Chladni pattern for a fanned fret guitar

[Doug Shaker]

Has anyone done Chladni patterns for a fanned fret guitar? If so, I'd love to see them. I'm interested in the effect of the tilted bridge on the modes of vibration.

[Michael Lewis]

There are lots of pics of the nodal patterns available on the internet. try googling "guitar chladni patterns - image".

[Doug Shaker]

There are lots of pics of the nodal patterns available on the internet. try googling "guitar chladni patterns - image".

Well, I can find lots of images of Chladni patterns of regular guitars and lots of images of fanned fret guitars, but no images of the Chladni patterns of fanned fret guitars.

[Markus Schmid]

What should the fret layout have to do with the vibration modes?

[Alan Carruth]

A lot will depend on how much the bridge tilts, and whether you make the bracing asymmetric. Also; are you interested in 'free' plate modes or assembled ones? The free plate will be affected much more; I would not expect much difference at all in the assembled modes unless things are really asymmetric. I've only done on fanned fret guitiar so far (working on another as we speak) so I don't have a lot of data.

[Doug Shaker]

What should the fret layout have to do with the vibration modes?

Usually the bridge is tilted and the bridge is both the main way in which the string vibrations are communicated to the soundboard and it is really a major brace. If it is communicating the vibration to the top on a tilted axis, I would expect the monopole vibration mode and at least some of the dipole vibration modes to be different. But maybe not.

[Doug Shaker]

A lot will depend on how much the bridge tilts, and whether you make the bracing asymmetric. Also; are you interested in 'free' plate modes or assembled ones? The free plate will be affected much more; I would not expect much difference at all in the assembled modes unless things are really asymmetric. I've only done one fanned fret guitar so far (working on another as we speak) so I don't have a lot of data.

I was thinking of the free plate modes, though I would also interested in the assembled modes.

[Alan Carruth]

I do the free plate tuning without the bridge on the top. I've also used symmetric bracing on both of the ones I've worked on, one of which is not strung as yet. The only angled part on the free plates is the bridge plate, and that's not enough to really make much difference in the lower modes. The one that I completed five years ago ended up with symmetric modes both on the free plate and the completed instrument. The one I'm working on now also has symmetric free plate modes. There's only a one inch difference in the scale length across the fretboard on these. The perpendicular fret is the seventh, so there's some tilt to the bridge, but not as much as some folks use.

Given that bridge rocking accounts for such a small part of the tone produced, it seems to me that angling the bridge really should not make too much difference in the sound. Nor can I see any reason to make the bracing asymmetric unless leaving it symmetric causes problems with the bridge pins.

[Doug Shaker]

Alan-
Thanks for your reply. Coherent and knowledgeable as always.

I was interested in this part of your reply:

Given that bridge rocking accounts for such a small part of the tone produced, it seems to me that angling the bridge really should not make too much difference in the sound. Nor can I see any reason to make the bracing asymmetric unless leaving it symmetric causes problems with the bridge pins.

I thought that bridge rocking was the major way in which string energy was transferred to the soundboard. Are you saying that isn't the case? Or are you saying, in effect, "Yes, that's how the energy gets there, but that's not how the tone is determined."? Can you give me a pointer to something I could read on this subject?

[Alan Carruth]

"I thought that bridge rocking was the major way in which string energy was transferred to the soundboard. Are you saying that isn't the case? "

Actually, it's generally only a very small part of what drives the top. It's hard to understand where that idea came from (although I have my suspicions), but a lot of folks believe it.

Fletcher and Rossing cover the forces that the vibrating string put on the bridge top in their excellent book:"The Physics of Musical Instruments". They calculate the two main forces; the 'transverse' and 'tension change' (which they call 'longitudinal') for a couple of typical cases. Several years ago there was some discussion about this whole issue on an on-line list I was on, and I decided that I'd take a stab at measuring the relative magnitudes of the two forces. It took a lot longer than I thought! When I finished up I wrote a paper on the subject, and gave a talk at an ASIA Symposium about it. You can see the paper, entitled 'String Theory' (I could not resist) on my web site. Part of the reason it took so long is that things are a lot more complicated than they 'ought' to be, which is pretty normal with guitars. I will try to resist going through the whole thing in this post.

Let's say you pluck a string such that it's moving 'vertically' with respect to the soundboard. There are two main forces on the bridge top:
1) as the string moves up and down it pulls the bridge up and down, causing the top to move like a loudspeaker cone, and
2) as the string vibrates the tension rises twice per cycle (once when it's 'up' and once when it's 'down'), and this tugs the top of the saddle toward the nut.

The up-and-down transverse motion produces a force on the bridge top that averages about seven times as much as the tension change does. This varies a lot depending on the string, but there are few cases where the tension force is as large as the transverse, and in some cases the transverse force is ten times or more greater than the tension change. Usually, of course, the string doesn't go perfectly vertically with respect to the soundboard, but since thew transverse force is so much greater than thew tension change you have to get pretty close to 'horizontal' motion for the tension change to equal it.

Guitar tops are made to resist torque on the bridge, but are fairly easy to move in 'loudspeaker' fashion. The 'loudspeaker' motion is also very much more effective at producing sound. In part this is due to the fact that bridge rocking pulls the lower end of the top 'up' and pushes the upper part 'down', so the two motions partly cancel each other out in terms of moving air and producing sound.

Keep in mind that the tension change force is octave-doubled: it's at twice the frequency of the fundamental of the string. Since arch top guitars use a tailpiece the tension change force doesn't drive the bridge: all their energy comes from the transverse force. If tension change was the main driver on flat top guitars you'd expect them to sound an octave higher than arch tops with the same strings. Do they?

I've got all sorts of data on this, some of which may not be in that paper. Suffice to say I'm convinced that Fletcher and Rossing got it right, and that tension change is not the main driver of the guitar. I've also done some experiments to figure out what it does do for the sound, but that's another post.

[Doug Shaker]

I thought that bridge rocking was the major way in which string energy was transferred to the soundboard. Are you saying that isn't the case?

Fletcher and Rossing cover the forces that the vibrating string put on the bridge top in their excellent book:"The Physics of Musical Instruments". They calculate the two main forces; the 'transverse' and 'tension change' (which they call 'longitudinal') for a couple of typical cases. Several years ago there was some discussion about this whole issue on an on-line list I was on, and I decided that I'd take a stab at measuring the relative magnitudes of the two forces. It took a lot longer than I thought! When I finished up I wrote a paper on the subject, and gave a talk at an ASIA Symposium about it. You can see the paper, entitled 'String Theory' (I could not resist) on my web site.

Thanks! I will take a look at the paper on your website and, possibly, take a look at Fletcher and Rossing. Thanks for the summary of the main points, though. If you assume the major force driving the top is the up-down motion of the bridge, it makes sense that the angle of the bridge doesn't make much difference to the Chladni patterns except insofar as the bridge and bridge plate constitute a brace.

[Alan Carruth]

An angled bridge can affect the Chladni patterns, particularly the higher pitched ones. However, it doesn't seem to change the monopole much, and that's the mode that counts in terms of the vertical translation of the bridge. Altering the string height off the top does change the way the rocking motion caused be tension change drives the top, an alters the timbre. It just doesn't have much effect on the power output. As I say, these things are more complicated than they 'ought' to be.