More mandolin thoughts

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peter.coombe
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More mandolin thoughts

Post by peter.coombe » Sun Mar 03, 2019 11:16 pm

Following on from the other mandolin thoughts thread which referred to my flat top mandolins, I have been measuring some arch top mandolins. The results have been very interesting.


Firstly some background. Many years ago I began measuring free plate modes in archtop mandolins after reading up on some of the violin research published by the Catgut Acoustical Society. I not unreasonably assumed that mandolins vibrated similar to violins. At the time the research on mandolins was absolute zilch so it was new ground. Purely empirically by trial and error I found that if I matched the frequencies of the ring mode of the top and back, then the resulting mandolin seemed to sound better (oval soundhole mandolins). By better I mean a more interesting sound and better balanced, more even sounding. This was consistent, and cannot be explained away as a chance thing. Absolute frequencies, however are not correlated with sound, the pattern is randomized.

Here are the links to the papers I wrote -
http://petercoombe.com/publications/jaamim7.html
http://petercoombe.com/publications/jaamim8.htm

Now I had no idea why this seems to work, but I did get independent verification from Allan Carruth in that he found the same thing in archtop guitars. The hypothesis is that by matching the ring mode the relationship between the top and back is about right in the completed instrument. What that is we had no idea. Since then Cohen and Rossing have published a nunber of papers that show mandolins vibrate much more like guitars than violins, and the Gore/Gilet books have been published. So by measuring the free plates and the competed mandolins maybe we can work out what is going on.

Firstly some vintage mandolins, difference between the main top mode and main back mode -
Two Gibsons - both one semitone
Two Lyon and Healy - 2.5 and 3 semitones

My mandolins with the free plate ring mode matched -
3 Lyon and Healy style mandolins - 3.5, 3.5, 3.5 semitones
1 mandolin of my own design - 4 semitones

One of my mandolas with the ring modes unmatched, ring mode of free plate of the back is 2.5 semitones higher, final interval is 7 semitones.

I have a mandolin that is unfinished with the back ring mode higher than the top so the final interval will be interesting for that.

I need a lot more data from more instruments, but it is looking like if the free plate ring modes are matched then you end up with an interval of 3.5-4 semitones between the main top mode and main back mode. SURPRISE, SURPRISE, it fits in with the book!!!

The really good thing about this is that if my hypothesis is correct, you can predict the final interval from the free plate modes. This is necessary for mandolins because there is no access to the interior once the box is closed, so you can't add weight to the sides, or adjust the back braces, like you can in guitars. I can, however adjust the main air mode downwards by adding a fingerboard extension over the soundhole. This is important because if the main air mode is G or G# then you get a big woofy note on the G string.

Lastly, there is no reason why this cannot be applied to guitars. My data is indicating it can be applied to guitars, but they are different from archtop mandolins, the interval on the free plates you need is different, but the relationship is consistent. Flat top mandolins are different again, but are much more like guitars. More data is needed, but it is very promising. I think I may be on to something big here.

I have been saying for years that the relationship between the top and the back is what you should be taking note of, not the absolute modal frequencies, but have mostly been ignored. Siminoff's tap tuning stuff is mostly rubbish IMHO. Now it is looking like I might be right after all, but not enough proof just yet.
Peter Coombe - mandolin, mandola and guitar maker
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peter.coombe
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Re: More mandolin thoughts

Post by peter.coombe » Sun Mar 03, 2019 11:22 pm

Forgot to mention that the last mandolin I measured with the interval of 4 semitones, recently finished, sounds devine. About as close to the perfect sounding mandolin I have ever had the pleasure of playing. I went through a similar process as in the book i.e. what is the perfect mandolin, and redesigned how I was making them about 3 years ago. This last one is damn close to perfect.
Peter Coombe - mandolin, mandola and guitar maker
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peter.coombe
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Re: More mandolin thoughts

Post by peter.coombe » Mon Mar 04, 2019 8:40 am

Here is a picture of the main top mode on the latest mandolin. You can see the fingerboard extension over the sound hole. Without it the main air mode was bang on G#, the fingerboard extension lowered it about 1/2 semitone. Mandolins are a bit more complicated than guitars because there is a tailpiece, and the tailpiece does change the frequencies, as does the tuners and pickguard, and the mass of the bridge of course lowers the main top mode. The tuners and tailpiece change all the frequencies quite a bit on flat top mandolins, but not much on arch top mandolins, but the interval between the main top and main back remains pretty much the same. The pickguard does add a bit of mass to the sides, so the main top mode is lowered a small amount.

The final frequencies of this mandolin are
main air - 205 Hz
main top - 507 Hz
main back - 633 hz
Attachments
main-top-507hz.JPG
main-top-507hz.JPG (119.74 KiB) Viewed 1582 times
Peter Coombe - mandolin, mandola and guitar maker
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Graham McDonald
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Re: More mandolin thoughts

Post by Graham McDonald » Sun Mar 10, 2019 2:59 pm

Peter, this is very interesting and really important information. You may have well found the Holy Grail of connection between the free plate modes and the assembled instruments. And it has only taken 20 years to work this out :D I have a blackwood/bunya mandolin just being started at the moment and a blackwood/sitka five course mandcello on the go as well, so I will see where we go with those two in applying your ideas.

Doubtless most of the Americans will ignore you, as they have Smallman and Gore/Gilet, but there will be some who pay attention. Have you thought of contributing an article to the GAL or RM Mottola's on-line guitar acoustics magazine, or even putting what you have here on the Mandolin Cafe? Write it up and get it out there.

Cheers
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peter.coombe
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Re: More mandolin thoughts

Post by peter.coombe » Sun Mar 10, 2019 7:35 pm

Thank you Graham. I was beginning to wonder if anyone would take any notice, but you did and you nailed it.

When I have more data I will write it up properly and submit to the GAL for publication because it is an important finding if correct. That is assuming the new data continues to support my hypothesis, but so far looks like everything I have so far does. There is a bit of scatter, but that is to be expected. I was holding off posting here on this until the latest mandolin was finished, and it turned out to be bang on as predicted so the probably of being correct just increased a significant notch. I already posted on the mandolincafe hinting at these findings, but nobody picked it up. I will post there again when I am more certain of being correct.

Graham, the instruments you are working on oval/round sound hole or F soundhole? My research was on oval hole mandolins only. I have measured 3 F hole mandolins, one of mine, a Gilchrist and a Kimble. All have a doublet for the main top mode and the main back mode is about 6 semitones higher than the main top mode(s) in all 3. Cohen and Rossing have said they often measure a doublet in mandolins so that is not unusual. I have the free plate mode frequencies for mine and the ring mode is not matched, the back ring mode is higher, how much I don't know because I am at Port Fairy right now. This supports my hypothesis. It is usually impossible to match the top and back free plates in F soundhole mandolins, the back is nearly always higher by at least 3 semitones. I usually aim for 5 semitones.

Actually it has taken 25 years, plus probably I need another year for more proof. Thank you Trevor Gore and Gerard Gilet, plus thank you Cohen and Rossing. We all stand on other's shoulders.
Peter Coombe - mandolin, mandola and guitar maker
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Re: More mandolin thoughts

Post by Gassy » Mon Mar 11, 2019 11:44 am

Fascinating stuff Peter, it will take me quite a while to wrap my head around it.
As with many things in musical instrument making, there is so much to do and learn and so little time.
So true, and thus the effort you have put into this has incredible worth and is amazingly generous.

When I got into bagpipe making I read a number of books and papers on how woodwinds work, but the maths does not really work for bagpipes. This parallels with your mode studies on mandolins vs violins/guitars. It's relatively easy to go down the empirical path, but chasing excellence and knowledge is what makes us truly human - and might keep the robots from taking over.

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Graham McDonald
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Re: More mandolin thoughts

Post by Graham McDonald » Tue Mar 12, 2019 8:51 am

Peter, I went back and looked at your recent comments of the perennial topic of tap tuning mandolins, and you certainly hinted at what you posted above, but only hinted. I think you should publish what you have above on the Cafe and see what happens.

The 'cello will be oval hole and the mandolin yet undecided, though this has pushed me towards doing that as an oval and as well see if I can match the free plate ring modes. I don't do more that hold the plate at the 10 o'clock position and tap at 4 o'clock, but I have enough of those pitches noted to know where I want to be with soundboards. A coffee at the NFF and a chat about this stuff?

Cheers
Graham McDonald
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peter.coombe
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Re: More mandolin thoughts

Post by peter.coombe » Tue Mar 12, 2019 3:00 pm

I am happy to have a chat with you at the NFF.
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Mark McLean
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Re: More mandolin thoughts

Post by Mark McLean » Thu Mar 14, 2019 8:46 pm

Many of us would like to be there sharing that coffee with you. Enjoy! And share the results of that meeting of minds with the rest of us. This is important........

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peter.coombe
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Re: More mandolin thoughts

Post by peter.coombe » Fri Mar 15, 2019 8:59 pm

One thought that has occurred to me since the first post - the Lyon and Healy type mandolins that I made have a different bridge from the more recent mandolin of my own design. The bridge is quite a bit lighter. That could explain why the difference is consistently 3.5 semitones rather than 4 semitones. With the same bridge they would have been closer to 4 semitones. The bridge does lower the main top mode, and how much it is lowered depends on the mass of the bridge, so it would have been lowered less in my Lyon and Healy style of mandolins. Take this factor into account and the results are even more remarkably consistent. 4 out of 4 is not winning the lottery, but the chances of it being a fluke by chance is quite low.
Peter Coombe - mandolin, mandola and guitar maker
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Re: More mandolin thoughts

Post by peter.coombe » Mon Apr 15, 2019 11:06 am

Has been some more progress on this. I have some more data from new mandolins, and I have managed to borrow a couple of instruments from a local customer to measure. Ideally I really need a research grant to make 20 identical mandolins or guitars and vary the tunings. I am suffering from a lock of quality and quantity of data. My guitars are not consistent, some have an Ebony bridge, some BRW bridge, and the most recent have Blackwood bridges. Also with archtop mandolins I have had to lump in together different models of mandolins to get enough points on the graph. Result is there is a fair bit of scatter when I plot the data, but I would be very surprised if a regression analysis is not significant for all of them.

So, what I have is the guitar graph is looking like a straight line with a lot of scatter, the archtop mandolins/mandolas is looking like a straight line with some scatter. The most promising is my pancake flattop mandolins where it is looking like a straight line with hardly any scatter. The pancake mandolins are by far the simplest and most consistent instrument, so that is what I would expect. However, at the moment I have a cluster of points at both ends of the graph and a big gap in the middle. So I need some more pancake mandolins to fill in the gap. I also need to work out what to use as a control. However, I think I can now reasonably confidently say that there is a strong correlation if you build your instruments consistently. So the holy grail of Lutherie has now been figured out, but there is still more work to do. This is so important it really needs to be nailed right down so there is no question about it.
Peter Coombe - mandolin, mandola and guitar maker
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Re: More mandolin thoughts

Post by meddlingfool » Fri Apr 19, 2019 9:43 am

Hi Peter,

Do you think the shape of the soundhole (oval vs round) has much effect on the resonant freq?

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peter.coombe
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Re: More mandolin thoughts

Post by peter.coombe » Fri Apr 19, 2019 6:47 pm

Do you think the shape of the soundhole (oval vs round) has much effect on the resonant freq?
No, the surface area of the soundhole, the volume of air in the soundbox, and the stiffness of the top, back and sides determines the main air mode frequency. The shape does not matter. In terms of the other modes, the soundhole only affects the modal frequencies in terms of how it affects the stiffness of the top.
Peter Coombe - mandolin, mandola and guitar maker
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