Here's on of my favorite exercises. You can cover most of the fretboard with a circular, repeating arpeggio comprising the notes G B D F A ascending, and A F D B G descending. When played as shown in the diagram — in the key of C — the same notes can be played in a symmetrical arrangement with the 5th fret at the center.
Notice that you can play G A B D F A starting with the 4th finger on the 5th fret of the 4th string (purple), but you may also start with the 1st finger on the same 5th fret 4th string G and move to B on the same string with the 4th finger, ascending from there through D F and A, yielding the same arpeggio (aqua).
There are actually 3 triads in this pattern; G major (GBD), B diminished (BDF) and D minor (DFA)
Name the notes as you play them.
Footnote:
Electronics geeks may notice that this pattern bears a resemblance to the hysteresis loop; a pattern which shows the magnetic induction of a ferromagnetic substance (as ordinate) against the external magnetic field. Whatever that means.
Anyway, here's an hysteresis loop;
You can read more about this here: http://www.daviddarling.info/encyclopedia/H/hysteresis_loop.html
and here:
http://en.wikipedia.org/wiki/Hysteresis
The similarities between these patterns is an interesting coincidence; hysteresis is a part of the science of sound engineering and you'll see it in discussions of the electronics of guitar effects pedals and the like. So although the only connection between the arrangement of these notes on the fretboard and the science of electromagnetism is graphic geometry it makes me wonder if the shape of things isn't actually more profound than we often think.
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