Note Names of Plucked Harmonics???

Discussion in 'Technique [BG]' started by jokerjkny, Mar 18, 2003.

1. jokerjkny

Jan 19, 2002
NY / NJ / PHL
i was wondering, i know that certain harmonics along the fretboard do and do not necessarily correspond with the notes that ring out.

but, when playing naturally plucked harmonics, is there a way to forumlize what those notes are?

2. moley

Sep 5, 2002
Hampshire, UK
Yes.

It's called the harmonic series.

Let's say that the fundamental (first harmonic) is the open G string.

The harmonics after that, in ascending order are as follows:

2nd harmonic: G (an octave up from the fundamental)
3rd harmonic: D
4th harmonic: G
5th harmonic: B
6th harmonic: D
7th harmonic: F
8th harmonic: G
9th harmonic: A
10th harmonic: B
... etc. (after this they get very close together, and very out of tune)

Now, harmonics always follow this pattern. The pattern itself, in relation to the fundamental:

2nd harmonic: Octave
3rd harmonic: Octave + 5th
4th harmonic: 2 Octaves
5th harmonic: 2 Octaves + 3rd
6th harmonic: 2 Octaves + 5th
7th harmonic: 2 Octaves + m7th
8th harmonic: 3 Octaves
9th harmonic: 3 Octaves + 2nd
10th harmonic: 3 Octaves + 3rd

Ok, if you know the fundamental (i.e. the open string, in the case of natural harmonics) - you can work out the harmonic series for that fundamental.

They relate to positions along the string as follows: To get the nth harmonic, there are theoretically n - 1 points on the string at which you can get this harmonic, and they are the divisons of the string corresponding to 1/n, 2/n, 3/n, 4/n ... n-1/n.

For example, the 2nd harmonic (the octave) can only be found at one point on the string - the 1/2 way point (i.e. the 12th fret). However, the 3rd harmonic (an octave & a 5th above the fundamental) can be found at two places on the string - 1/3 of the way along the string length, and 2/3 of the way along the string length. The 4th harmonic can (theoretically) be found at three places along the string - 1/4, 2/4, and 3/4 of the way along the string. However, 2/4 = 1/2, and 1/2 the string length gives you the 2nd harmonic. Now, you can't have two harmonics at one node - and it's always the lower one that you get. So, while theoretically you would get the 4th harmonic at that point, you don't, you get the 2nd harmonic.

Likewise, the 6th harmonic, would theoretically be at 1/6, 2/6, 3/6, 4/6, and 5/6 of the string length. However, 2/6 = 1/3 - which gives you the 3rd harmonic, and 3/6 = 1/2 - which gives you the 2nd harmonic, and 4/6 = 2/3 - which gives you the 3rd harmonic.

So, actually, you only get the 6th harmonic at the points 1/6 and 5/6 of the way along the string length.

So - that gives you a formula whereby you can work out where harmonics occur and what notes you get. But you'll find some harmonics are stronger than others, of course.

Here's a guide, I've given you some harmonics, the note, the divisions of the string, and the fret(s) at which you'd probably play it (+ means just above fret)

2nd harmonic = octave = 1/2 = fret 12
3rd harmonic = octave + 5th = 1/3, 2/3 = fret 7
4th harmonic = 2 octaves = 1/4, 3/4 = fret 5
5th harmonic = 2 octaves + 3rd = 1/5, 2/5, 3/5, 4/5 = fret 9, fret 4
6th harmonic = 2 octaves + 5th = 1/6, 5/6 = fret 3+

Does that make sense?

3. labrat

Very good explanation Moley. Haven't seen it done better since some old Manring Bass Player lessons from a few years back. Well done.

One small point you missed is that when playing a harmonic with multiple nodes, it's better to finger the node closest to the end of the string being plucked, to better resolve the string into it's vibrating sections.

For instance, the 5th harmonic has 4 nodes. If you pluck the second node, the string has initially 2 different sized vibrating sections; a 2/5 section and a 3/5 section. It is then hard for the string to resolve into five 1/5 sections from that. As opposed to fingering the last 1/5 of the string, which lets the string subdivide easily.

And through using your left hand to fret the string and change the fundemental, and right hand to finger a node and pluck it; a very wide variety of notes are possible.

Dec 15, 2002
McKinney, TX
5. moley

Sep 5, 2002
Hampshire, UK
Yup, fair point.