Toward the Musical Frontier

Why bother with music theory? Do rules constrain your writing?

Well, I'll tell you what I believe. Rules are rules if you treat them as rules. I believe that the perception of music theory as a set of rules comes out of two things: bad books, and bad lessons. Theory is not memorizing cold, heartless patterns. That's practice, schoolmaster-style. Theory is just a conscious knowledge of the things that sound inherently good. You don't need it to write great songs. You probably don't always want to use it. But I've found it to be great in three circumstances.

What if you're stuck and uninspired but want to write? What if you hear something you love so much that you want to bend it and make it your own—why not name it, remember it, then tweak and own it? And finally, what if you have a great song and nothing you try takes it forward? Theory can help with all of that. Your fingers and musical mind usually work better when they're a mainline to an unfiltered emotion. Try to think about what you're doing, and you might squelch that magic. So why not treat theory as a tool, a seperate thing? Think of it as a set of excavating tools, an archaeologist's pick. Use it to dig out ideas. Use it as a magnifying glass to better understand the things that you like musically.

Then put those tools away, and treat your discoveries as playthings. You do have control of what you pay attention to!

Music theory is fractal, an endless maze. Once you learn a few basic things, you'll see other doors in the distance. If all goes well, you'll want to get to those doors and open them, too. There's no end to the mathematical and spatial relationships you can find once you understand a few basic things.

When I started with theory, I just wanted to get to the point where I had some consciousness of notes that worked, even if I could never be a fast player like my friend, Jason, who could fly around the fretboard. But I didn't want to actually learn anything about theory. I also didn't want to memorize a bunch of garbage scales and the like, and so I bought books that looked like they had some secret principle or shortcut. I don't know what I was looking for! I just knew I wasn't going to pollute my mind with patterns, because I knew it wouldn't show me anything about how or why music worked. And of course, I would have to insane to try to learn anything about real theory. It would be far too complicated. I just wanted the knowledge in me, and I didn't want to work for it.

I'd asked Jason how he knew which notes to play. He told that me had more or less memorized the fretboard and knew about three basic scales. He was able to keep his bearings while improvising by focusing on the sounds and lines he played, while understanding with his ear where he was within whatever scale he was using. ‘Wasn't that restrictive?' I asked him. Not really, he said, because he could also judge more or less how to ‘misreach' to grab a foreign note if he wanted it. Because he knew where the gaps in the scale were—the unplayed notes—and because he had a good ear for tones, he knew which dissonances lay where.

That same spring I'd bought an instructional bass video starring Flea. I remembered the part where he effortlessly hummed the notes he was playing while he played them, and he was dead on each time. That was mastery. I approved of ear-training, because although I could read printed sheet music, I was essentially an ear-player. I thought it was more honorable and more impressive, more flexible, and cooler. Obviously, Flea approved of the ear too. And Jason. They were both in some weird place where they could understand how a certain reach could produce a certain note. They had perfect relative pitch.

I'd taken piano lessons for six years as a kid. I could read music, but I didn't understand the subarchitecture of it. Now I had the idea that I was going to learn the names of those jumps, those intervals. That would be the key, the shortcut. It was a part of music that my teacher had never mentioned, those six years. No talk of intervals, no talk of why chords were what they were, nothing more than the idea that a minor chord (as opposed to a major) had the middle note lowered a half step.

I'd recently "become attached to" my first interval, that spring. The minor third interval was the one that made Nirvana songs sound like Nirvana songs. I'd seen it mentioned in a book somewhere. A lot of Nirvana progressions would rock from one stable chord up to one that was based on a note exactly three frets higher. That was the minor third jump. It sounded tense for a moment, then it would resolve back to the first chord.

What other intervals were there? I'd never bothered to think of music in these terms. I went looking in books for that specific piece of information, and quickly encountered something I didn't particularly want to encounter again: the major scale. The intervals took thier names from this scale. Fine. Whatever. I'll learn the names, even though I can hum the scale in my sleep.

The major scale was made of these intervals: unison, major second, major third, perfect fourth, perfect fifth, major sixth, major seventh, and octave. I looked at the C major scale on the piano, since it was the easiest place to start: all of the white keys from middle C to the next to C. This was the scale, and if you took each note in relation to the middle C, you'd see that they were numbered according to thier place within the scale, with an additional prefix.

That was easy. Now I knew the interval names in a major scale. The key of C on piano is the easiest because all of the black keys are non-scale notes. They all had intervallic names too—but those intervals didn't belong in the major scale.

It was easy to think of the black-key intervals as deviations from the "normal" intervals of the major scale. Weird younger brothers. The black note right below the white major sixth was a minor sixth, a young punk. He wasn't in the major scale. The black note right below the white major third was a minor third. He was one of the black sheep in the family. In one sense, there were no minor intervals in the major scale: all the interval names were either major or perfect. A stumbling block to grasping this was that there were no black keys between the major third and the perfect fourth, or between the major seventh and the octave—and yet these jumps in themselves were not "skips" (they were not whole steps). That is, in relation to themselves, they were minor intervals: technically to move from the major third to the perfect fourth, you were moving forward by a minor second interval; it just wasn't viewed that way when speaking about a key, because when speaking about a key you were thinking in relation to the starting tone or root note. It was just a bit of oddness I'd have to keep in mind. The scale moved from one note to the next by way of either major second intervals or minor second intervals (whole steps or half steps). In relation to the root note of the scale, however, you could speak about these higher-numbered intervals.

The scale was made this way: whole step, whole, half, whole, whole, whole, half.

I wasn't going to get too into it on guitar just yet, since there were no black keys to use as markers. But I could see how you would do it. (To this day I only formally know the first position major scale pattern on guitar—I haven't bothered to memorize the others yet. I can find others by ear but I lose the info—it refuses to coalesce into a pattern I can pull out later. My head can only hold like, a few patterns? Good!)

In any case, there were the intervals, and, when you jumped to them from the first note of the scale, (in this case, from C) they all had a characteristic sound which you could practice and learn to recognize. The minor third was my first "marker." I knew its sound. I also knew the minor fifth (which usually goes by the name augmented fourth or ‘tritone')because it was, to my ears, the most evocative possible interval when played against the root note of the scale. It appears all the time in indian sitar music, and was once banned by the medieval church for being too discordant. Only in some settings, I guess. In eastern music it has a otherworldly sound equal to none. And then there was the beloved minor sixth, more frequently known as the augmented fifth. That's another mysterious interval. The Rivendell theme in Lord of the Rings is haunting because the riff hangs on that interval and the chord progression uses chords based on the tonic note (step one of the major scale) and the minor sixth (not part of the major scale). Notice that these three intervals don't fall within the major scale. So what. They're great!

So, what to do with this information? Through reading lots of books, I came to see that even though had been suspicious of it in the past, many useful chord changes came straight out of the major scale. Up till this point I was always reaching for the oddball chords because I wanted my music to sound unique, weird, different. You always heard that the I, IV, and V chords were the foundation of western music. That they were really important. Bah, I'd said. I'm not trying to play blues, I hate all that early New York punk, why should I bother? I'll just keep hammering on this set of nine horrible chords I found while I was drunk. They have to fit together somehow!

Then I found out about the musical principles of tension and resolution. I'd thought I knew what they meant, but I hadn't thought about it enough. Tension, in music, or art, or film, or writing, doesn't automatically equal high-adrenaline and danger and weirdness, although that is often an effect. What is it? At the most basic level, tension is a lack of resolution. Waiting for something expected that hasn't yet come. If music was (among other things) a journey along a path of chords, then you could create tension by creating an interesting path among even very familiar stones. And home base was the "one chord." (I) The tonic.

The ear experiences the one chord—whether you're working in a minor key or a major key or a modal key—as the "resting place." Things are resolved when your progression arrives there. It turns out that, despite the fact that the IV and V chords are burned into our minds at this late day in history, they're still extremely useful. V has a strong tendency to resolve down to I. It acts as a pointer. You can use this fact, and deliver the payload by heading to I, or trick the listener out by going to V and then dashing off to somewhere new. Play these chords: C major, F major, then G major. Hold on G. What do you feel? Where is it trying to go? Try lots of different chords, but the true resolution is at I. That's because the notes of G major—G, B, and D, have a weird relation to C. More about this in a minute. (By the way, add the note ‘F' to that g chord, to make a G7 and increase the pull.)

Now what's all this talk about roman numerals?

Roman numerals are used by musicians to indicate the scale step on which the chord is based. Understanding this requires a quick lesson on just where chords come from.

First, in western music, the major scale is important as the foundation for just about everything. You should know the step formula to make one, and the names of the intervals within it.

whole, whole, half, whole, whole, whole, half.

Every subsequent fret or key is called a half step. Every time you skip a note, call that a whole. Trace out this pattern, and you get a major scale.

The easiest way to quickly understand what "key" is (and to learn everything in this article as fast as possible) is to use a keyboard. Playing the white keys from middle C to the next C gives you the C major scale—a major scale in the key of C. If you count the intervals, you'll see that the scale follows that whole step/half step pattern which is the unique identity of the major scale.

A jaunt over to the key of D will help illustrate the definition of "key." Let's tranpose that step pattern up two half-steps to D. Now the new starting note will be D, and, using the step formula from this new starting note, you'll find that you must add two black keys—F# and C#. That's how you preserve the whole/half step pattern. Is there a reason you add two sharps? Yes, but it has to do with something called the circle of fifths, which is a very useful tool, but one which will add needless confusion at this point. (As a general rule, though, I think it's important to not settle for this sort of answer. Always stick with "why." If you lose track of "why" you'll miss the point of all of this, which is to reveal that the deep structure of theory is perfectly logical and, because it is, can quickly become intuitive and automatic. If you keep asking why, you'll find that it all has a reason.)

Okay, so. The thing to take from this is that a major scale is defined by a set of specific intervals, and that it persists throughout the keys. Only the note names change. The architecture of the scale is constant.

But what is a "key?" A key is a set of chords that are yanked directly out of the raw materials of a particular scale. Major scales create major keys. Minor scales yield minor keys. Modal scales, like the phyrgian mode, can yield a phrygian key. A result of this simplicity is more simplicity: all major keys consist of the same seven chords in the same order. This article will focus on triads, and exclude the seventh notes. It's easier, at first.

Major, minor, minor, major, major, minor, diminished. That's the chord structure of a major key.

Look at a piano keyboard. See the white notes between C and C. Put a finger on C, skip a white key, put a finger on E, skip a white key, put a finger on G. That chord is C major, the first chord in the key of C. Now do the same exact thing, but starting on the second note of the scale, D. You get a chord made up of D, F, and A. The D minor chord. Keep going up the scale in this way. You're treating each note of the scale as the root of a new chord. You're building the new chord out of the remaining scale steps, eventually reaching into the next octave, using a "skip every other one" formula. Every note in every chord is taken from the scale. This process yeilds all seven chords in the key.

Take this time here to note the difference between major and minor chords. A major chord's middle note lies four half-steps away from the chord's root note. A minor chord's middle note lies only three half-steps away. It's the difference between happy and sad.

The principles above hold true for all keys. Sharps enter the picture, of course, as you shift the scale to keys which must use sharps to maintain thier internal structure. But sharps are not important now. "Sharp" is just a word. The key skill here is to learn to recognize the major scale as an eternal pattern. Focus on the pattern, and move it around, recognizing that you're moving a constant shape. On the guitar, you ARE moving a shape. Piano forces you to see the why of it. Give it a try. Extract the chords for the key of D major from the D major scale. Move along the scale, making a new chord on each note. When forming the chord, first visualize the scale steps that lie ahead of you still. Choose every other note.

Here's the roman numeral designation system: I, ii, iii, IV, V, vi, vii dim

They're the scale steps of a major scale, coded in upper and lower case to also show whether the chord built on that particular step will be major or minor.

Not everyone does it this way—a lot of times all of the roman numerals will be shown in uppercase. You're just supposed to know which chords are minor. This system is just how I began to overlay the different types of information—the seven steps of the scale, and the chords that you form on each step. Notice that I, IV, and V jump out. The archetypal progression is the only possible progression in a major key that uses all major chords. That's why it's so bright and acessible and happy.

If someone says "V, ii, iii, I in the key of C," you can now (with some practice) know that they mean "the chord starting on scale note 5, which is always a major chord; the chord starting on note 2, always a minor; the chord starting with note 3, always a minor; and back home to the one major chord."

Now, backtracking for a moment, why did that G7 chord have such a strong pull to the I chord? Look at the notes in the chord: G, B, D, and F. The B is just a half step away from the tonic. That's one of the most unstable and precarious situations—it's just a half step away from its "home," and is poised to "rise there." The D is smack between C and E—and E would be the third note of the tonic chord. It experiences two pulls. F is a half step from E, the middle note of the I chord—it wants to fall there or rise to G, the fifth note of the I chord. And G is by definition the "dominant" note of the scale, a straight arrow back to I. All in all, that chord has lots of internal biases, and feels strongly compelled to come to rest back at I.

Hopefully, if you've digested this info and played around with learning the sounds of the thirteen individual intervals in an octave, you should be ready to take your ear-recognition skills to a new level. Put on a song, preferably a slow one. As you listen to the chords go by, try to do what Flea does. Listen for the bass note. The note at the very bottom. You can listen for the bass guitar note, or try to pick out the lowest tone in the guitar chords. Ignore the chord, and just watch this one bass note jump around on the keyboard intervals in your head, which you've already learned. For me, those minor thirds still jump out. Steps of a major second or minor second are very easy. I visualize everything in the key of C on a piano keyboard. Key doesn't matter. Just the interrelationships do. (Some of the intervals may eventually come to trigger an automatic kinesthetic response...you'll hear minor thirds and feel yourself perform that very reach on your mind-guitar).

As you do all of this, recognize whether the chord you're hearing is major or minor. Bright or downtrodden?

Sometimes what you hear will gel completely with "the way it's supposed to be"...with "the legal chords." That ii chord will be minor. That IV chord will be major. You'll feel oriented! You will know that your favorite artists are using the largely unknown language of theory to communicate emotions, whether or not they know that language themselves! This will happen often enough that you'll find a certain confidence in the well-trodden land of traditional harmony. Lots of other people are using it. You'll hear it all the time.

Other times while listening, you'll be wrong and you won't know why. If everything seems to check out, but you're still wrong, you're probably hearing an "inversion"—someone is playing a major chord, for instance, but using a bass note that's something other than the tonic. These just take practice. Find the bass notes and explore the keyboard for the other notes that fit what you're hearing, and then you can see what you're hearing, identify the notes, and deduce the name of the chord, even if its notes are disordered.

Sometimes you'll put on a rule-breaking band. Something by Radiohead, for instance. Maybe the song Creep. You'll hear them hit the IV and drop it down to iv, a chord which contains one note that's not in-key but which sounds so very good. You know that Jon, having attended the guitar institute, knows exactly what he's doing. He's put a weird but highly logical change in a very basic song and stepped though one of those cool forbidden doors. There are lots more to find! It's finding the right paths to them, in your progression, that makes all the difference.

So, listen to music. Trace the tonic paths at the bottom of chords. Determine the basic chord types. Think of the roman numeral system and classify chords as average joes or outlaw punks. Pay attention to the journey of the bass note, how it journeys away from the I chord and how it returns. Notice the flaws in this article and then seek an answer somewhere else—why don't you ever hear the vii dim chord? Why do you always hear VII instead, even though that's not in key? What's a bIII major chord doing in all these songs? That E flat doesn't belong in the key of C major!

Once you've done all this, then go learn all about minor key harmony. Here's something to whet the appetite...

Every minor key has the exact same chords, notes, and chord structure of the major key that lies three half steps above it. Just in a different order.