Main body Resonance

Construction and repair of Classical Guitar and related instruments
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geoff-bristol
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Main body Resonance

Post by geoff-bristol » Thu Oct 12, 2017 2:14 pm

Given a finished guitar body - neck finished and board fretted etc - unpolished - but no bridge fitted.

A few questions.

What is the best way to determine main body resonance I'm just tapping the top in various places to a decent tuner ?

If you have a main body resonance - say G# . What effect will the bridge have generally once fitted ? Will it raise or lower - and how does its size and weight alter any effect ?

Basically - although not a huge fan of plate tuning etc - I do see some merit in determining the main resonating chamber of the finished box - given it has tuned strings on it. Knowing what adding the bridge does would be useful ?

Generally - on a finished guitar, with the next one in mind - what effect would raising the sides/ altering the soundhole size or placement, achieve. Just with regard to main body frequency.

Alan Carruth
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Re: Main body Resonance

Post by Alan Carruth » Thu Oct 12, 2017 9:29 pm

First, tattoo this inside your eyelids so you can see it any time you want: "Your mileage may vary". Guitars are complicated beasts, made up of lots of small parts. The details can vary a lot, and the result you get depends on how all of those details come together.

In my own experience, in general, gluing the bridge to the top usually results in the top monopole mode dropping by some amount in pitch. As a rule of thumb I count on a change of about 1/2 semitone. If you do things differently than I do, such as making the bridge wings thicker or thinner, or longer or shorter, or the tieblock heavier or.... You get the picture.

What most people refer to as the 'body resonance' is actually the 'main air' mode, which is roughly an octave lower in pitch than the 'main top' or 'monopole' resonance. The top and the air (and the back, and maybe the sides) conspire to produce a pair of output peaks in the low range. At both frequencies the top moves a lot, and there is air pumping strongly through the sound hole: what you're hearing is not 'the air' or 'the top', but 'the system'. We use the terms 'air' and 'top' resonance as a shorthand to connote where most of the energy in the system is stored, but they're not independent. When you tap on the top at the bridge location you are activating the whole system, and producing sound peaks at both frequencies. What you tend to hear is the lower pitched 'air' frequency because:
a) low pitches tend to mask higher ones, and
b) they're normally about an octave apart, so the 'top' pitch sounds like an overtone of the air mode, and is not perceived separately.
Blocking the sound hole allows you to hear the 'top' resonance more clearly.

Altering the top pitch doesn't have a linear effect on the 'air' mode. You can add a fair amount of mass or stiffness to the bridge without necessarily changing the sound of the tap much. OTOH, sometimes something like changing the mass or stiffness of the back will make quite a difference.

The 'main air' pitch works like a Helmholtz mode; it's more or less similar to what you hear when you blow across the mouth of a wine bottle. The major variables for a 'pure' Helmholtz resonance on a guitar-like box are the size and location of the sound hole, and the box volume. Most acoustics texts will tell you how to calculate that reasonably accurately. The problem is that's all predicated on a rigid box, and guitars are not rigid. Vibrations of the walls of the box, particularly the 'monopole' resonant modes of the top and back, will alter that pitch. Note, however, that those alterations are on top of the basic 'Helmholtz' resonance: they won't change the pitch a lot, but details matter on guitars.

So:
1) the larger the sound hole the higher the 'Helmholtz' pitch, all else equal.
2) The closer the hole is to the middle of the top the higher the 'Helmholtz' pitch.
3) Adding something like a 'tornavoz' will drop the Helmholtz pitch, sometimes drastically, and also reduce it's strength.
4) Using something like a 'rose' in the hole won't alter the pitch much, but will reduce the activity of the Helmholtz' mode a lot.

Making the sides of a guitar deeper (again, all else equal) does surprisingly little to the 'main air' pitch. Fred Dickens did that experiment. If the box were rigid deeper sides would yield a lower Helmholtz pitch. In a guitar the flexibility of the walls, particularly the top and back, drop that, yielding the lower pitched 'main air' resonance that looks like a Helmholtz mode. The more strongly the top and back couple with the air pressure change in the box the more the pitch drops. Making the box deeper reduces the pressure change for a given amount of top motion, so the 'main air' pitch is not pushed down as much as it is with a shallower box. This cancels out most of the pitch change you'd expect from the deeper box. Fred cut the sides of a guitar down from 6" deep to something like 2", and only saw a 7% change in the 'main air' pitch. Sadly, I was not there when he did the experiment, and can't say how the timbre of the guitar changed.

You can ask simple questions about the guitar, but there are no simple answers.

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geoff-bristol
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Re: Main body Resonance

Post by geoff-bristol » Thu Oct 12, 2017 9:54 pm

Thanks Alan - will copy your post off and digest !

mitch lees
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Re: Main body Resonance

Post by mitch lees » Fri Oct 13, 2017 12:11 pm

Alan,

Thank you for a fascinating post, but I think I will have to do some work to be able to have sufficient understanding to make the most of it. I have a reasonable understanding of the basics of 'sound propagation in water' because of my previous career, but how sound behaves in enclosed air spaces is a 'dark area' and I would like to know more. Can you suggest decent 'primer' that I could study please.

And here is another of those 'simple' questions - if I wanted to improve the bass response of my guitars, which of all the many variables do you think might deliver the greatest gains?

thanks

Mitch

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Re: Main body Resonance

Post by Alan Carruth » Fri Oct 13, 2017 5:49 pm

An old, but still good, take on the basics of guitar acoustics is Jansson's "Acoustics for Violin and Guitar Makers" 4th edition. Best of all, it's available free by download from:
http://www.speech.kth.se/music/acviguit4/
You will need to get part1.pdf through part9.pdf.

A more mathematical treatment that has been around for a while is in Fletcher and Rossing's "The Physics of Musical Instruments".

One of the more recent (and expensive) works is the pair of books by Gore and Gilet: "Contemporary Acoustic Guitar - Design" and "...-Build". Gore did most of the technical stuff, and gets into some involved math in the first book. They also break it down in explanations that those of us with lesser math chops can use, and include software for some of it.

The old 'Journal' of the Catgut Acoustical Society used to publish papers on guitar acoustics from time to time. Since that organization was folded into the Violin Society of America they stopped doing that (drat!). There is a juried on-line journal: the 'Savart Journal', that is trying to fill the gap, and has some interesting papers.

There is other material around, but that will get you started.

Mitch:
As always, the 'best' solution depends on what the problem is. Without the guitar on the bench it's impossible to say. Sorry I can't be of more help.

mitch lees
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Re: Main body Resonance

Post by mitch lees » Fri Oct 13, 2017 8:07 pm

Alan,

Thank you for your post - I am looking forward to exploring this topic. I will make a start with the Jansson. I see what you mean about the cost of the Gore and Gilet - I am not sure my maths is up to it, but it looks like a substantial work!

My question on the bass response was really a more generic one rather than about my own guitar builds - I just wondered by adjusting which variable was one likely to produce the greatest effect.

Mitch

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Re: Main body Resonance

Post by Dave M » Sat Oct 14, 2017 3:49 pm

If you are interested in a more technical approach to building then the Gore/Gilet books are worth every penny. You do not have to follow the maths too closely as they always describe the phenomena in ways that a non mathematician can follow.

The general principles they establish can be used by a builder of any style of guitar. The build volume then also provides step by step instruction for building several styles, both classical and steel string.

The answer to the one of the OP's questions is there in the book, describing the use of free software to look at the spectrum of sound from the guitar to nail down the frequencies of the main resonant modes as Alan has described above.

Oh and I not on commission!
Dave

Alan Carruth
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Re: Main body Resonance

Post by Alan Carruth » Sat Oct 14, 2017 10:20 pm

A broad generalization is that:
1) the larger the box the more 'bass balanced',
2) a relatively small sound hole moves the pitch of the 'real' Helmholtz resonance down,
3) stronger coupling between the Helmholtz mode and the top monopole pushes the 'main air' mode down further, and
4) coupling between the top and back monopoles drops it still more. You increase the monopole coupling by increasing the area of the modes and by placing them closer together in pitch.
5) too much coupling, or a top that is too responsive, can produce a 'wolf'.
6) Tuning the lowest 'bar' type mode of the entire guitar (often called the 'neck mode') so that it matches the 'main air' pitch can give a particularly 'dark' timbre in the bass. It's hard to do on demand.

So, when I'm talking with a customer about a new guitar, the first thing I try to determine is how they want the bass balance, since that establishes the size of the box. Then I go into other stuff. Since the hard thing to get on a Classical is usually clean and full trebles I don't generally worry too much about enhancing the bass unduly.

Everything about the guitar can be seen as an exercise in balance. It's possible, for example, by making the hole very small and/or moving it up into the corner of the upper bout, to move the 'main air' pitch down to match the low E string pitch. Some folks like that sound, but to me it loses fullness around the A string pitch, and doesn't really recover until you get to the open G: in other words, it leaves a 'hole' in the response. There is no free lunch; every choice you make has some cost to weigh against the benefit.

mitch lees
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Re: Main body Resonance

Post by mitch lees » Sun Oct 15, 2017 8:19 am

Alan,

Very grateful for this excellent answer, and for the time you take in answering amateur builders questions so comprehensively. This has now inspired me to learn more about the 'technical' approach to building. Interestingly, I am told by good players that the treble response of the instruments I have made is good, so I do not want to make too many changes just to achieve a small gain in bass response (which is all that is required) as this might degrade the treble - balance is the goal as you say. Like most things that are worth study - the more one learns, the more there is still to learn!

thanks

Mitch

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Re: Main body Resonance

Post by Alan Carruth » Sun Oct 15, 2017 11:42 pm

I often feel that treble response 'lives' in the top: it's a function of getting the balance right between the top thickness and the bracing. Bass response is more tied to what the air in the box does. So long as you keep doing what you're doing on the tops, you should be able to work on the box size/depth and soundhole to get the bass to work better. IMO treble is harder to get, so you're already most of the way there.

mitch lees
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Re: Main body Resonance

Post by mitch lees » Mon Oct 16, 2017 7:36 am

A little knowledge can be a dangerous thing! But my early thoughts are that I will only make on change with the current build and see what happens. I am thinking of increasing the diameter of the sound hole by about 5mm which should change the Helmholtz resonance which, as I understand it, is a major contributor to the lower end response. However, the 5mm only comes from comparing measurements of as many guitar plans as I can find. This would take my sound hole diameter from 85mm to 90mm which seems to be about the top end of the envelope. Clearly there is an upper limit beyond which the air mass becomes too great to move and so response probably falls off quickly (?). I have not made the sound hole/box volume calculation you mentioned earlier. At the risk of becoming a nuisance, is the relevant equation available on line anywhere?

Again - thank you for your help

Mitch

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Re: Main body Resonance

Post by mqbernardo » Mon Oct 16, 2017 8:23 am

If you want to lower the "helmholtz" resonance you should reduce the hole diameter, or maybe add a tiny wooden tornavoz.

mitch lees
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Re: Main body Resonance

Post by mitch lees » Mon Oct 16, 2017 10:10 am

I had just assumed, naively it seems, that an increase in sound hole diameter would increase the size of the air column around the sound hole that is being moved, and hence produce a louder response. The mention of a toravoz introduces a whole new dimension which I had not considered at all. I have seen Michael Thames building a guitar with one on UTube but that is as far as my knowledge extends.

thanks for the post

Mitch

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Trevor Gore
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Re: Main body Resonance

Post by Trevor Gore » Mon Oct 16, 2017 11:13 am

mitch lees wrote:
Mon Oct 16, 2017 7:36 am
At the risk of becoming a nuisance, is the relevant equation available on line anywhere?
If you google "Helmholtz resonator" you will likely find a number of formulae for the resonant frequency of a Helmholtz resonator, including this one. The problem is that they assume the body of the vessel is rigid, which a guitar most certainly is not, and so give an incorrect answer that is far more misleading than being of any real use. However, the equations given usually show you which direction things move if you select a variable and change it; it's just that the magnitudes are all wrong. To get the magnitudes right, you need to be a lot more sophisticated in your modeling, taking into account the mass, stiffness and mobility of the other main vibrating components of the "vessel", namely the top, back and sides of the instrument, all of which couple with the main air mode and alter its frequency.

You then need to be able to ascertain what is the "right" answer, for your set of circumstances, i.e. what resonant frequency are you aiming for and why is that a "good" frequency, and how will that frequency relate and react to the other major low order resonances of the guitar, which all couple. All of a sudden you're into modal tuning. The modes of vibration of a finished guitar are what you hear when an instrument is played and so define the sound of that particular guitar. What differs from guitar to guitar are the amplitude, bandwidth and center frequencies of those modal resonances, and indeed, whether or not a particular modal resonance exists on a particular instrument. If you want to change the sound of a guitar, it's the modal resonances that you have to deal with and you have to be able to link those modal resonances to particular features of the woodwork. Free plate tuning only gets you some of the way, because there is no easy pathway between free plate modes and completed instrument modes because of the substantial changes in conditions between one and the other: constrained edges, coupling effects, the effect of additional components likes bridges, finish, etc..

So yes, a guitar "is a lot more complicated than it ought to be" as Alan is wont to say. But many of the hard yards have been done.
Trevor Gore: Classical Guitar Design and Build

mitch lees
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Re: Main body Resonance

Post by mitch lees » Mon Oct 16, 2017 12:36 pm

Thanks to everyone - current build on-hold - I need to do some work first.

Mitch

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