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→Beginner Excercises
Now, we get to the tricky part. When you fret the string, you shorten the resonant portion of it. This means that the resonant divisions of the string for a harmonic have been shortened as well. Let's take a simple example to illustrate:
2nd 4th 2nd 4th e--0--<512>--<24>--12--*12--*12
First we have the open E string, then its2nd harmonic, then its 4th harmonic (using the last pivot point at the 24th fret rather than the first at the 5th fret). The pitches played should be the open-string E4, its octave E5, and the next octave E6. Then we play the 12th fret and sound the 2nd and 4th harmonic using artificial harmonics. We keep the 12th fret held with the left hand. The pivot points each shift halfway closer to the bridge. For the 2nd harmonic, the pivot point moves from 12th fret to 24th. Just like the 12th fret cuts the open string in half, the 24th fret cuts the portion of the string from the 12th fret to the bridge in half. For the 4th harmonic, the pivot point will be halfway between the 24th fret and the bridge. The notes should be all one octave higher, so all 6 notes are: E4, E5, E6...E5, E6, E7. This should plainly illustrate how fretted notes shift pivot points; however, it's a very academic example, where everything is either cut in half or doubled. Let's look at a messier example: 4th 4th e--0--<5>--3--*3-- String length and pitch are inversely proportional. The third fret G is 15/12ths higher pitched than the open string E. The distance from the 3rd fret to bridge is ~12/15ths the distance from the nut to the bridge. This means all the last pivot points (those closest to the bridge) for harmonics are now 12/15ths their open-string distances as well. In other words, you need to move your right hand 3/15ths closer to the bridge to maintain the same pivot points. 4 4 4 4 4 4 4 e--*1--*2--*3--*4--*3--*2--*1 Here we're just moving up and down chromatically. This illustrates the necessity of moving the right hand pivot point to match the left hand fret. Let's get fancy: 4 5 6 5 4 4 4 5 6 5 4 4 4 4 e--*1--*1--*1--*1--*1--*2--*3--*4--*4--*4--*4--*4--*3--*2-- Now we are practicing holding the fret constant and changing the harmonic achieved, as well as changing the fret while keeping the harmonic order constant.