Wulf's Webden

This evening I’ve had a rehearsal for an event coming up in September and then I’ve been exploring and explaining harmonics for a post in the forums of the scottsbasslessons.com site. For anyone who isn’t familiar with the theory of harmonics as applied on bassists and other stringed instruments, here is a brief primer. When you play a note, we call it after the name of the lowest vibrating frequency (or fundamental). Your in-tune A string should be bang on 55Hz. However, you also hear a whole sequence of overtones mixed in. The reason you can tell a bass guitar apart from a tuba and the reasons that two basses can sound different to each other is down to that they have characteristic mixes of the different parts of that sequence. It is also why the “same” note played in two different places your bass sounds different – again, you get a shift in the balance of frequency components resulting in a distinct “timbre”.

You can calculate the components by multiplying by a series of integers. If we start with 55Hz, the next few are 110Hz (x2), 165Hz (x3), 220Hz (x4) and so on. They divide the string into a number of equal sections, based on the multiplier. If you touch the string exactly halfway along (above the 12th fret), you mute all the components that don’t pass through that point. That kills 55Hz (the vibration of the whole string from nut to bridge), 165Hz and several more but it leaves 110Hz, 220Hz and anything else with an even multiplier still sounding. On many basses, that second harmonic component can be pretty much as loud as the fundamental, so the harmonic rings out clearly but it sounds cleaner because all the odd-numbered components have also been filtered out and you are just left with a series of octaves (110, 220, 440, etc).

The same is true when you touch just above the fifth fret (or 1/4 of the way along the string), except you are also filtering out 110Hz. Now you are hearing a mix of 220, 440, 880, etc but it will sound quieter as fewer components of the sound are left and you are getting to the point where the combined volume is starting to drop. You would get the same filtering effect by touching 3/4 of the way along – above the 24th fret or where it would be if your bass has fewer frets.

What about the 7th fret harmonic? You’ll get frequencies starting with 165Hz (and any multiple of 3) coming through. What note is that? If you look up a frequency chart, you won’t find it exactly but it is very close to the E (164.81Hz) which is an octave and a fifth above the open A string. Most people would still hear that as in tune but it is the start of a drift. The next one comes when you divide the string into five portions (ie. fundamental x 5) and that is close to two octaves and a third although, under equal temperament tuning, it doesn’t quite land on the 277.18 Hz you’d get playing a C# on the 18th fret of the G string.

The pattern continues. For the non-even harmonics you start to get notes that don’t have a fretted equivalent on an extended range bass and, with all of them, you can find them in an increasing number of points up and down the strings. On the less positive side, the non-even ones can get even more “out of tune” and they all become quieter and harder to hit. That last point is probably a blessing in disguise though, other wise our plucking hand would more often accidentally hit them!