 2010 [1 favorite]

So it's funny to see the songs all stacked together and conceive of that structural debt they're all collectively shouldering, but it doesn't have to stop at being funny. It can be educational as well. Framed not as a gotcha but as an exciting proof-in-practice, it makes a great way to start a conversation about how there's this whole school of thought lurking underneath the seemingly miles-from-academic, too-cool-for-school world of pop/rock music. And I think my desire to turn that conversation around a little was really why I left that askme comment in the first place; I think this stuff is wonderfully fun and exciting, and I hate to see it misunderstood and dismissed.

this. THIS is why cortex (and his ilk) should be the ones to write... shit, I dunno "music theory for Dummies?" or be Theory 101 profs. Or just be dads with musically inclined kids.

At age 3 I had already begun doing stuff like picking out the progression for one of the Brandenburg Concerti, and making mashups with it and some of the melody from "Here Comes The Sun", because I really liked the pretty sounds it made on dad's piano. But any desire I had to really play got pretty much tossed aside through his over-zealous formal teaching practices.

see, my dad (bless his heart) was a music major in college at the time, studying to be a composer. He's also one of those people who can pick up any instrument and play it by ear. At the first sign of musicality on my part, he took the Toddler lfr and completely confused and bored me by attempting to teach me "formal" piano lessons and talking about major and minor chords and tonics and harmonics and all that shit. Seriously, preschoolers don't care about that stuff (yet), they just want to make pretty sounds! And my "banging on the piano" as my parents called it, really wasn't as much dissonantly banging around, I was (trying to, anyway) learn how to play stuff I heard on the radio / record player, and I was doing a damn decent job of it (for a toddler) until formal teaching got in the way, and they forced me to sit down and endlessly play scales and "twinkle twinkle little star" Seriously, fuck that noise, that song sucked when I was three, and it sucks to this day.

I gave up piano around six because I just didn't "get it" the way dad was trying to teach me. I am still a good singer with excellent relative pitch to this day, but I somehow never shook that initial turnoff that "instruments are hard", and seriously, fuck playing scales and nursery rhymes. If your kid wants to try for Bach and the Beatles, it's your job as a music teacher to show them (in a simple way) how that's done. Accessibly, like those Aussie comedians were doing for the crowd.

sigh. cortex, I just really wish you were my dad, I guess. Not in a creepy way, besides which it's physically impossible because I'm like, ten years older than you. But whatever.
posted by lonefrontranger at 9:24 AM on April 20, 2010 [2 favorites]

Leonard Bernstein's lectures at Harvard are certainly illuminating, if you are willing to invest nine hours or so of viewing. He has a pretty adamant agenda, employing Chomskyian linguistic theory to music. But he is a great lecturer and starts at the foundation of Western music. You can easily find the DVD set online, and more intrepid folks could probably find them somewhere else for significantly less than $100. A few clips available on YouTube.
posted by barrett caulk at 9:53 AM on April 20, 2010

As I said in that thread just now: this book by Victor Zuckerkandl introduced me to music theory but also went deeper into the Why of music's inner workings than any other textbook probably ever.

It also convinced me that music is an innate sense in human beings, and that Western Music's historical development has been characterized by a methodical exploration of that innate sense--not to say other cultures haven't done this also, just without the method. I could go on but I'd end up sounding like a weird Mike Allred comic.
posted by Potomac Avenue at 10:22 AM on April 20, 2010

Metafilter: sigh. cortex, I just really wish you were my dad
posted by haveanicesummer at 10:48 AM on April 20, 2010

"Everything until this sentence sounded like science. Please define "tension" and especially "resolve". What does it mean to "resolve" a sine wave?"

Well, there are a couple of aspects to it, but I don't think this question is so unapproachable. In one sense, "tension" means "dissonance" and when we "resolve" we return to "consonance." Consonance and dissonance can be described mathematically, as detailed in the tuning and timbre essay I linked to above.

However, this is only a basic answer, because we're talking about intervals, or the interaction of two pitches. Two pitches with a 2:1 frequency ratio (i.e. an octave apart) will have a maximum amount of consonance, while two pitches that differ from each other by just a few Hz (i.e. two strings that are slightly out of tune) will have a maximum amount of dissonance.

But a C major and a G major chord have the exact same structure, so we can't say that a G major chord is more "dissonant" than a C major. And in practice, if all I play is C and G, I haven't truly established a tonality or key center and so the sense of tension and resolution will be ambiguous. Some people might hear G as the key center and perceive a IV I progression, and others might hear C as the key center and perceive a I V progression.

However, if I make the G into a G7 chord, the situation changes. The G7 contains a tritone interval between the pitches B and F, or the 3rd and 7th of the chord. That tritone makes the G7 chord more dissonant, in the mathematical sense, than the C chord, and western composers have traditionally chosen to resolve that dissonant tritone into a more consonant major third.

Here we start to stray into the subjective, learned aspect of consonance and dissonance. In this sense, dissonance is merely something that is subjectively perceived to be "unresolved." For example, in the classical period, a major 7th chord would be considered a dissonance. A classical composer would not end a piece on a major 7th chord because it would sound (to them) unfinished -- the 7th would be perceived as a dissonance that required resolution to the octave. This is also why some classical pieces in minor keys conclude with a major chord (aka the Picardy Third). To them, ending with a minor chord was not an acceptably stable resolution. However, to our modern ears, minor chords, major 7ths, and plenty of others are heard as perfectly acceptable. I recall a quote from Arnold Schoenberg that his 12-tone system was "freeing the dissonance," meaning that all interactions between pitches became acceptable. Nothing required a particular type of resolution, because all 12 pitches were equal -- there was no longer a hierarchy where one pitch (the key center) was the basis of the work.

And all three of those markers are important and have some function of making us feel comfortable and on familiar ground, but none of them is more important than the root. That C note is the biggie. The E and the G are playing second fiddle (or, really, third and second fiddle respectively, the G is a bit more important than the E for making us feel comfy).

I would nitpick this -- the third of the chord is much more important than the fifth. The fifth is often left out completely when voicing some types of chords because it doesn't provide any information about the chord quality -- that is, C major, C minor, Cmaj7, Cm7, C7, C9, etc., all have the same 5th, but they have different 3rds and 7ths. 3rds and 7ths are known as "guide tones" in jazz because they provide the "flavor" of the chord.
posted by ludwig_van at 11:13 AM on April 20, 2010 [1 favorite]

You're not going to make us part write Bach chorales now, are you?
posted by The World Famous at 11:21 AM on April 20, 2010

I would nitpick this -- the third of the chord is much more important than the fifth.

Fair enough, though I think it's also not as simple as saying that the third is more important than the fifth. I'm having trouble thinking of how to articulate what I meant there, but in any case I'll argue it might make more sense to say they're important for different reasons.

The fifth is often left out completely when voicing some types of chords because it doesn't provide any information about the chord quality

True; I think what I'm wanting to argue here is that it's important even in its literal omission from some voicings, because it is implied. That, in fact, it can be omitted only because it's so fundamental to our sense of the tonic that we can get away with letting it be assumed to be there unless that assumption is challenged.

So while the third and the seventh degrees do a great deal of tonal work in shaping how the current harmonic state feels, the tonic and the (at times implied) fifth are doing the work of holding down the fort (or abandoning it and thereby creating tension).
posted by cortex (staff) at 11:43 AM on April 20, 2010

I would nitpick this -- the third of the chord is much more important than the fifth. The fifth is often left out completely when voicing some types of chords because it doesn't provide any information about the chord quality -- that is, C major, C minor, Cmaj7, Cm7, C7, C9, etc., all have the same 5th, but they have different 3rds and 7ths. 3rds and 7ths are known as "guide tones" in jazz because they provide the "flavor" of the chord.

Well obviously I-V isn't enough. All of the interesting stuff happens in the other notes.
posted by empath at 12:17 PM on April 20, 2010

I think what I'm wanting to argue here is that it's important even in its literal omission from some voicings, because it is implied. That, in fact, it can be omitted only because it's so fundamental to our sense of the tonic that we can get away with letting it be assumed to be there unless that assumption is challenged.

Well, I guess I could rephrase and say my point is about necessity rather than importance. A perfect fifth is not a necessary chord tone, in that a C7 chord can be clearly implied by the notes C, E, and Bb. Sometimes even the root can be missing and the chord will still serve its harmonic function. This is why tritone substitutions are effective -- dominant chords whose roots are separated by a tritone will have the same 3rd and 7th, so they can stand in for one another. However, if you have a chord with a 5th but without a 7th or a 3rd, the chord is ambiguous.

This isn't to say that the sound of the open 5th, as in power chords, can't be used as an effective compositional device. But if we're talking about classical or jazz harmony, perfect 5ths don't carry much harmonic information.

Well obviously I-V isn't enough. All of the interesting stuff happens in the other notes.

Er, not sure what you mean there empath. Typically Roman numerals refer to chords and arabic numerals refer to individual scale degrees. I was talking about the latter.
posted by ludwig_van at 2:25 PM on April 20, 2010

This is all interesting discussion, guys. Hat's off to all of you for putting effort into it. When my daughter was playing violin in high school and learning scales, she couldn't figure out the chords for some Beatles tune she was trying to work out. It puzzled me as well, until I remembered modes from my own high school music theory class. Turned out the piece was based on a Phrygian cadence.

I was sort of stunned to learn from my daughter that theory was no longer taught in High School at all, but I'm gratified to see that a lot of you kids learned it all on your own somehow. I had the great advantage of an extraordinary high school music teacher.
posted by pjern at 5:16 PM on April 20, 2010

I learned it from trying to learn how to use a synthesizer, which is probably why I'm focused on the math aspect of it.
posted by empath at 5:29 PM on April 20, 2010

You're not going to make us part write Bach chorales now, are you?

When Bach comes chorale at you,
Drop it like it's prog
Drop it like it's prog
posted by Fiasco da Gama at 5:43 PM on April 20, 2010

So I'd love to see suggestions as well, really. It'd be fun to read a text that really tackled theory but in maybe more of a contemporary context—use pop music as the grounding for by-example explanations of some of these things instead of expecting someone new to the subject to immediately buy into piles of Bach and so forth.

A couple of people mentioned it on the other threads, but I'll suggest Daniel Levitin's This Is Your Brain On Music. He used to be a rock producer/engineer, then went to grad school in neuroscience and is now a professor at McGill. It fits the bill perfectly.
posted by asterix at 6:57 PM on April 20, 2010

I just came in here to say: holy crap, cortex (and anyone into music theory at all), if you haven't read Pollock on the Beatles, block out a weekend. That shit will be right up your alley.
posted by danb at 7:18 PM on April 20, 2010

I enjoyed the original comment, but this is some great music geekery.
posted by archagon at 9:19 PM on April 20, 2010

I was sort of stunned to learn from my daughter that theory was no longer taught in High School at all, but I'm gratified to see that a lot of you kids learned it all on your own somehow.

Depends on the school, like most every other "this never happens in ____" comment. I'm not sure when your daughter was in high school/where she went, but my high school taught theory as part of an IB music class. There's also the AP Music Theory exam...not the most popular exam, I guess, but a fair number of people took it every year. This was 2-3 years ago, and they obviously still have the exams around.

I've been playing music for a decent amount of time and took a decent amount of theory, but never really threw myself into it, so this is fascinating.
posted by kro at 4:50 AM on April 21, 2010

I just came in here to say: holy crap, cortex (and anyone into music theory at all), if you haven't read Pollock on the Beatles, block out a weekend. That shit will be right up your alley.

Yeah, I didn't want to be too Hipster Light Bulb Joke about this* but now that danb has broken the dam, READ IT NOW CORTEX.

*Q: How many hipsters does it take to change a lightbulb?
A: YOU DON'T KNOW??!?!?!
posted by SpiffyRob at 6:56 AM on April 21, 2010

At this moment, that AsklMe answer and this resultant MeTa thread are my favorite things ever, except for my fiancee and my dog. Thank you all for making my day!
posted by trip and a half at 11:04 AM on April 21, 2010