Guitar Harmonics and Math/Physics

http://en.wikipedia.org/wiki/Guitar_harmonics

Found this nice layout of the harmonics on a guitar fretboard, and noticed it is identical to the wave-forms I've been using to try to work on the Goldbach Conjecture and other problems with prime numbers/divisibility.

I find it amazing that the physical phenomenon that we hear as music is essentially just waves of tones/frequencies that directly relate to the divisibility of integers.  I've always liked the quote:  "Music is the pleasure the human mind experiences from counting without being aware that it is counting." (Gottfried Leibniz).  With this layout of the harmonics, you can easily see the symmetry that arises when multiple waves are overlapped. 
Why does that matter?  Well, I guess it depends on your perspective of our universe... is it infinitely divisible (yielding smaller and smaller particles as you get smaller and smaller, never reaching a "smallest" particle) or is the universe finite (if so there would have to be some "smallest" particle, from which all other matter is created)? 

If finite, then each larger and large particle could possibly be defined in terms of these "smallest" particles.  However, there could be some order to the crazy quantum mess that we currently understand to be random.  Look under the red domes in the picture above... when all of the waves are overlapped, and their wave-lengths are not coinciding, it looks pretty chaotic, but once you zoom out, you can see that the apparent chaos is actually just a small portion of a fully symmetric structure.

If the universe is truly infinite, and infinitely divisible, then questions of continuity and differentiability come into play.  Most of our physics is contingent upon equations involving limits and infinite sums, which would require this infinite divisibility.  But we can't ever really know at the smallest or largest scales how "accurate" our math/science is. 

I believe the same symmetries that exist in music are also present in mathematics (discrete and continuous), and that it is those symmetries which we have detected as reproducible patterns in our physical world (yielding functions and formulas based on our observations).  We may not have the exact formulas or functions to yield perfectly accurate results, but at the same rate, our approximations of objects like spheres and circles would never come close to the "real" shape, which can't exist in our universe as we understand it - but even though the shape can't physically exist, we can figure out an exact formula for that shape to base our approximations on. 

It is the same with the laws of physics.  Our formulas and functions are just trying to explain the perfect shape that we see should be there, but that we may never acheive due to our finite limitations.

I wonder if Music Theory has ever been directly applied to quantum mechanics and particle physics?  Sounds like a blog for another day...  will do some research and see!

seeing the chords on top of scale patterns

The image below is showing the major scale pattern in the key of G.
If you want to try to play the 7 possible triads within G major, this chart makes it easy to see which chords fit in where!


The I, IV, and V chords are all major, and the II, III, and VI chords are minor.  The VII chord is a minor, but with a flatted fifth - since F# minor would have a C# in it.  G major doesn't have C# at all, so the chord gets a diminished kind of sound.

So far, looking at the chords this way on top of the major scale has really helped to pick out the arpeggios when I'm in a scale.  The chart helps to see where to aim in the scale when you're in a major key that matches a chord progression (for example, if the song has a part with the chord pattern: G D Am C, you could focus your lead guitar's soloing to the I, V, II, and IV notes shown in the image above).

These patterns aren't just restricted to the key of G - you can slide this left or right by any amount of frets, and the patterns remain the same - it is just the key of the major scale that changes. 

Many songs don't stay in the same key signature for long, but knowing where to play when the key signature is well-defined is critical if you want to clean up your soloing and improvisation while jamming.

Enjoy!

TIPS: 

- Try to fill in the names of the notes on the above image - each chord is only 3 notes, repeated over and over again in the patterns.  By doing this, you'll be learning the next level of detail (which note is which, and where octaves of each note can be found) - and once you are comfortable with that, playing scales along with any chord progression can be mastered!

- Practice these same patterns in key signatures other than G major.  Just slide the whole major scale pattern to match the fret you wish to be your root note - everything else stays the same!

Easy Octaves on Guitar

In standard tuning, there are easy locations to jump up an octave for whatever you wish to play.

This picture shows where notes can jump up an octave:

The red/blue dots represent octaves of each other as you move left to right going up in pitch.  So for example, 2nd fret on low E string is an octave below 4th fret on D string, which is an octave below 7th fret on B string...

The significance of this layout is that any pattern you wish to play on two strings that are next to each other (string pairs low E & A, D & G, then B and high E), can also be played one or two octaves higher using the exact same pattern, but just by shifting over a few frets and down 2 strings.  I've tried to show this in the following picture:

So the green box is around each of these 2-string pairs, and the pattern repeats at each level. 

Try it out!  Doesn't matter which fret you start on so long as the spacing is the same as shown on the chart.

I've been playing around with different patterns and switching from octave to octave rapidly, makes for some good effects/sounds.

Have fun!