Some thoughts on guitar back and sides woods

  • door Guy D'haenens
  • 15 aug, 2017

Do we need expensive wood?

There's a story that the Spanish luthier Antonio de Torres, AKA the Stradivarius of the guitar, build in 1862 a good sounding 'spanish' guitar with a body made out of papier-maché. With that guitar, he wanted to prove that the top plate is responsible for the sound qualities and the character of a guitar.
Hundred years later, Ovation started creating excellent guitars with fibreglass bodies.

So, if papier-maché and fibreglass are suitable materials for guitar bodies, why does every luthier get excited about the tap tone of some hard-to-get back and sides sets? Is it because they are hard to get, is it because they are expensive or is it because some wood species really add so much depth and 'luminance' to the sound of a guitar?

From experience I can say that the type of wood used does matter: guitars build in a similar way with top plates cut from the same tree, using exactly the same bracing pattern, build simultaneously, will sound different depending on the wood species used for the back and sides. For instance: Mahogany, Rosewood and Monkey Pod have a noticeable longer sustain than Maple, while Mahogany, Monkey Pod and Walnut will produce a warmer sound than Bubinga and Kotibe. But the impact of different species of wood on the sound and on the colour of a guitar is only revealed if the correct construction methods are applied.
Sam Carcagno, a postdoc researcher at the Lancaster University in the UK, is conducting an online listening experiment similar to those of the Leonardo Guitar Research Project folks to determine the extent to which listeners can differentiate steel string guitar back and side wood. You can participate in this listening experiment via  http://www.psych.lancs.ac.uk/hearing/the-guitar-experiment/online-tests/ .

As far as the construction of acoustic guitars is concerned, there are 2 types of backs: reflexive and responsive. Reflexive backs are rather rigid and reflect the sound waves; responsive backs are flexible and act as a second membrane. Ovation guitars with their shell shaped fibreglass bodies are typical or rather obvious examples of guitars with a reflexive back. But there are also many all-wood guitars with reflexive backs; most of them are made of high quality veneer covered plywood. The only way to distinguish the difference in type of back on an all-wood guitar is to pick it up. Guitars with reflexive backs are noticeable heavier due to the thicker back and the heavier bracing.

Building a fine guitar with a reflexive back takes less skill than for one with a responsive back simply because there's only one membrane: the top plate. Responsive backs have 2 membranes and both membranes have to work together to enhance each others frequencies and voice. If they are not in symbiosis, the sound is muffled, the guitar lacks power and luminance and playing such a guitar will be as exciting as tapping on an empty cigar box.

When it comes to choose between a guitar with a reflexive or a responsive back, the only point of consideration is the type of music you want to play on it. A guitar with a reflexive back is very well suited for music styles where a loud and 'less sophisticated' sound is appropriate such as in pop music but it can be used with great results for ragtime and fingerpicking too (Marcel Dadi used many types of Ovations on his recordings and on stage).
Guitars with a responsive back are used whenever a well-balanced and more sensitive sound is required: instrumentals, ballads, singer-songwriters performing solo, unplugged recordings, ...

While guitars with a reflexive back are all more or less in the same price range, prices for guitars with responsive backs can really rock the sky. These price tags not only reflect the qualities of the guitar but also the looks, the exuberance and the scarcity of the sometimes endangered woods. For instance, Brazilian Rosewood, the so called Holy Grail of Guitar Woods, has a price tag of $1000 and up for a back and sides set. In general, figured wood is more expensive because it's hard to find: only 1 to 1000 trees exhibit quilt or any other special figure.
Is this price tag a guarantee for a better guitar? Not really. The choice of wood is important but the dominant factor is the luthier who makes a guitar out of it. The ideal piece of wood, whether it is to be used for a top or for a back, should be quarter sawn. But quarter sawn wood doesn't exhibit lots of figure; extravagant figure is only obtainable in slab sawn or less quarter sawn. So, the heavier the figure, the higher the skills that are needed to create a top instrument.

As I've said before: don't buy a guitar only for its looks unless you can afford a bad bargain. If you want a guitar with a back with lots of figure, don't settle for the first one you see. Luthiers who know how to build an excellent guitar out of highly figured woods do exist.

Guy's Blog

door Guy D'haenens 15 aug, 2017

It’s cold and it’s freezing outside. -8°C.
Inside the house, it’s warm and cozy with family and friends dropping in for Christmas and New Year. But do you think that your precious guitar is having a good time too? Well, think again.

Wood is a living organism, even if the tree it originated from was harvested 20 years ago. It will keep on expanding and shrinking as the relative humidity of the air it is surrounded with changes. In the summer, when relative humidity levels are sometimes as high as 70%, the overall size of a piece of wood will be greater than in the winter when the freezing cold and the cranked up heating of our living room has squeezed out the last bit of moisture in the air. Although the changes affect the length, width, height and weight of a piece of wood, the differences are most notable along the width (across the grain) and have a greater affect on slab-sawn wood than on quarter-sawn wood (figure 1). That is one of the reasons why luthiers insist on using quarter-sawn tops and backs.

door Guy D'haenens 15 aug, 2017

The traditional way of attaching a guitar neck to a body of an acoustic guitar is by fitting a precisely cut dove tail tenon into a dovetail mortise that is cut out of the guitar body. The fit should be so precise that almost no glue is needed to hold the two pieces together. This type of guitar neck is called a “set neck”.
As you probably can image from the illustration below, cutting a tenon and a mortise with that precision is not an easy thing to do. It takes years to master. Even with the help of a router, the fit must be hand-tailored to ensure that all the sides of the tenon and mortise are flush and meet with a maximum tolerance of a thousand of an inch. The idea that glue can fill gaps and still hold wood together is an illusion. Glue – even epoxy – works on the principle of (molecular) adhesion and has no strength in itself. The difficult part is that the neck is slightly tilted backwards and the slant of the dovetail of the tenon is not the same as the one of the mortise. It takes a lot of time to get a perfect fit, believe me. But when it’s perfect, the neck is no longer a vibration absorbing piece of wood but a sound transmitter to the body. As it should be.

A less time-consuming way of attaching a guitar neck to a guitar body is by using bolts. There are no difficult dovetail cuts involved here, only a straigth tenon and mortise. And the biggest advantage from my point of view is that the neck can be attached and removed until a perfect fit is achieved. Bolting a neck is by no means an excuse for sloppy work or cutting a tenon that doesn’t fit perfectly into the mortise.

door Guy D'haenens 15 aug, 2017

Some years ago, I was in a renowned guitar shop when I overheard a conversation between a young female guitarist and the shop owner who also happens to be a fine guitarist. She told him about the difficulties she had playing bar (barre) chords. His answer was that she’d have to practice more to enforce finger strength. Looking at his hands and large muscular fingers, it was obvious that he had no problems whatsoever with bar chords. Although I didn’t interfere, I felt that his answer was a bit short-sighted. Guitarists with small/tall and less muscular fingers can practise all day and yet never reach that level of ease with bar chords. IMO, he should have told here that she could go for a guitar with a shorter scale or for strings with less tension. That would have solved her problem.

Strings with less tension
Every guitar is set up for a particular string gauge. This gauge is an indication that the company or person who created the guitar thinks that with this particular gauge, the best sound is achieved and the risk of structural damage is minimized. You, the owner, may disagree and opt for a lighter or heavier gauge.
Light gauge strings will be more comfortable because they are easier to fret and bend. The opposite goes for heavy gauge strings: harder to fret and quite difficult to bend.
Another option is to stick with the same gauge but choose strings with less tension such as the well-known “Silk and Steel” strings or the Newtone Heritage strings which are designed to have a reduced and almost equal tension on each string.

When you start searching for strings with less tension, you will find that only a few string manufacturers publish tension tables. If you are fond of a certain brand, you might contact them directly and ask for advice.

You may find that by using strings with less tension, the action of the guitar (the height of the strings from the fingerboard at the 12th fret) is decreased and by using strings with more tension the action is increased. In both cases, you probably will have the truss rod adjusted and the saddle adjusted or replaced by a qualified repair person or guitar builder. Apart from that, switching gauges may also require the nut slots to be filled (lighter gauge = smaller diameter) or filed (heavier gauge = larger diameter). These adjustments are reversible and require only a small investment in time and/or money.

All this being said, putting strings with less tension on a guitar with heavy or even normal braces could be disappointing: because the strings have less mass and tension, the decreased transfer of energy to the top plate could result in a weak, tiny tone which even playing harder won’t solve. The positive news is that you won’t inflict any structural damage to your guitar.
I would definitely advise you against putting strings with higher tension on a guitar with normal or light braces. You will have a guitar with a strong tone and increased fundamentals but only for a short time. The immense pull of the strings will make the belly of the guitar swell with the risk of braces falling off (literally), the top plate cracking (presumably on both sides of the glue joint) and an action so high no truss rod adjustment can cure.

The golden rule is: only go 1 gauge up or down. If the recommended gauge for your guitar is 12, go no further than 11 or 13. If you are not sure about the recommendation, inspect the braces of your guitar or have them inspected by a luthier to see which gauge would be suited.

If changing strings is not satisfactory, start looking for a guitar with a short scale.

Short scale guitars
You can easily check how a short scale guitar feels by tuning the guitar half a note down (to D#A#F#C#G#D#) and putting a capo on the first fret. The increased comfort in fretting the guitar will be quite notable. If you don’t mind the capo, the fact that you’ll only have 11 frets from nut to body and in most cases a slightly weaker tone , this trick might just work for you.

But how comes that this 5.6% reduction in length has such a major effect on comfort?
Each string has to be tuned to a certain pitch. The longer the string, the more it has to be stretched to obtain that pitch. And by stretching a string, it becomes less flexible and thus harder to fret. It is that simple.
So why does everybody use larger scales then? Well, the answer is also simple: shorter and more flexible strings have the tendency to act more “floppy” which reduces the time they can exert force to the top plate and produce sound. A guitar with a longer scale will sound fuller and richer with more overtones than a guitar with a short scale. Unless… the short scale guitar was build by a good luthier.
Note that the scales of electric guitars are shorter than the scales of acoustic guitars. As electric guitars don’t rely on the transfer of energy to the top plate but on the changes in the magnetic fields of the pickups, they benefit hugely from “floppy” strings.

Where am I heading at? In a world where mass production is the only way to reduce costs, chances that you will come across a good sounding short scale mass production acoustic guitar in a shop are almost nil. There is simply not enough demand to justify the production setup nor the distribution. Fitting a shorter neck to a regular body simply won’t do, the body size too has to be slightly smaller and the braces have to be lighter and shaped differently.
In short: if you want a good sounding short scale guitar, contact a luthier. He or she can do wonders for you.

door Guy D'haenens 15 aug, 2017

Guitar players who go out to buy a guitar hardly ever think about string length and the number of frets clear to the body. That is because there isn’t much of a choice. All the major acoustic steel string guitar building companies standardize on 25.34″ and 25.51″ and 14 frets. Once in a while, you can come across a 12 frets 0, 00 or 000 model that is sold as a “blues” guitar. And yet, the string length and the number of frets is not an axiom.

The first acoustic steel-string guitars had 12 frets from nut to body and various string lengths ranging from 23.5″ (59,7 cm) to 26.38″ (67 cm). This variation is easily explained by the fact that all those guitars were made by hand in small shops or ateliers. The Martin guitar company was one of the first to offer standardized models. One of their first models (1860-1870!) was almost an exact copy of a ‘Spanish’ guitar with 12 frets clear to the body: the 0-model. In 1877, they released a guitar with a slightly larger body, the 00. In 1902, model 000 was released and this model became the flagship of the company until the end of the roaring twenties. Tens or hundreds of each model were sold which was, taken into account that guitars were far less popular than banjos and mandolins, a very good sales figure.

In 1929, Perry Bechtel, an extremely popular and talented banjo player and guitarist, approached Martin III asking to build him a 000-model with 14 frets clear to the body so he could use the higher register of the guitar just like he was used to on his tenor banjo. He also asked for a solid peghead – also like on a banjo – and a louder sound. A couple of months and several modifications later, Bechtel received his OM (orchestra model) and started performing with it. The guitar became so rapidly popular that by 1933, the OM-model with its 14 frets became the standard model for Martin. After 1933, Martin added an ‘S’ to the names of all 12-frets guitars. ‘S’ for standard, not for the slotted peghead as many assume. In short, this is how the OM-model became the standard for all acoustic steel-string guitars. In figure 1 you can clearly see the evolution of these models. 0-28 and 00-28 both have a 24.9″ (63,9 cm) scale length while 000-28 and OM-28 have a slightly larger 25.4″ (64,36 cm) scale length.

door Guy D'haenens 15 aug, 2017
There's a story that the Spanish luthier Antonio de Torres, AKA the Stradivarius of the guitar, build in 1862 a good sounding 'spanish' guitar with a body made out of papier-maché. With that guitar, he wanted to prove that the top plate is responsible for the sound qualities and the character of a guitar.
Hundred years later, Ovation started creating excellent guitars with fibreglass bodies.

So, if papier-maché and fibreglass are suitable materials for guitar bodies, why does every luthier get excited about the tap tone of some hard-to-get back and sides sets? Is it because they are hard to get, is it because they are expensive or is it because some wood species really add so much depth and 'luminance' to the sound of a guitar?

From experience I can say that the type of wood used does matter: guitars build in a similar way with top plates cut from the same tree, using exactly the same bracing pattern, build simultaneously, will sound different depending on the wood species used for the back and sides. For instance: Mahogany, Rosewood and Monkey Pod have a noticeable longer sustain than Maple, while Mahogany, Monkey Pod and Walnut will produce a warmer sound than Bubinga and Kotibe. But the impact of different species of wood on the sound and on the colour of a guitar is only revealed if the correct construction methods are applied.
Sam Carcagno, a postdoc researcher at the Lancaster University in the UK, is conducting an online listening experiment similar to those of the Leonardo Guitar Research Project folks to determine the extent to which listeners can differentiate steel string guitar back and side wood. You can participate in this listening experiment via  http://www.psych.lancs.ac.uk/hearing/the-guitar-experiment/online-tests/ .

As far as the construction of acoustic guitars is concerned, there are 2 types of backs: reflexive and responsive. Reflexive backs are rather rigid and reflect the sound waves; responsive backs are flexible and act as a second membrane. Ovation guitars with their shell shaped fibreglass bodies are typical or rather obvious examples of guitars with a reflexive back. But there are also many all-wood guitars with reflexive backs; most of them are made of high quality veneer covered plywood. The only way to distinguish the difference in type of back on an all-wood guitar is to pick it up. Guitars with reflexive backs are noticeable heavier due to the thicker back and the heavier bracing.

Building a fine guitar with a reflexive back takes less skill than for one with a responsive back simply because there's only one membrane: the top plate. Responsive backs have 2 membranes and both membranes have to work together to enhance each others frequencies and voice. If they are not in symbiosis, the sound is muffled, the guitar lacks power and luminance and playing such a guitar will be as exciting as tapping on an empty cigar box.

When it comes to choose between a guitar with a reflexive or a responsive back, the only point of consideration is the type of music you want to play on it. A guitar with a reflexive back is very well suited for music styles where a loud and 'less sophisticated' sound is appropriate such as in pop music but it can be used with great results for ragtime and fingerpicking too (Marcel Dadi used many types of Ovations on his recordings and on stage).
Guitars with a responsive back are used whenever a well-balanced and more sensitive sound is required: instrumentals, ballads, singer-songwriters performing solo, unplugged recordings, ...

While guitars with a reflexive back are all more or less in the same price range, prices for guitars with responsive backs can really rock the sky. These price tags not only reflect the qualities of the guitar but also the looks, the exuberance and the scarcity of the sometimes endangered woods. For instance, Brazilian Rosewood, the so called Holy Grail of Guitar Woods, has a price tag of $1000 and up for a back and sides set. In general, figured wood is more expensive because it's hard to find: only 1 to 1000 trees exhibit quilt or any other special figure.
Is this price tag a guarantee for a better guitar? Not really. The choice of wood is important but the dominant factor is the luthier who makes a guitar out of it. The ideal piece of wood, whether it is to be used for a top or for a back, should be quarter sawn. But quarter sawn wood doesn't exhibit lots of figure; extravagant figure is only obtainable in slab sawn or less quarter sawn. So, the heavier the figure, the higher the skills that are needed to create a top instrument.

As I've said before: don't buy a guitar only for its looks unless you can afford a bad bargain. If you want a guitar with a back with lots of figure, don't settle for the first one you see. Luthiers who know how to build an excellent guitar out of highly figured woods do exist.
door Guy D'haenens 15 aug, 2017

When you’re into steelstring guitars you may have noticed that nowadays the type of bracing is almost always mentioned in the specifications. So it seems that the type of bracing is quite important to the sound of a guitar. Or not?

Well, let me first explain what bracing is all about. In a next post, I’ll talk about the different types of bracing.

Bracing is the combination of wooden bars glued to the underside of a guitar top to give the top plate  enough strength to withstand the enormous amount of pull exerted by the strings. Without bracing, the guitar would get completely deformed once you start tuning the guitar: the area in front of the bridge would be pressed down and the area behind the bridge would get pulled up. Imagine the curves of the letter S. The seam (where the two halves of the top plate are glued together) would last only a couple of hours before opening up. And in case the seam would hold, the top plate would crack on both sides of the seam.

So, the solution is to reinforce the top plate. But how? Adding extra wood to the underside of the top plate changes the way the top plate reacts to the  altering tension of the strings. To much wood has a deadening effect to the sound whilst not enough wood will fail to hold the top plate intact. And where should those little bars be placed?

All modern bracing patterns on steelstring guitars are based on the bracing of the early Martin-guitars. C.F. Martin, a German immigrant to the USA, built originally small ‘classical’ guitars. Classical guitars have a very light bracing: 5 to 7 flat wooden strips glued in a fan shape just underneath the bridge. Don’t forget we’re talking about gut strung guitars - nylon wasn’t invented yet - and of guitars that were most of all used in the outback by cowboys.

With the emerge of steel strings (not of the quality we know of today), Martin wanted to put those new gimmicks on his flat-top guitars and had to come up with something more rigid. After a few attempts, he finally settled for an X-shaped pattern of quite massive tall bars. The cross was placed just two inches or so in front of the bridge to counteract the downward pressure of the forward tilting bridge. To prevent the pulling up of the belly (the area behind the bridge), he installed long diagonal bars. On the outer sides of the X he installed small ‘finger braces’ and where the fretboard is glued to the top a fairly massive bar to counteract deformation caused by the fretboard. And it worked. The tone of the guitar was completely different but who cared, it was a different instrument with a different, much louder sound. Those steelstring guitars became rapidly very popular and other guitar builders soon followed.

Sure, there have been guitar builders who tried out other bracing systems - Mario Maccaferri (the ‘inventor’ of the gypsy-style guitar) to name one. And I have to admit, I too tried out a bracing system of my own invention for a while. The sound was great but the belly of my guitars started to deform after a year or so. Now I stick to a variation of Martin’s tried and tested X-bracing.

Frank Ford has a  fine collection of photo’s of top-braces  on his excellent website.

Now that we have answered the question of where those braces should be placed, we still have to deal with the effect of braces on the sound of a guitar.

Think of a top plate as a massive membrane. The strings put the membrane in motion (up and down, swivelling and tilting) and by doing so, the membrane compresses and expands the volume of air inside the guitar box. And it is this compression/expansion of air that creates sound. In order to get a sound that is both pleasing and full of expression, the membrane must be flexible in multiple but controlled ways. It shouldn’t be floppy but not to rigid either. And it’s in ‘tuning’ this membrane that the real craft shines. The species of wood used for the top plate, for the braces and for the protective strip under the bridge, the thickness of the top plate, the width, the height, the shape and the position of the braces, the thickness of the protective strip and the thickness and shape of the bridge itself, the height of the saddle... everything has to match. And the main problem - or the genius - is that, even with the same procedures, every guitar will have it’s own voice. The differences will be small but obvious to the trained ear. The reason for this is that very, very small differences in amount of moisture, the internal structure of the wood used to create the braces and the top plate, even the type and amount of glue used to hold everything together can result in a slightly different colour of sound.

Every guitar builder has his or her own methods to test if the top plate has the right resonance and flexibility. Most of them, me included, tap the top plate at various positions while holding the top plate between thumb and forefinger right beside the ear. Others test the flexibility by exerting a certain amount of force on the top plate. And those who have access to sophisticated tools use frequency tests. The Kungl Tekniska Högskolan of Sweden  published in 2002 a  very interesting paper  on those tests.

There is no such thing as the golden formula, there are hundreds of formulas, and each guitar builder does his utmost to create the ultimate sound. Some stick to a method that works for them, others try to improve constantly by experimenting. Large guitar building companies have optimised their construction methods to manufacture guitars of a relative constant quality at a high output volume. But don’t be fooled, even factory guitars of the same type and brand can have enormous differences in quality and sound for the reasons mentioned above.

Ultimately, it’s up to you, the guitar player, to keep on searching until you find the guitar with the sound of your dreams.

door Guy D'haenens 13 aug, 2017

In my previous article I referred to the pictures of braces taken by Frank Ford. As you may have noticed, almost all guitar models depicted have scalloped braces. Scalloped braces look neat; it’s almost like one is looking at a modern bridge.

If the big guitar manufacturing companies put them on their tops, then it must be a good thing to do. Or not?

Braces are wooden bars glued to the underside of a guitar top plate. Flat wide bars are very flexible but have little strength while tall small bars are less flexible but possess huge strength. Nylon strings exert only a limited amount of stress on a top plate. So it’s only natural that guitar builders put flat wide bars on a classical guitar. Steel strings on the other hand exert a huge amount of stress on a top plate. Only a top with tall small bars will be able to withstand that kind of stress.

After the braces have been glued to the underside of the top plate, they have to be shaved, scraped and sanded. This is all part of the "tuning" process. The goal is to end up with a strong yet flexible top plate.

In order to give the braces just the amount of flexibility we look for in a well voiced guitar, one can (or use a combination of):

  •             taper the ends
  •             use parabolic shaped braces
  •             scallop the braces

Taper the ends

A flexible guitar top is a membrane. In order to get a flexible top, braces are tapered or scalloped towards the end. Thinner ends allow the top to vibrate more easily. The amount of taper or scallop is very important. A scallop that is too steep will have little or no effect, too long a scallop will weaken the brace significantly.

door Guy D'haenens 12 aug, 2017

Guitars are designed for the 12-tone equal tempered tuning (12-TET). In a 12-tone equal tempered tuning, an octave is divided in 12 semitones at an equidistance of each other: C, C# or Db, D, D# or Eb, E, F, F# or Gb, G, G# or Ab, A, A# or Bb, B.
12-tone equal tempered tuning assumes that e.g. C# is soundwise exactly in the middle of C and D. As you could have guessed, in real life it’s not, it’s only in the mathematical middle and soudwise a bit on the sharp side.

Guitars and all other instruments are tuned at A4= 440 Hz. In 1939 musicians world-wide came to a consensus on that pitch. Before that time, the pitch had been 435 Hz, 374 Hz (1648) and 503 Hz (1361) but those were merely guidelines. Each maestro was free to compose or direct at a lower or higher pitch.
(Hz is the unit to express the number of oscillations of pressure in a sound wave. 440Hz means that there are 440 oscillations per second.)

When you pull an unfretted A-string on a tuned guitar, you’ll hear 110 Hz. When you fret that string at the 12th fret, you’ll hear 220 Hz. That’s exactly the double. Double or half the Hz of any tone is called an octave. Fret that string at the 24th fret and you’ll hear 440 Hz, again one octave higher or 2 octaves higher than the tone of the unfretted string. What you have done each time, is shorten the string by half. A shorter string vibrates at a higher speed thus producing more oscillations per second. A string at 440 Hz oscillates twice as fast as a string of double that length.

The guitar is fretted so we can easily pick the correct notes. Those frets are laid out according to a simple calculation.
Assume that the scale length of your guitar is 25.4″ (actually it’s 25,34″) or 643,636 mm. The scale length is the distance between the nut and the top of the saddle. The 12th fret will be exactly at 12.7″ (25.4″/2) or 321,818 mm. And since an octave in a 12-TET scale is divided in 12 semitones at equidistance of each other, the math should be fairly simple, no? Alas, dividing 12.7″ by 12 won’t do. That is because we can’t use the distance as input for our calculations, we have to use the frequences. In a 12-TET scale, the ratio of frequencies between two adjacent semitones is the twelfth root of two. And the twelfth root of two is 1.0594630943593.

So starting from the 12th fret, the exact position of the other frets is easily calculated by multiplying or dividing the position of a (previous) fret with 1.0594630943593.
The position of the 11th fret is 340,9543 mm (321,818 * 1,0594630943593); the position of the 10th fret is 361,2626 mm (340,954294100521 * 1,0594630943593); that of the 13th fret is 303,7557 mm (321,818 / 1,0594630943593) and so on.

Another way to determine the fret positions is by using the constant 17.817. The scale length divided by this value gives us the distance from the nut to the first fret.
The following table will make it more clear:

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