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I've been digging into the "main resonance modes" for about a year now;
Why is a dreadnaught sound hole ~3.90" diameter?[/b]

The main air resonance of my dreadnaughts [ T(1,1)1 ] is so very close to 6th String Open E (82.4hz) that it dampens that note, and some of the fretted octaves of that note. With the body sizes being a MOL common factor (that is; the air volume) why is that 3.90" [edited] sound hole size become a "standard"?


Guitars I measured (sound hole with calipers, frequency with REW analyzer):

• J-45
• Mexican Martin
• Yamaha Dread
• 3 "Borum-built" dreads (of course the same hole size, specified by my plan/ drawings)

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Measure Twice,

Karl Borum

My 1974 D18 and 1980 D12-28 both have 4 inch sound holes which I thought was standard. There are also the various large sound hole D-28's, usually 4.25, credited to Tony Rice. There are some discussion at UMGF.

I haven't bothered to measure the main air resonance, I mostly build OM's and use 3-7/8.

4.9 seems like a pretty big sound hole, and would raise the main air frequency considerably. How confident are you in you REW measurements?

I guess I could take a spectrum (I have Alan Lambert's software) of the D18. Its tricky to get in a form that is easy to post someplace like this (a jpg or pdf) but I certainly mail one to Karl. I assume you are just measuring the response to a tap on the bridge

EDITED in OP: 3.9" - thank you for catching that, 4.9" would be a monster.
Very confident in REW measurements- I shelled out $100 for a mic with a calibration file and validated REW frequency measurement with an independent tone generator application.

I also did a repeatability test, performing 3 different acquisitions on the same guitar and overlaying the graphs. The frequency capture was virtually exactly the same, frequency wise


Yes, tapping on bridge, 32 samples, measuring mic distance, mindful of mic placement directed at the bridge, quiet area, striving to make all the measurement criteria equal across samplings.

Other plots builders have plotted of D-28 styles have same 83hz peaks, yet some "book" references are 96-100 ish hz. Cant wrap my head around the relatively large variation between plots online and values referenced in books (p2-16: ... [i]Volume 1: Design; Trevor Gore) et. al.

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Measure Twice,

Karl Borum

Don’t forget depth of body plays a role as well…

OK, I just took a bunch of samples of my old D18 (and yes the sound hole is 4 inches. I pulled the strings off, tapped the bridge with a little "hammer" made with an eraser stuck on the end of a wire probe (its my standard). Alan's software. Guitar on its back on a towl.


Dominate peak is 176 hz (F3), othe peaks at 218 and 228. Very consistent. Did two taps on its side, one was 197 hz, the other 176.

I had always heard that dreadnaughts have an air resonance right around G3, this is a little lower but certainly lower than the OM's I build (G# or A).

Hope that helps, I could always try to save this to a file if you want to see the whole spectrum. Let me know

The numbers are only correct measured with the strings on and up to pitch, an ideally in playing position.

I know the graph is rather inclusive, so to add clarity, the question is concerning the main air resonance frequency- T(1,1)1 - the first peak, and its relationship with a dreadnaught's sound hole diameter. The two things that significantly contribute to that frequency are the volume of the box, and the diameter of the sound hole. As the volume of the box is fixed, the question relates to the diameter of the soundhole, and why is 3.9" so "universal".

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Measure Twice,

Karl Borum

In that graph, is your main top resonance 155.7hz, and your back at 196hz?

Just to confirm - you’re asking how the sound hole size influences the frequency, correct?

I’m going to ask a dumb question here because I only understand this stuff enough to populate the spreadsheet and thickness my tops, but….the 4” sound hole comes before anyone was tapping anything with bouncy balls on bamboo skewers.

In a parallel timeline where everyone universally loves a D shaped guitar with a 2” sound hole the formulas and target frequencies would be in an effort to recreate that config.

Right? I mean, the whole thing here is working backwards from guitars that are universally accepted as great guitars and the math is derived from them not the other way around. So 4” or 3.9” is universal not for anything to do with frequency analysis, material properties, or the formulas in Gore’s book but because of decisions made by luthiers and instrument companies.

Again, all the math is way above my pay grade and as usual I’m probably looking at it way too simply.


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That is correct, 191hz back, although I had not considered the back active.
Top resonance 155.7

Side note, I probably removed too much stiffness from my braces.

Main pain is the air resonance too close to Open E 6th string
AIR Resonance 83.5
E note: 82.4

Can of worms I've opened here with that graph.... and I'm exposing my poor knowledge of brace carving and top stiffness to the group.

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Measure Twice,

Karl Borum

My question was really just why is the dreadnaught hole 3.9" in diameter.

The question was motivated by playing the guitar up the neck and the 12 fret, 6th string, volume and sustain just died. I also notice my tuner needle wanders on the bass E string. I believe it is because the air resonance is too close to the 6th string open E. I've discovered several dreads I have do that, not just my builds.

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Measure Twice,

Karl Borum

Can of worms I've opened here with that graph.... and I'm exposing my poor knowledge of brace carving and top stiffness to the group.[/quote]

Asking questions and making mistakes is how we learn -

Thanks for asking - I’m learning something.

M

No surprise your air resonance is low compared to what it ‘should’ be in the books. Your top and back are very low too. For a dread the top ‘should’ be about 170 and the back 215. If those numbers were present, it’s likely the 96-100 would be there as well. 15hz discrepancy in the top is a lot. 20hz on the back is a lot.

I would measure your factory made guitar again, I would very very much doubt them to be in the 155 top range.

Anyway, to fix the guitar with the confused E string, punch in a sound port to raise the frequency of the air chamber to decouple it from the main top resonance.

On a side note…while the measuring apparatuses have come a long way, the fundamental understanding that the top, back, and air chamber have fundamental resonant frequencies has long been known, and it has long been known that having the top and air chamber couple is a bad thing. The size of the sound hole has been worked out by trial and error over time to accommodate most ‘averages’.

You are correct Sir. I re-measured six guitars: REW; Real Time Analyzer Tab v5.32.3.
I attached the values for postarity.....
Thanks for the excellent information/ explanation. Back to the drawing board.

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Measure Twice,

Karl Borum

I’m not sure why, but I can’t access the info. It shows as downloaded but has zero data.

Any chance you’d type out the info air, top, back for the six guitars?

This is probably as good as I can get it on this platform. The first three are my builds:

Air Monopole Non Active Back
#1 Dread 94.80 169.80 221.40
#2 Dread 85.50 157.10 207.00
#3 Dread 83.30 156.40 191.00

Gibson J-45 121.10 182.10 281.10
Mex XD Martin 95.30 172.10 216.80
Ymha FG-700s 105.10 209.10 248.20
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I really thought that the air frequency was the product of ONLY the sound hole diameter and body volume. I have learned a lot today. The 83 hz dreadnaught data I though was mine, I believe I saw on another group. I remember the section on coupling in Volume 1 of Trevor's book; I will have return to that section at an earlier hour.

The frequencies (and probably stiffness) are trending lower the more I build; I'm going the wrong way ( like my eyesight and hearing ha). My fourth dread, in the white, is likely similar, based on the trend. Wonder if I need to start listening for specific pitch to guide the brace shaping so I don't remove too much stiffness.

_________________
Measure Twice,

Karl Borum

In case it helps….



Brad


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Thanks Brad!

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Measure Twice,

Karl Borum

Ed is mostly correct, here.

A first point about the "right" resonant frequencies is that they just came from what a few blokes in Australia thought were good sounding guitars when measured (compared with a truck load of others, which were indifferent). To us, they were "right" with respect to D guitars because guitars with lower resonant frequencies tended to have muddy or thuddy basses and indifferent trebles, whereas as those with generally higher resonant frequencies lacked bass. Others may prefer a different balance depending on the genre of music they use the guitar for.

The air resonance of a guitar (the T(1,1)1) is mainly affected by the hole size and the flexibility of the panels. The body depth does not have much effect, because the body is not really a Helmholtz resonator, the equations for which demand a rigid enclosure. On a guitar, the top and back are flexible and the coupling between top, back and air increases as the body gets shallower, negating the effect of the body losing volume. That's why Helmholtz's equations don't work for guitars and a much more sophisticated method (e.g. a 4-DOF model) is required.

Any body resonant frequency that closely matches the frequency of a played note (e.g. low E at ~ 82 Hz or A at 110Hz) has two main effects on the played note. The first is the wolf tone effect which most people here understand, so I won't elaborate. The second is that coupled resonances "repel" each other in frequency. So when the string and guitar body couple around those frequencies one resonance will increase in frequency and the other will decrease. So the note plays out of tune or "warbles", (is unstable as the frequencies alternately repel each other in opposite directions) which is why a tuner has difficulty measuring it. Those are the two main reasons for tuning the resonant modes of a responsive guitar off of scale tones. Of course, if you're not building responsive guitars (most manufacturers don't) you don't hear this effect and is one of the reasons why they don't make responsive guitars because of the extra work involved in working around these issues.

So why is a D sound hole ~ 4" in diameter? Because someone at Martin thought it was a good idea and if you make all the panels the right flexibility and mass you will get a nice sounding instrument. But the flexibility of the panels is largely uncontrolled, because wood properties aren't measured and whatever tap frequencies are present in the top when brace carving are largely irrelevant when the box is closed and bridges of random mass are glued on. None of the manufacturers deoes routine tuning of the closed and finished guitar. This is why independant builders who know what they are doing can produce a much better result than the factories.

If you want to tune the T(1,1)1, making the sound hole smaller or increasing the flexibility of the panels reduces the resonant frequency, whilst stiffer panels and a larger sound hole increases the frequency.

You know where you can find all the details!

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

Mostly correct, here, is good enough for me, lol.

Thanks for the extra data Karl. You can clearly see the correlation between the top and back being in the ‘correct’ range and the air freq being where you expect it to be, and the panels being lower or higher affecting it as expected.

I’m curious as to your opinion about your dread 1 vs 2 and 3…

To me it shows that if your panels are in the ‘correct’ range, a 4”ish sound hole will get your box in the ‘correct’ range.

Dread #1 is more resonate in touch, feel and sound, it sounds richer to my ears. My wife used to prefer the mahogany J-45 (1974 ish) but after a couple of years she favors #1. Numbers 1,2 and 3 sound (and feel) better to my ear than any Taylor I've ever heard, but then I guess I'm not in their target sonic market.

I'm not a very complex or talented player so it's challenging for me to describe the differences, I can mostly feel the differences in my hands and body.

Thanks everyone for the comments and feedback.

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Measure Twice,

Karl Borum

Here's a really great paper on this subject...

https://mwguitars.com.au/2019/03/29/guitar-resonance-and-the-geometry-of-soundholes/

My undestanding from the paper is that as the soundhole gets smaller the total volume decreases across all frequencies, but proportionally more in the higher frequencies, hence why a smaller soundhole seems to boost the bass response.

I enlarged the sound hole of a dreadnaught* (cut a soccer cone to 3" and affixed PSA paper strips to it).

Diameter was increased from 3.81" to 3.98"; an increase of .170" diameter (4.3mm).

An increase of .170" in diameter increased the sound hole resonance (first peak- "coupled" as Trevor would say):
FROM: 83 hz
TO: 84 hz which was less than I expected, but I'll take it, I have to.

This was measured with FFT, guitar suspended, microphone directed at the bridge, tapping the bridge with a marimba mallet.
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Math

I will do the math (Gore; Vol1: p. 2-13; equation 2.3-15; solved for fh) after I get the top frequency with the sound hole plugged. I started spraying finish today so it might be some weeks....what was I thinking.

Equ. 2.3-18 comes close, with estimating and some very slight adjustment.

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*The whole point of this thread was to move the sound hole resonance away from the open E frequency, which was a result of having shaved the braces too low (I believe). Secondly, I wanted to justify the sound hole diameter somehow.

Going forward, I will cut them 4" diameter minimum. My current plan specifies it less than 4". I don't see a downside. And it will make it .170 easier to get my arm in there. I may just make them ALL 4"

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Measure Twice,

Karl Borum