Backs

[John Bertotti]

So after years of reading everything I still only have a vague sense of how the backs interact with the tops in flat and carved instruments. I am at this time curious how the bowl of a bowl back interacts with the top and modes. Anyone have any data on this? John http://www.mandolincafe.net/iB_html/non-cgi/emoticons/smile.gif

[Dave Cohen]

I gave an invited paper on this at the 75th anniv. ASA meeting on May 27.

Basically, the bowls in Neapolitans (bowlbacks) do nothing below about 1.2 kHz. Even above that frequency, the bowl mode shapes bear little or no resemblance to what the top plate is doing.

Carved and flat mandolins are similar to guitars. Pretty good interaction in most types of mandolins between the top plate and back plate in the (0,0) or "trampoline" mode. Usually a doublet in tops, occasionally a triplet or higher multiplet, and the backs do the same thing. Most backs really like the sideways rocking or (1,0) mode, and are much less coordinated w/ the tops for higher modes. You can find most of this for guitars in the Fletcher & Rossing text ("The Physics of Musical Instruments", 2nd Ed. chapter 9) and for mandolins in the Cohen & Rossing CASJ paper (Nov., 2000) and the Cohen & Rossing paper in Acoustical Science & Technology (Jan., 2003). I sent a manuscript accompanying the ASA talk off to Tom Rossing, but we haven't submitted yet.

[John Bertotti]

Thanks Dave, I guess some of what you discovered is actually physically apparent, when playing a bowl, due to the lack of vibration noticed in comparison to to flat and carved backs. The bowls then must contribute to the sound through cavity volume? How does the reflectivity of the inside of a mandolin effect sound? I believe that it has been stated that the sound isn't reflected as much as it is the air mass moving creating the sound waves of course being driven by the plates. Not being very adept at playing I am going to make an observation based on previous topics. Chop being much more punchy in carved top and back instruments, and flat top and back instruments, in comparison to bowl backs. I then am led to believe that the back has a lot to do with chop.
Thanks again John http://www.mandolincafe.net/iB_html/non-cgi/emoticons/smile.gif

[Dave Cohen]

Sound is not "reflected" inside the body cavity of an instrument. The air in the cavity has normal modes of motion just as the strings do and the body does. The lowest frequency air mode is the "Helmholtz resonance". Again, the interaction between the air modes and the body modes is described quite nicely in Fletcher & Rossing. Rossing also did a series of three articles for American Lutherie which are now compiled in the first two volumes of "The Big Red Book of American Lutherie". One of his articles was entitled "Sound Radiation in Guitars". Those articles were written for luthiers and lay readers, so if you are worried about the math and the jargon, those articles would be a good place to start.

I can only speculate about the "chop". The back plays a part, but is certainly not all there is to it. There are numerous other differences. The narrow, ladder-braced tops in the Neapolitans are very stiff; the lowest top plate mode occurs at ca 500 Hz, while the Helmholtz air mode occurs at around 140 - 200 Hz. By contrast, in a parallel-braced f-hole mandolin, the lowest (0,0) mode occurs around 270 - 300 Hz, and the Helmholtz air mode frequency is around 280 - 300 Hz. The stronger interaction there is probably at least partly responsible for the "chop".

[John Bertotti]

Thanks Dave the exact info I was looking for. John http://www.mandolincafe.net/iB_html/non-cgi/emoticons/smile.gif

[Martin Jonas]

Very interesting, Dave. I wonder, though, how this ties in with my experience that my bowlback sounds much more muted when the bowl is pressed firmly into my midriff, compared to when I hold it more loosely. In carved mandolins, there's the toneguard to protect against this muffling (though I understand that not everybody agrees that it's a real effect), but if you're right in that the bowl has little or no oscillation modes of its own, then this should not happen in bowlbacks.

Martin

[Bob A]

Not all bowlbacks are ladder-braced. I have several examples in which the two main braces form an acute angle (not quite a triangle; the two braces converge, but do not meet); the narrow portion is on the bass side of the table.

I have often noted the fact that the entire instrument (especially the more lightly constructed examples) resonates strongly when sounded. Surely this must contribute to some degree in sound amplification and dispersion?

[Dave Cohen]

The two Neapolitans which I studied were a 1921 Calace and a 1908 Martin. The Martin was the stiffer of the two, with nothing happening in the top plate below about 540 Hz, and nothing happening in the bowl below about 1.4 kHz. I think that neither of those instruments was an El Cheapo Neapolitan in its time.

There is neither question nor ambiguity about whether or not I was 'right'. Several different types of experiments all gave the same results. The fact that the holography alone saw nothing below the frequencies which I mentioned is unambiguous in itself. However, FFTs of body taps gave the same result, as did accelerance spectra. Further, I measured characteristic (decay) times for all of the played notes from the 196 Hz open G (4th string open) to the 880 Hz a (1st string, 5th fret). I have a nice little graph of characteristic time vs frequency, showing that at just below 500 Hz, when the top plate becomes active, the characteristic times start to drop off to less than 5-10% of their values below about 450 Hz. That is very indicative of the body motion stealing energy from the strings above 500 Hz, causing the string vibration to decay much more quickly, while the much longer characteristic times below 450 Hz indicate that there is no body motion stealing energy from the strings at those lower frequencies. It is certainly possible that what you feel when you hold a played Neapolitan to your midriff is the sum of the motions above 1.2 kHz.

It is conventional in scientific measurement to do as many different types of measurements for a given system as is possible and practicable. Generally, the results of any one type of experimental measurement are considered to be subject to systematic error and/or ambiguity. The more different types of measurements that corroborate the same results, the less ambiguity there is.

Stringed instruments do NOT amplify the "sound" from the strings. The body does steal energy from the strings, and the air both inside and outside of the body cavity in turn steals energy from the body (All of this is called "coupling"). The process is very inefficent (max maybe 4% efficient) and most of the energy is wasted as heat, which in turn is dispersed very quickly by the surroundings.

The stiffness of the Neapolitan mandolin bowls is consistent with that of other similar instrument bodies. Very similar results were observed with lutes, and one of Tom Rossing's grad students, Andy Morrison, did an early project with Balalaikas a few years ago which also gave very similar results. If anything, parts of the balalaika bowls were somewhat less stiff than either lutes or the Neapolitan mandolins.

In my ASA talk in NYC, I was careful to stress that though Neapolitans radiate sound less efficiently than other types of mandolins, that does not make them 'worse' or 'inferior' to the other types of mandolins. They are just different, and they certainly have their adherents. As far as the science is concerned, I am not interested in making judgements about the relative quality of different types of mandolins. That is impossible to do anyway, if not foolish. I am only interesting in understanding how each of them 'works'. The comparison of different types of mandolins has been very helpful in that regard.

[John Bertotti]

Dr. Cohen thanks for all the great info but you know we'll pick your brain till we're so confounded that we can't reply. http://www.mandolincafe.net/iB_html/non-cgi/emoticons/wow.gif
This being true here is another question based on some of your replies which I'll paste here first.

1) Basically, the bowls in Neapolitans (bowlbacks) do nothing below about 1.2 kHz. #Even above that frequency, the bowl mode shapes bear little or no resemblance to what the top plate is doing.

2) The narrow, ladder-braced tops in the Neapolitans are very stiff; the lowest top plate mode occurs at ca 500 Hz, while the Helmholtz air mode occurs at around 140 - 200 Hz. #By contrast, in a parallel-braced f-hole mandolin, the lowest (0,0) mode occurs around 270 - 300 Hz, and the Helmholtz air mode frequency is around 280 - 300 Hz.

3) inefficient All of this is called "coupling"). #The process is very inefficient (max maybe 4% efficient)

When we discuss bracketing a carved instrument, we are trying to get a top plate just above the Helmholtz frequency and the back just below.
Do these plates have to physically enclose the air chamber? I ask because I'm thinking of the double top bowl back instruments. The space between the two tops being relatively small would have a higher Helmholtz resonance itself maybe improving on that coupling. From my point of view at the moment it looks like this type of instrument has two air chambers.
I'm not sure where my train of thought is going just sharing some observations and seeing if others agree or not. I will ask that if the bracketing is good will this increases efficiency? What plays in the increase of efficiency in our little instruments. Does an increase even equate to a better instrument. Obviously we don't want instruments that will ring on forever. Then again some of us might. Thanks John http://www.mandolincafe.net/iB_html/non-cgi/emoticons/coffee.gif

[Dave Cohen]

Several very basic questions here, John. I think that this is where you should start looking at the Rossing articles in the Big Red Books.

Your understanding of bracketing is not quite right. The (0,0 mode in mandolins is usually a doublet. That means that it occurs, e.g., in f-hole mandolins, at slightly below 300 Hz, and again at about 400 Hz. The sound radiation will be most efficient when the Helmholtz resonance frequency is between the two (0,0) mode frequencies. This is completely analogous to guitars. In guitars, the (0,0) mode is typically a triplet, occuring at around 100 Hz, again at around 165 Hz, and again at around 200 Hz. The Helmholtz resonance frequency is around 110-120 Hz. You can see that it is "bracketed" by the (0,0) multiplet. The back plate (0,0) mode frequencies in the assembled instrument will not be a lot different (if at all) from the top plate (0,0) mode frequencies (unless you immobilize the top plate and the sides). They are working together, and no, that does not necessarily result in a "wolf note".

If the coupling between body modes and air modes is strong, the efficiency will approach the 4% figure. It is probably a llittle less than that in mandolins, since the mass of air in the mandolin body cavity is so much smaller than that in guitars. Mandolins are heard better than guitars only b/c their playing range is in a better portion of the range of human hearing. More efficient sound radiation doesn't necessarily equate to a "better" instrument, though it does result in a louder one.

In order to have a Helmholtz resonance, you have to have a cavity with an opening in it, i.e., a "soundhole(s)". I don't know about the double top Neapolitans. Are the two sound chambers completely isolated from each other? I looked at some mandolins w/ Virzis and some without last Winter. The Virzi didn't affect the Helmholtz resonance frequency at all. For that matter, scrolls had little or no effect that I could discern.

[John Bertotti]

Thanks you that certainly clears a few things up. The big red books are hopefully going to be a Christmas present from the wife this year. As far as the double top instruments I'll try and find a jpg of the top. Thanks John http://www.mandolincafe.net/iB_html/non-cgi/emoticons/smile.gif

[John Bertotti]

Heres one. I haven't seen inside so one of these so I wonder if it isn't just a big virizi. Maybe one of the classical guys with one will pop in and tell. John