Hi. I'm back to pester you into grabbing that guitar for a while and giving it a twang or two. There's nothing better for the soul than to listen to a simple chord ringing out of a well tuned guitar.

The Nature of Music

Whatever it is about music that makes so many us sit up and take notice and some, like you, want to create it - it's not man-made. It comes from nature, from sound waves blending together in a mathematical way. I know this for sure because my cat Buster will sleep happily away for hours while I play in tune, but as soon as I start playing discordantly, he wakes up and leaves the room; and what would Buster know about intervals and the diatonic scale?

Harmonics are a neat way of hearing and conceptualizing the physics of music. Grab your guitar and very lightly place your fingertip on any string directly above the twelfth fret wire. That point divides the string exactly in two. Now, pluck the string as you would normally, but at the very instant you do, remove your fingertip from the string. You should hear a very pure ringing note, higher in pitch than the string normally sounds. Try it a few times if it doesn't work right away. What you're trying to achieve is to get both halves of the string vibrating simultaneously. The combined waves emit the pure ringing.

The twelfth divides the string exactly in half and produces a note one octave above the original open string.

What about other fractions?

Well, you can play a harmonic at the 7th fret too. That point is exactly one third the way along the string. When you get it ringing, you get a note that's one octave above the V of the string's note. That's one third blending with the other two.

The 5th fret produces another octave of the string note because quarters are half of halves, and halves produce octaves. So that's one quarter blending with the other three.

The 9th fret, where there's a dot, also produces a harmonic. This is a point two fifths along the string from the nut. When you play a harmonic here, it's a note an octave above the major third of the open string note. That's two fifths blending with the other three.

If you move your fingertip away from these points even by an eight of an inch, no ringing, no harmonic.

This is all irrelevant to the playing of the guitar by the way, so you needn't remember the details, and there's a lot more to it than I have touched on, but the point I'm trying to make is the Music is a system that is ruled by mathematical relationships. What I've just written about above shows that the major scale, that do re mi thing, comes from simple fractions -- halves, thirds, quarters, fifths -- of vibrating strings. The guitar is just an elaborate contraption designed to amplify the sounds of those vibrating strings, and changed their lengths via the fretboard. There again: look at the ever diminishing distance between frets as you go up the neck to see the mathematics involved.

Once you realize that there is a structure to music, set up by the physics, (I imagine it as a kind of three dimensional grid), then it becomes easier to see how to navigate it.

Here is a condensed view:

The laws of physics and mathematics generate the major scale, which subdivides into the chromatic scale -- all 12 notes. The Major scale generates 7 chords (3 major, 3 minor, one diminished). The 12 note chromatic scale allows for 12 starting notes for the major scale, thus allowing for 12 sets of 7 chords.

Once again, don't let any of this scare you. It should be making you feel comfortable that, even though it seems non sensical and complex, it's all built on a solid base, one that is constant, logical and reliable.

The easiest way to get to the point where you can get a mental image of all this and actually hear the mathematical relationships is to concentrate your efforts on learning chords. Chords are boss when it comes to music because they crystalize the moment. If you know the chord and its context, you know the scale, you know the mode, you know the rules for harmony, you know the key, you know it all.

To simplify your thinking, imagine all chords as being modified major chords (I -III-V -- One - Three - Five). By that I mean: minors are majors with a flat third; major 7ths are majors with a 7 added; sus4 are majors with a 4 replacing the 3; augmented's raise the five -- all chords can be compared to the plain old majors for analysis. You can do that just by looking at the chord shapes on the fretboard. When you play a D to a Dsus4 for example, that note that gets inserted IS the 4th of the scale.

It doesn't take long to start hearing the context (the mathematics). Country Music is a great example of a musical genre that favors certain chord progressions. Most tunes are based around 3 chords (the three majors), and any tunes that don't just ain't country. If any others are allowed, it's the Six Chord, the relative minor. Even with this restriction however, countless tunes are written and are consumed by country fans. You can imagine how easy it is, once you can hear it, to define the chords of a country tune. What you make of them and how well you play along is another matter, of course.

If you are at a stage in your playing when you feel you're stuck in a rut, wondering what the next step is, wondering how some players can invent as they go, then drop in to visit PlaneTalk - The Truly Totally Different Guitar Instruction Book, http://planetalk.thatllteachyou.com, where you can find out more about my method of keeping track of it all, my way of instantly seeing the mathematical context on the fretboard. What you can see, you can play if you can get your fingers there, and that's just a matter of practice. I describe the book as being the exposition of the TRICK to playing guitar, and from the feedback I receive, so do others. The method is available online too, and I've just set up the PlaneTalkers Forum for those who have bought the book and/or video. Already 220 players have joined and we're having a good time discussing music and the PlaneTalk technique.

If you want to read more articles like this, go to http://articles.thatllteachyou.com. There are over 60 archived there.

If you're interested in my speciality, slide in dropped D, go to http://planetalk.thatllteachyou.com and find the Lessons page. There are a dozen or so free QuickTime Movie lessons with TAB there.

All the best -- now get them strings a vibratin' and them fingers loosened up and callused. I'll be back.

Kirk

A local archive of Kirk's columns is located here.