Simplicity It Works For Me

Music seems immensely vast, but is it?  My response is that music is actually immensely simple ... but also immensely vast.  Now before you accuse me (hat tip to Mr. Clapton) of giving an obviously lawyer answer allow me to explain.

Music is immensely simple.  Western music is made up of twelve distinct pitches.  For those not familiar with musical theory, the easiest way to visualize this is by looking at a single octave of a piano keyboard:

Note there are seven white keys and five black keys.  If you play your way through each of those twelve notes you have played every note used in western music.  Wait a second, I hear you saying.  I've seen pianos before and they have way more keys than that.  It's true they do, but the above pattern just repeats a little over 7 times.  As the pattern repeats, so do the pitches they just sound in a higher register, so we've only got 12 notes to choose from - simple right?  But wait, that's not all!  Conventional notions of melody and harmony are based on scales, groups of fewer than all 12 notes.  The two most common types of scales, major scales and minor scales, consist of seven notes each.  So, if you restrict yourself to only playing "right notes" your playing will be made up of no more than seven of these twelve.  Even simpler.

Or so one might think until one reads about one George Van Eps who helps us unfold the immense vastness of music.  In addition to being a performing musician, George also wrote instructional books, one of them entitled Harmonic Mechanisms for Guitar.  I can't begin to say I'm at a point in my musical journey where I can grasp the content of this work (it's made up of three hefty volumes) but it is basically an analysis of all the different ways to string notes together along the fretboard of a guitar.  Now you might say, we're only talking about twelve notes, why would he need three hefty volumes to talk about that?  Some understanding of the answer to that question lies in an early section  starting on page 17 of Volume 1 titled General Remarks - Selectivity.  Van Eps observes that if six objects are placed side by side that there are 720 unique ways to arrange those objects (this is a factorial calculation).  If the six objects are strings on a guitar and you were playing each sting "open" (without putting any fingers on the fretboard) then you would have to play 720 different 6 note sequences before you would repeat.

On a guitar fretboard the frets are spaced in a way so that as you place your finger on the next highest fret and pluck the string you are getting the same change in pitch as if you played the next highest key on a piano.  Fretboards vary in lenght but usually have 22-24 frets.  Therefore you can play more than one cycle through the 12 available notes on each string of the guitar.  To simplify things lets look just at one cycle through the twelve notes.  If we look at those twelve notes and think of how many unique twelve note combinations we can make up the answer is going to be to calculate the factorial of twelve.  Since factorials progress geometrically, the factorial of twelve is way more than twice the factorial of 6; 479,001,600 to be exact.  That's right, to play through all the combinations of the note in one octave on one guitar string would require almost half a billion combinations.

There are six strings on a standard guitar, so if you were going to perform this exercise on each of the strings you would have to play 6 x 479,001,600 combinations.  If however you wanted to include combinations that would contain notes played on different frets and different strings the calculation would actually be 720 x 479,001,600.  To keep our calculators from shorting out let's just round the answer down to the next lowest billion and we'll see that we would have to play over 344 billion combinations to get through the various ways to connect a sequence of six notes on a standard guitar.

On a standard guitar then these twelve simple notes can produce over 344 billion six note combinations.  If Van Eps hadn't blown people's minds enough, he went on to point out that if you could play each combination in a second and you were to play 24 hours a day, 7 days a week, 365 days a year then it would take over11 thousand years to play through every combination.  He went on to point out that contemporary musical theory has existed for about 400 years, compellingly leading to the ultimate conclusion - we've just begun to scratch the surface of what can be done with these twelve simple notes.

The takeaway to apply to mediation is this.  Disputes are not either simple or complex, they are both simple and complex.  At the heart of any legitimate dispute be it two neighbors arguing over a tree growing over a fence or billion dollar corporations arguing the fate of multimillion dollar projects is a basic and simple truth.  At least one party feels a wrong that needs to be redressed.  Figuring out the details of that simple truth is often incredibly complex.  As mediators we need to be able to operate with both the simplicities and the complexities to be effective.

Today's post title is the opening line from a song called Simplicity by Bob Seger.