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I've read and seen many reviews of the sound of guitars and there's almost always a discussion of the 'fundamentals' of the sound and of course the 'overtones' as well and these concepts seemed to be fairly well agreed upon in the world of the luthier. (Whoa did this forum just flag luthier as misspelled? - again?) Anyway, here's a couple of terms that get thrown around and it seems like there's some kind of agreement on their usage. Perhaps unlike other terms like bright, warm, full, focused, sparkly highs etc. which are subjective at their very best, 'overtones' and 'fundamentals' seem to be characteristics that can be fairly well discerned when listening to a guitar - by some at least. Or are these terms just as subjective as all the other attempts to describe 'tone' accurately?

OK, so my question is - what do the terms mean and how do I know when I hear them? Am I liking the sound I hear from a guitar because of the overtones? Or the fundamentals? Both?

Did all experienced Luthiers go to a school where these terms are discussed and agreed upon? Is there a guitar video that clearly shows each characteristic for all to hear and agree upon? I'm asking, of course, because I'd like to know what sound my guitars are producing and how to design for each characteristic but don't really know what each really sounds like. Any help appreciated.

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Thank You and Best To All

I would like to understand that as well. I have trouble deciding why I like the sound of a particular guitar. Sometimes, I find it easier to describe what I don't like.

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Under Compensated Nut!

I think there are two different things you could be talking about here. Harmonics of a string being one of them and also the guitar top. I am certainly no expert but from what I understand the lowest frequency of vibration along the the string is known as the fundamental, while higher frequencies are referred to as overtones. The fundamental of the guitar top (and back) is the lowest frequency as well and has to do with thickness, density, size and so on.

So a guitar that only produced a fundamental frequency would sound rather dull. This of course doesn't happen and you get harmonic overtones and the more of those you get the more open and airy or however you want to describe it the guitar is. IOW it sounds better.

But I don't think the terms fundamental and overtones are used the same way to describe the tone like bright, airy, open, woody and so on.

Some one will chime in shortly with more physics then I care to know about and clear the whole thing up though

My understanding of these two concepts (fundamentals vs overtones) is the following.

As JF pointed out, the fundamental of a strings is the lowest note you get out of when it vibrate, which is normally the loudest you hear. Like the 6th string fundamental, when played open, is E.

Now you certainly understand harmonics of a strings. There is the 12th fret harmonic, the 7th, the 5th, etc, etc. (actually all frets have their own harmonic). When a string vibrate, all these harmonics vibrate with it at the same time, and that's when we call them overtones. The ability of a guitar to let you hear more overtones is usually described as a richer sounding guitar. (And a dull, or thin sounding guitar when less overtones are heared).

And yes, this aspect of the tone of a guitar is indeed one of the less subjective one.

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Alain Moisan
Former full time builder of Acoustics, Classicals and Flamencos.
(Now building just for fun!)

'Harmonic' overtones adds a bit of definition that helps me understand better..



Unless you want less overtones and more fundamentals because you think that sounds better - and I'm not trying to simply be contrarian because I've seen discussions just like that where it's preferred by some to have more fundamentals and less overtones for a very specific taste in tone, where less overtones sounds 'better'.

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Thank You and Best To All

Thanks Alain, that gives me something to listen for.



It seems I have also heard guitars described with fewer overtones as 'focused' maybe? Anything but dull and thin, curious.

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Thank You and Best To All

Well, that's totally possible. Here we start to slide toward subjective matters, so your milage may vary. Depending on the style played, one may want less overtones indeed. Like jazz players, for example, tend to like guitars with less overtones. When they may say 'focused', a player who likes to strum his dreadnought a lot will find it 'dull'.

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Alain Moisan
Former full time builder of Acoustics, Classicals and Flamencos.
(Now building just for fun!)

There is a big difference between words like "fundamental" and "overtones" vs. words like "warm" and "bright". The fundamental and overtones of a sound are physically describable phenomena. They can be shown mathematically and have an objective scientific definition (as given above). Terms like warm, focused, piano-like, rich, etc. are much more subjective and don't have a scientific definition. When two people listen to the same sound, one might call it warm while another calls it hollow. Someone might call a different sound bright while someone else thinks it sounds harsh.

The relative strength of the overtones is what gives an instrument it's voice or timbre or sound quality. Imagine a plot with frequency (note) on the x-axis and strength on the y-axis. If you play A (440 Hz) on your guitar, then that is the note you hear and it is usually (though perhaps not always?) the strongest harmonic. (Harmonics and overtones are almost interchangeable words. The fundamental is the first harmonic. All higher harmonics are overtones.) So on our plot we have a peak at 440 Hz, and then we will have another at 880 Hz, another at 1320 Hz, and so one with one at each multiple of 440 Hz (these are the harmonics). You don't hear these as additional notes, but they influence the character of the note (A 440) you hear. Imagine the peak at 440 Hz is the highest, then the one at 880 Hz is half as strong. But the peak at 1320 may be stronger than 880, only slightly weaker than 440. Then the harmonic at 1760 may be almost non-existent. (I'm making up the relative strengths as an example, I don't know exactly what it would look like.)

Now imagine somebody comes along and plays the same note (A 440) on an oboe. The pitch you hear is the same, but it sounds different. If you do the same plot, you will see different relative strengths. Maybe 440 is the highest, 880 is only slightly down, 1320 is very weak and 1760 is half as strong as 440. The relative strengths of the overtones are one thing that make an oboe sound different than a guitar. So guitars that have different timbres will also have different spectral shapes, though they won't differ as much as a guitar and an oboe. Note that when we talk about timbre we are really only looking the steady state characteristics of an instrument. Then there are also the transient characteristics (attach, decay, etc.) that have an effect as well.

Overtones can get even more complicated. If you have a choir singing a perfect fifth you will get one set of overtones. It will sound like there is another voice singing a higher note that no one is actually singing. Then when you add in the third, some overtones disappear while others emerge. On top of that, the overtones may seem to come from a particular spot in the room. Then there are UNDERtones. Physics says these don't exist, at least not like overtones in a string. But musicians often hear them. Is this an effect of the acoustics of the room? Or something within the complex frequency processing of the brain?

Fun stuff. /nerdTime

I was checking a post for accuracy in terminology (which is was) and found this little primmer that might help explain some stuff: http://www.physicsclassroom.com/Class/sound/u11l4d.cfm

Now something to consider which is really important when thinking about this stuff - each string and each note played on a guitar has an overtone series and the guitar itself has the same. I'm trying to think of an analogy and one could think of the resonances of the guitar itself as behaving like a graphic EQ on an electric guitar. The vibrating string provides energy at certain frequencies and then the guitar "amplifies" and "attenuates" certain frequencies depending on where its resonances lie.

I

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In the Gore/Gilet books, the sound of guitars is broken down and described in terms of hz.
Much like amps have both a treble and a presence knob.
And while it's still all subjective and stuff, it certainly helps one to describe a guitars sound in terms that are quantifiable.

Let's not forget that player technique has quite an influence on fundamental/harmonic content. If the open string is plucked lightly near the 12th fret, there will be more fundamental and less harmonic content than if the string is plucked sharply near the bridge. These are extreames, and even I can hear the difference.
I believe a responsive guitar can have strong fundamental, or strong harmonics, or both, depending on the player's technique.

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A man hears what he wants to hear, and disreguards the rest. Paul Simon

When a physicist talks about sound, they tend to break it down into sinusoidal components; 'pure' tones that can be added together to form more complex sounds. If you tap a tuning fork, the sound that it makes after the initial 'clang' is usually pretty close to a 'pure' sine wave tone, and it's pretty boring. Nobody goes to tuning fork concerts. For various reasons people prefer more complicated sorts of sounds, and strings can provide them.

It's possible, with an electronic driver, for example, to get a string going in such a way that it produces a 'pure' sine tone. Actually, you can get a really large number of these sorts of sound from a string. That's because the string is a 'distributed' system: every part of it has some mass and some elasticity, so each little segment can move differently from the one next to it, and that produces lots of possible way for one string to vibrate. The problem of analysis is usually to keep it from doing too many things at once! A tuning fork is actually just two 'simple' oscillators (the two arms) each of which can only vibrate at one audible pitch (the higher order vibrations are too high pitched to hear, or damp out really quickly: they're the initial 'clang'). The two arms are there to balance each other by moving in opposite directions, so that there's no net rotational force. They actually pull the stem up and down, which is why you can hear a tuning fork when the stem is held perpendicular to a table top. But I digress.

If you drive a string at it's lowest resonant pitch it will form a single loop, with each little section of the string going the same direction at any given time. This is the 'fundamental frequency' of the string. If the string is moving 'vertically' with respect to the soundboard, the end attached to the bridge will push the top in and out like a loudspeaker cone, and produce a lot of sound. If the vibration is 'horizontal', the main force will be across the top, but there will be a twice-per-cycle tension change that will tug the top of the saddle toward the nut, rocking the bridge. This is a smaller force (often around 10-15% of the 'transverse' force) and it drives the top less effectively, so it produces less sound. When I did this experiment on one string of a guitar the 'vertical' motion produced 20 dB or so more sound than the 'horizontal' (about 100 times as much. Again, I digress...)

It's also possible to use the same sort of rig to drive the string so that it makes two loops, or three, or four, or whatever. These will also be 'pure' tones, and will drive the bridge in a similar fashion. If you've got an 'ideal' string, these 'overtones' will be at exact multiples of the fundamental pitch; 2x, 3x, and so on. In this case they are called 'harmonics'. You can't buy 'ideal' strings any place; they are a textbook fiction. Ideal strings have mass and elasticity, but no stiffness: they have wight and can be taken up to tension, but if you held one by one end it would droop worse than cooked spaghetti. The stiffness of real strings adds to the restoring force of the elasticity to make the overtones a little sharper than they should be. The more the string has to bend, the the more sharp the overtones get, so the higher ones get pretty sharp, particularly on fat strings. This is a real problem on small pianos, but again, I digress. The point is that it's not technically correct to talk of the higher string overtones as 'harmonics', since they're not exact multiples of the fundamental, even though the first few are really close.

Another nomenclature that you run into (just in case you are not confused enough yet) is that of 'partials'. Each resonant pattern of the string (one loop, two loops,whatever) is a 'partial', so the fundamental is also the 'first partial', two loops make the 'second partial' and so on. One advantage of using the 'partial' nomenclature is that there's no implied relationship between partials: they can have any pitch they darn well please (and usually do).

So far we've been looking at a string that's being driven with a special driver at 'pure' pitches. How is plucking different? Well, imagine that you pluck a string exactly in the middle. The first partial/fundamental frequency of the string moves a lot at that point, so you'll get a lot of sound out of it. The second partial doesn't move at all there; it's two equal loops and that's the stationary point. Thus you can't drive the second partial by plucking in the middle. In fact, when you pluck there you get all the 'odd order' partials (1, 3,5,7,9, etc) going, and none of the 'even order' ones (2,4,6,8,10). That's why the string has the particular sound it does when you pluck in the middle. (Yeah, I know, it's not that simple. Remember the 'tension change' signal? It rocks the bridge at all the 'even order' pitches since it's at multiples of twice the fundamental, and the moving bridge reacts back on the string to cause it to vibrate with some even order energy. But, again, I digress).

The point is that any place you pluck on the string will be an 'active' point for some partials, and less active, or even a 'null' for others, so you'll get more or less energy at different frequencies depending on where you pluck, and the different mixes sound different. Any sound can be broken down into some mixture of partials that are more or less harmonically related, with different amplitudes and phase relationships, but you knew that. Our ears don't seem to use phase information to determine timbre, but it is important in locating a sound source in space, but this risks another complicated digression.

The guitar has it's own set of partials, 'tap tones' or whatever, and they can be more or less easily driven from the bridge, and produce more or less sound, depending on all the usual variables (the way the guitar was built, the wood, the relative humidity, the state of the stock market, the phase of the moon, whether Venus is in Sagittarius, the wholesale price of coffee on the spot market; the usual stuff). I'll note that it's not just the tap tone pitches themselves that matter: how easy it is for the energy from the string to get into the guitar (the top in particular) and how fast the guitar can turn it into sound matters too, In other words, it's not just the spectrum of the tone, but also the time history that counts.

We understand some of this, but not nearly as much as we'd like. In particular, I don't think nearly enough work has been done on the 'time' aspect of all of this, and how that contributes to the sound. What it all comes down to is that a particular instruments might tend to produce a sound that has more fundamental in it, or whatever. Now, whether that instrument actually strikes most listeners as having a 'fundamental' timbre is another whole can of worms: if you think physics is complicated, wait'll you get to psychoacoustics!

The problem with all of this is that while we may be able to scientifically, without a doubt, define what fundamentals and overtones actually are, as builders we are still dealing with players who tend to use these terms like they do all the others. In whatever way they wish.
In most of the guitar forum discussions I've read, in general a guitar that's more focused on the fundamental tone is a guitar that's very focused and clear, whereas with overtones a guitar can sound quite nice, but can also have so many of them that a particular player might find it a bit muddy. These definitions are from the players perspective, not builders. And even among players the definitions can differ.
And it doesn't matter how well we as builders can quantify the definition, it doesn't do a thing to change the average player's thinking on the subject. And they happen to be the ones we're building for. Therefore, they are the ones who will define what they mean. It's up to us to ask enough questions to get a good understanding of what they mean when they start throwing these terms around.

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Mike

The only thing nescessary for evil to thrive is for good men to do nothing.

Now I'm perplexed. I certainly agree with what Mr. Carruth has so clearly stated, but does that agree with what I said?

So my retorical question is "Which is more important in fundamental/partial content, the guitar itself or player technique?"

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A man hears what he wants to hear, and disreguards the rest. Paul Simon

"So my retorical question is "Which is more important in fundamental/partial content, the guitar itself or player technique?" "

That depends on both the guitar and the player. Some guitars will respond to the players technique to vary the strength of fundamental / partial strength, and some guitars will not. Some players have poor technique and can't effectively bring out the variety of tones a guitar might offer.

It is much easier for a player to damp overtones than it is to bring out overtones in a guitar that is weak in that regard. Guitars with stiff, lightweight tops tend to accentuate overtones. Euro spruce is famous for that characteristic. Sitka spruce is generally considered more fundamental in tone.
The type of pick (or fingers versus fingernails) can have a dramatic effect on the tonal 'color' (overtone content) that a guitar displays.
On many occasions, I have heard flattering comments that allude to the fact that the guitar sounds better when I play it. IMHO, it is largely a learned skill.

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John

There are a number of things that can kill overtones, but one of the biggies is high damping. This is really evident in strings.

Nylon strings have high damping, both intrinsically within the material, and also because, being fatter, they have to slosh their way through more air when they move. If you pluck a nylon string and a steel one in the same place with the same force, the initial sound will be the same, with the same number of overtones and the same energy in each one. After a second or so all of the high frequency is gone from the nylon string signal, while the steel string will still have plenty of energy out to 5-6 kHz. It's the fundamental difference between classical and steel string guitars, and accounts for most of the other differences in the designs.

The same is true of woods, of course. Redwood and Western red cedar have much lower damping than the spruces most of the time. The rosewoods are all known for having low damping; that long, clear 'ring' in the tap tone is the giveaway. From this, you'd expect that rosewood guitars with redwood tops would have lots of high frequency overtones in the sound, and might be considered 'bright'. Instead they are often thought of as 'full' or 'rich'. It's possible that part of that is the way the ears work. Given a stack of pretty much harmonic overtones, we tend to assign all of the energy in the sound to the fundamental., so it's possible that a tone with lots of strong harmonics will end up sounding 'full' rather then 'bright'. It also seems to me that instruments with a strong attack ad fast decay are often heard as 'bright' even when the spectrum doesn't have as much high frequency in it. This is some of what I mean by the complexity of pschycoacoustics. Add in the fact that everybody uses the tone descriptors differently, and it gets tricky. A big part of being a successful luthier is learning to decode what different players mean by 'bright' or 'balanced' or whatever.

Wow Al, after over 10 years of reading your posts I think I'm finally starting to understand what you're saying

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Steve Smith
"Music is what feelings sound like"

Al said," Nobody goes to tuning fork concerts" Made me laugh out loud. Good one, Al. :)

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Under Compensated Nut!

I liked that one too:) Also I notice you have a strange 'b' in the middle of your handle for no good reason.

Must be a Canadian thing.

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If trees could scream, would we be so cavalier about cutting them down? We might, if they screamed all the time, for no good reason. - Jack Handey

Steve Smith wrote:
"Wow Al, after over 10 years of reading your posts I think I'm finally starting to understand what you're saying."

Sorry about that: if I was any good at explaining this stuff, you'd have gotten it all by now. I'll try to do better.

Actually, these lists are a real help in that regard: I can gauge my progress by the number of 'huh? what?' replies that come back. The way I figure it, if I _really_ understand this stuff I should be able to explain it to almost anybody, so my ability to explain it is one measure of how well I know what I'm talking about. Just part of my effort to be sure I'm not fooling myself.

Sounded good to me Al!

Of course I'm still waiting to hear back from my R&D team with the ultimate confirmation or rejection of your oh so lovable "theories".....

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If trees could scream, would we be so cavalier about cutting them down? We might, if they screamed all the time, for no good reason. - Jack Handey