Bridge Principles

[Strabo]

I am working to increase the volume of a mandolin to be heard through the din of other loud instruments. After reading about solid bridges here and on Red Henry's site I have fabricated bridges from red oak and maple. These have successfully increased volume very noticeably, especially on the treble strings.

This mandolin has always had somewhat weak and muddy sound from the bass strings, and my solid bridges have so far not changed that. Now I'd like to see if I can improve volume and tone of the bass strings by adjusting the design of the solid bridge. To do that I need a better understanding of the principles of sound transmission and filtering through the bridge.

I understand that a lighter bridge transmits more vibrations than a heavy one because it takes more energy to move the increased mass of a heavy bridge. Volume seems to be inversely related to mass of the bridge. I do not understand if a lighter bridges favors treble, bass, or both equally.

Contact between the bridge and the top plate is important, and bridge feet must be made to fit closely to the top of the instrument. There are some other variables in play here (full contact vs. feet, wide feet vs narrow feet, location over tone bars, etc.) that I do not understand very well.

Configuration of the bridge is also important, but in ways that are somewhat mysterious to me. Number, size, and location of cutouts and presence/absence and shape of wings are apparently important factors.

Material plays a big role, with maple the apparent favorite. I do not have access to lots of exotic woods, so I don't plan to try different materials unless I have good reason to believe that a particular material will increase transmission of vibrations from the G and D courses. (I have also tried various strings, but haven't had much success there.)

I'd like to see if I can improve the bass response of this instrument by modifying the bridge. Can someone help me understand how a solid bridge could be (re)designed to strengthen bass response?

Strabo

[jshane]

This is way beyond anything that I could contribute, except to wonder if posting this in the builders section might yield more informed responses.

[High Lonesome Valley]

I made a vertical three ply bridge out of western red cedar with a mahagony saddle for my bouzouki. It increased the volume for live playing, but for recording I'm using a bridge made out of all mahogany which is much warmer and present sounding.

On the saddle area, I've found that using bone or some such under the non wound strings increases their overall volume and clarity, under wound strings some type of hardwood, as bone causes wound strings to sound too tinny.

Also, proper placement regarding the feet is crucial to the mix.

So many threads on bridge development, placement, etc. on the MC Builders Forum, just check it out.

[Stephen Perry]

In part, the bridge is a filter. Much of the perceived projection of any note is its energy in frequencies other than the fundamental. One of the more important frequency ranges to have energy in is the singer's formant range. See, e.g., http://www.ncvs.org/ncvs/tutorials/v...al/singer.html If the bridge is filtering out these frequencies for some or all of the strings it is likely to sound less projecting. My assessment, anyway.

Control of this filtering is, in part, what I am working on at the moment, with some overly complex success.

[Dave Cohen]

Vibrational motions are not transmitted from strings to bridge to body parts. The bridge and the nut are seen as high mechanical impedance junctions by the string. Hence, the vibrations of strings stay in the strings. They are damped by internal losses in the string itself, and by losses to motion of the end supports (i.e., the bridge and the nut). What the strings do is impart pulses of force each time the antinodes of the string vibrations pass through zero amplitude. Those force pulses from the strings in turn excite all or most of the characteristic vibrational motions (called normal modes) of the top plate and of the other instrument body parts, and of the air mass(es) in the soundhole(s) and that in the body cavity.

You can find some basic information in the Fletcher & Rossing text, "The Physics of Musical Instruments", 2nd edition, Springer, NY, 1998, ISBN# 0-387-98374-0. Another source is "The Science of String Instruments", edited by Thomas D. Rossing, Springer, NY, 2010, ISBN# 978-1-4419-7109-8, or e-ISBN# 978-1-4419-7110-4.

Don't make the common mistake of trying to apply what is known about bowed string instrument bridges to mandolins. Plucked string instrument bridges are much shorter, stiffer, generally more massive, and function much differently than do bowed string instrument bridges.

[Mandoplumb]

If the vibration doesn't pass thru the bridge why is the fit of bridge to top so critical, not disagreeing just want clairification. I agree that a bowed bridge doesn't act as a plucked bridge, although I don't know why. Also how much vibration can a bow produce?

[Dave Cohen]

If the vibration doesn't pass thru the bridge why is the fit of bridge to top so critical, not disagreeing just want clairification. I agree that a bowed bridge doesn't act as a plucked bridge, although I don't know why. Also how much vibration can a bow produce?

The effects of bridge fit have nothing to do with vibrations "passing through" the bridge itself. The bridge serves as a rigid conduit for the force pulses from the strings. If the bridge does not fit the top plate well, the forces are not interrupted or redirected, but they can be partially dissipated. Partial dissipation of the force pulses would mean less efficient excitation on the body and air motions than would be the case if the string force pulses were not dissipated at all by the bridge.

Most lay people seem to visualize tiny traveling waves moving through parts of an instrument. In fact, all of the instrument body and air motions are actually 2D and 3D analogues of standing waves. Those are what we call normal modes of motion. Consider the following constraint for the lowest possible frequency of a standing wave motion in a ~1" tall mandolin bridge: Wave motions typically move through wood with a velocity (aka "speed of sound in wood" or "velocity of propagation") of around 3,000 m/s. The relationship between velocity, wavelength, and frequency is given by the simple formula

(wavelength)x(frequency) = velocity of propagation.

If we consider that the shortest possible wavelength for a standing waveform could be twice the height of the bridge (same condition for a string fundamental), the relation gives a minimum frequency of ~60,000 Hz, or 60 kHz. Human hearing usually quits considerably lower than 20 kHz, maybe half that for older men. So if there are any standing wave motions in mandolin bridges, they would not begin and have any effect until >3x the maximum frequency of human hearing. Even for much taller violin bridges, the minimum frequency for a standing compression wave motion in the bridge would be ~40 kHz. Violin bridges, though, are much thinner and more flexible than mandolin bridges. So there are bending motions that occur at much lower frequencies. Even then, the so-called "bridge hill" bending motion in a violin bridge occurs up around 2 kHz. For reference, the fundamental of the E(first) string in a violin or mandolin is ~659 Hz.

What exactly do you mean by "How much vibration does a violin bow produce?" Is that string vibration? And by "how much", do you mean amplitude? Frequency?? wavelength??? There are detailed answers to more specific questions than yours. Both the Fletcher & Rossing book and the Rossing book references in my previous post have entire chapters on that. The violin bow produces what is called "Helmholtz motion". You can probably look that up in Wikipedia or some such for a more complete answer than I can reasonably post here.

[pops1]

I have found that the wood makes a difference in sound, not different types, but different pieces of the same species. Had a mandolin that i could not get the G strings to sound the way i wanted, made a different saddle a couple of times finally sold it. Trying to make it sound as good as i could i made one more saddle and bingo the sound was incredible, i wanted to keep it. All were made of ebony, one of bone but the last must have been from a different piece of ebony. Not sure what happened, but loved the sound just before i shipped it out.