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It's not what you don't know that hurts you, it's what you do know that's wrong.

Ah, the 'Art vs Science' thread; as if it always had to be a 'versus'.

Why would you NOT want to understand your job in a rational way?

Senses can be very accurate. They can also be very inaccurate. Some tests that have been done show that some luthiers who think they can accurately gauge the stiffness of a piece of wood are correct, and some are not. The problem is that many of the folks who can't do it think they can.

Often what your senses 'measure' is much different from what a tool does. There is no agreed upon way to translate your perception of 'loudness' to a number on the dBA scale. Neither is 'wrong', neither is 'better' in every circumstance, but they sure are different. You have to use them for what they are.

No measurement is 100% accurate, no matter how it's done.

The best measurement in the world might not mean anything. As far as I'm concerned, you can measure the conjunction of Venus and Jupiter to the milisecond, and it won't make any difference in the weather tomorrow. 'Validity' is just as important as 'accuracy'.

There is no quantitative definition of what a 'good' guitar is. Still, if you measure the response of enough guitars you'll start to notice that the good ones (as judged by players and listeners) tend to work in similar ways. If you can figure out how to make your guitars work that way, you are more likely to make good ones. Your 'standard of mediocrity' will go up.

As far as I know, we don't have a clue in any measureable sense as to what the difference is between a 'good' guitar and a 'great' one. There is every reason to think that it's in the high frequency region, where we won't have any specific control anyway. Still, some poeple do manage to make 'great' instruments more often than others. Partly, I think, they start from a higher standard of mediocrity, but there is probably something else involved as well. Maybe it has to do with what they did at the crossroads with the goat at midnight?

The guitar is a very complicated machine, and there are lots of variables involved, none of which seem to be totally independant of the others. It seems to me as though getting most of them 'right' (whatever that is) will result in making a good guitar. It almost doesn't matter WHICH ones you don't get right, just so you get most of them. Some poeple work with a different set of variables than I do, and some of the things I consider important might not be on their radar. We both get good results, but they're different. It keeps things interesting.

No measurement is 100% accurate, no matter how it's done. Yep, hard to argue that one Al.

I always liked these examples of measurements ...

Consider the math equation for a line segment, 0<x<10. How long is the line segment ??? Well, we can see that its shorter than 10 units .... however, no matter how many decimal places you use, the line can always be made longer .. it is in effect, infinite.

My grandmother was always one for a measured shot in her rye and ginger ... one day, I free-poured a shot as I mixed her a drink, to which she replied "Tony, how much is that ?". I replied back, holding my finger to the level of the rye in the glass ..."its EXACTLY this much". You cant get more accurate than that. BTW, I still have a scar where the evil eye of death ray hit me.

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Tony Karol
www.karol-guitars.com
"let my passion .. fulfill yours"

While I agree with your point (arbitrary precision is theoretically impossible), I don't like your math. It's not a line equation, it's a bound on a variable of nonnegative value less than ten. It is the exact opposite of infinite, it's as finite as can be! (Of course, we don't actually have any way of telling if we live in a discrete universe or not so it might well be that the length of something real can only have a certain number of decimals...)

We don't have to deal with strictly abstract objects in lutherie, it can all be measured to tighter tolerances than it needs to be if we had the money for the instruments and any idea what to do with the data. If guitars with a certain sound could feed, move, or kill people more effectively than the current way we do it you can bet in short time we'd have some pretty efficient and repeatable ways to measure and adjust all kinds of properties we never thought we could.

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Bob Garrish
Former Canonized Purveyor of Fine CNC Luthier Services

Al, you put it much more eloquently, but this is what I was trying to convey…
It is often those set on the idea that there must be a formula to build the perfect guitar who insist that "emotions" or "senses" cannot be trusted. Probably remnants of Anglo-Protestantism, and deep in the culture.
For the rest of those who happily use whatever technology/science to build, they also realize that it brings them only so far. And I think anybody strives to reduce the unknown-unknowns to known-knowns, or at least known-unknowns.
But the last leg of the build, so to speak, must be done on the consciousness level.
Nothing magical with that, this is what I call the working of experience. Clearly if the senses have no experience in the matter they hardly can be trusted. It's never too late to train, we tend to forget the potential we have in ourselves and the enormous range available in our hearing and touching.
To take a simple example, it's great to take notes on builds (and I do), but writing can also hamper our ability to memorize.
I think Brave Buffalo once said "writing is forgetting", answering the question why Sioux, in spite of their enormous vocabulary, didn't develop a written language.
So perhaps, there is a balance to strike there, and no art vs. science.

A final note on higher frequencies: theoretically we only hear up to about 20KHz, which is why the first digital standards (CD, DAT etc.) were sampled at 44.1KHz (about double). Interestingly, when I was doing recording/sound engineering, I slowly switched to 48KHz because of DVD mastering, and I thought it sounded slightly better than 44.1KHz most of the time. I couldn't really describe it, but it was there -providing good audio equipment-. Then 88.2KHz and 96KHz came and I used that, because again, it had an elusive "better" quality to it, even when the project was finally dithered and down-sampled to 16bit/44.1KHz.
Some people prefer analog recording and vinyl pressing, in spite of the higher floor noise level, because there is no sampling limit. The only limiting factor is the recording and playback equipment (usually analog as well).
So if theoretically we can only hear up to 20KHz, why do we hear a difference with sampling rates that go far beyond our perception, and that get dithered and downsampled anyway (and later played on average equipment…)?
There is something up there in those frequencies, and they affect dynamics and lower frequencies as well, that we can't measure (yet, perhaps…) but yet makes a difference.

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Laurent Brondel
West Paris, Maine - USA
http://www.laurentbrondel.com/

Hey Bob .. its not my math .. you will have to take that one up with one of my high school math teachers. If its so finite, tell me how it ends ???

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Tony Karol
www.karol-guitars.com
"let my passion .. fulfill yours"

Laurent,
I think that Al is talking about a much lower high frequency. When we measure the sound coming off of a guitar and do a spectral analysis, the information that we get between 0 and 1Khz has noticeable patterns in it. The signals above 1Khz look pretty random. We are just now starting to draw correlations between the patterns that we in the lower frequencies and subjective listening test. These correlations seem to be in the range of what is an average or poor guitar and what is a good guitar. As to what is a great guitar, that seems to be in the frequencies above 1Khz. We don't know what or how to measure the higher frequencies yet.

As for your recording experiences, your observations are probably correct. While we cannot hear above 20Khz, that doesn't mean that signals above 20Khz don't affect what we do hear. Consider that you have two signals, one a 30Khz and the other at 31Khz. You shouldn't be able to hear either of the two signals. However, there is a beat frequency at 1Khz that would be produced if those two signals were heard at the same time and 1Khz is something that you can hear. That is why a CD player has to filter out signals above 20Khz. The signals above that are just noise. Because you want the output at 20Khz to be at the same strength as the rest of the signal and you want the signal at 22Khz to be almost 0, you have to put in a very steep filter. As it turns out, steep filters introduce phase distortion in the signal that they pass. This distortion is very detectable to the human ear. That is why CD players do something called over sampling. If you generate 4 or 8 samples for every one read from the disk, you can interpolate the missing information. You can then use a filter with a much shallower slope and those filters don't have as much phase distortion.

Over sampling with interpolation isn't as good as having real signal information, however. So using a higher sampling frequency during the recording process means that the signal loss that you get when you master for the CD will be the only place that the loss occurs and you get a truer representation of the original. If you record at the lower sample frequency and then do other processing on that signal, any distortion introduced during that processing will more likely affect that audible result.

I've never been a recording engineer and what I know I got from "book learn'n". I don't have very good ears either so a lot of what other builders say about the sound of an instrument is lost on me and I just have to take their word for it.

Mike, thanks for the detailed clarification. We also could get into the bit rate, but that mostly affects dynamics…
BTW Bob Katz has a lot of excellent papers on engineering and mastering.
IME few people were able to differentiate between high sampling rates.
What I hear coming out of a steel-string guitar is a lot of partials, what we variously refer as "overtones" or "air". Tastes vary widely, but those who seek a "rich" guitar tone tend to like the bass/mid registers ladden with partials, but still clear, and fairly fundamental high registers, especially up the neck where strings do not have a lot of power and can sound thin.
IMHO the frequencies coming out of those partials, especially with wound strings, are way up the frequency range.

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Laurent Brondel
West Paris, Maine - USA
http://www.laurentbrondel.com/

It's not that we can't measure what a guitar is doing above 1 kHz, or whatever. The real problem is that we lose control over what it's doing at fairly low frequencies.

When I did the 'corker' experiments that you can read about in the latest American Lutherie, I found a lot of 'top', 'back' and 'air' resonant modes, starting at around G on the low E string. In fact, of course, none of the modes I saw was simply a 'top' mode, say, which is easily seen by the fact that opening a port in the side changed the pitches of many of them. If it was only the top vibrating that would not happen; each of those modes was really a mix of things. We call the 'main top' mode that because most of the energy is in the top, but other things are moving as well.

You can plot out the activity at a resonance that is not near any other by feeding in a uniform amount of power in a sweep signal, and measuring the amplitude at different frequencies. In this sort of case you'll get a 'bell curve', with the peak activity at what we normally call the 'resonant frequency'. If you drop down the curve to the point on either side of the peak where the activity is 3 dB less (one half the power) for the same input energy you will have defined the 'half power band width' of the resonance. This is a measure of how much loss there is in the system. It's really easy to drive a resonance when you're within it's half band width.

Let's suppose, just for grins and giggles, that your 'main top' resonance happens at 200 Hz and has a band width of 5 hz. If you take the resonant pitch over the band width, you get a number called the 'Q value'; in this case, 40. It's interesting to note that, on the average, the Q values of all the resonances of a given guitar tend to be about the same. This means that as you go higher in frequency, the band width also get bigger: if the band width was 5 Hz at 200, it will tend to be 50 Hz at 2000, so the Q value stays at 40 (remember, this is an _average_, the actual Q value of any given mode can be quite a bit higher or lower).

Any one sub-system on the guitar will tend to have resonances at more or less regular intervals, say every 50 Hz or so (just for arguments sake). This spacing does not change much as you go up in pitch. You can see, then, that as you go up in frequency the band widths of the different resonant modes can be as large as the spacing between them. What this means is that, at some point, it gets to be very hard to drive only one resonance at a time; you are always within the band width of something else. This is called the 'resonance continuum'. On guitars it seems to set in somewhere around 600 Hz, more or less.

What you see in the response curve of the instrument in this range is a lot of peaks and dips. It's easy enough to find the pitch of any one of these spectral features, and you can even find out where on the guitar the sound is coming from. However, that might very well not be the part that is most important in the resonance. Adding weight at that spot may or may not alter the sound much. In fact, even in theory it's impossible to label any one of these peaks as a 'top', 'back' or 'air' resonance; all you can say is that the guitar is moving and making sound. The people who do computer modeling of this sort of thing use 'curve fitting' programs to try to come up with resonant modes that make sense, but they say that the results are totally dependant on the assumptions you put in, and can change wildly with small changes in assumptions.

What you _can_ say, though, is that the spectrum in this range shows a certain avarage level, a certain degree of 'peakiness', with so many peaks per octave, say, and a certain average difference between the height of peaks and the bottom of the dips in between. These, rather than the actual pitches of the peaks and dips, seem to be what's important in determining the overall timbre of the guitar. That is, two instruments with a similar peak _structure_ will sound similar, even if the actual pitches of the peaks are somewhat different.

Will they sound 'the same'? That's a tough one. I suspect that the higher you go in pitch the more difference you can tolerate in the exact shape of the spectral curves. This is not easy to study; sort of like Douglas Adams' 'Somebody Else's Problem Field', which would hide things well if you looked right at them, although they could often be seen if you looked out of the corner of your eye, and didn't seem to care much about what you saw. As you go higher in frequency you need more and more to sneak up on things, and it takes more and more time.

Is it worth it? It's hard to say. This is the sort of thing that some people seem to do quite well subconsciously; the sort of thing people do well and computers do poorly. Many of us feel it's a problem worth chipping away at. At least it represents job security.

It's not a number, strictly speaking, it's the box we know we can put it in which has been defined (it's a 'set' in math terms). The proof that X is finite is that it fits inside a finite box. It's less than ten, ten is finite, so X is finite.

The decimal system as a language can only name a specific subset of numbers with finite digits, and even then simple things like 1/3 don't have a finite decimal expansion. Numbers like pi and the square root of two don't even have a repeating decimal expansion so we can't even do the 'put a bar over the numbers that repeat forever' thing.

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Bob Garrish
Former Canonized Purveyor of Fine CNC Luthier Services

Next years OLF membership man purses should include pocket protectors and calculator cases with belt loops..........

Tony, 0<x<10 is not an equation for a line or a line segment. It's not an equation at all. To have an equation, you need an '=' sign. 0<x<10 describes the set of numbers greater than zero and less than 10. It's true that the set has an infinite number of members, and does not have a highest or lowest member. But those highest and lowest members do approach finite limits, namely 0 and 10.

"When I think of all the crap I learned in high school, it's wonder I can think at all." --Paul Simon

Laurent, I'm a child of the Enlightenment and a Laplacian with regard to all things physical. I believe the guitar is a physical object, and a finite one, and is in all its parts subject to the laws of mechanics. I don't see any reason to believe otherwise. It follows that the mechanics of the guitar can have a finite physical description. Whether they ever will is a different issue, as is whether human senses are more sensitive and selective in discerning information about the guitar than non-human measuring devices. At present, it's pretty clear that human senses can access more relevant (although often less accurately quantified) information than the non-human devices. That may not always be so, and the guitar's mechanics may one day be fully described in physical terms. If so, that will not settle the question what is the best guitar, since that's a subjective question. But it may settle the question what is the guitar that is considered best by the most people. So what? Well, we may be able to build guitars that come closer to what people want. But that doesn't necessarily threaten our values. Science leaves things as they were, but often with better descriptions.

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Howard Klepper
http://www.klepperguitars.com

When all else fails, clean the shop.

Howard Klepper wrote:
"Well, we may be able to build guitars that come closer to what people want. But that doesn't necessarily threaten our values. Science leaves things as they were, but often with better descriptions."

THANK YOU!!!!!

Howard, I do not disagree with the fact that the guitar is a physical object subject to the laws of mechanics. But again the way we understand the physical world is subject to changes, corrections and paradigms. I definitely do not dismiss the scientific method.
Again it is not an either/or proposition.
This is not the place to discuss the role of the Enlightenment in our culture. For this see the excellent essays and books of the British thinker John N. Gray, "Heresies", "Straw dogs" or "Al Qaeda and what it means to be modern".
My problem has more to do with the fringe of the Enlightenment, i.e. Positivism and Comte, that exerted a great influence on modern thinking. I call it the religion of Progress where the scientific method is the dogma replacing all metaphysical yearning.
To me, this is magical and toxic thinking.
See the latest Stradivarius "find", now it's the wood again that did it… What will be the next one? The only thing we cannot possibly test is the effect of centuries, but perhaps those instruments were as good sounding when they came out of the Cremona shop with their Baroque set up. People seemed to think so at the time. Who will ever know? Maybe the violins of Jacob Steiner will become more popular than Strads again and then Steiner's secret will have to be uncovered…
Perhaps the guitar as a physical object will be understood better, scientifically. I have doubts and I think this may lead to huge disappointments. As you say it is subjective, and I would add emotive. As music should be.
But you're right, that doesn't threaten our values, there is just a lot more noise to sift through, and a lot more players in utter confusion about wood, finish and so on. But this is nothing new, the great Isaac Stern believed the sound of his Strad came from the magical varnish…
I think we already know what the best sounding guitars are, in terms of quality (not aesthetics) of tone, as well the 18th century violin makers knew what a violin ought to sound like.
As for the assumption that science leaves things as they are, I beg to differ. I believe we live in a zero-sum universe, and according to the laws of thermodynamics, there is no free lunch…

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Laurent Brondel
West Paris, Maine - USA
http://www.laurentbrondel.com/