The Heart of the Matter: The Formula of Equable Temperament<\/h2>\n\n
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\n<\/div><\/p>\n\n\n\nLet's start from the beginning. Why do guitar strings have to be divided in a certain way? The answer lies in the concept of equable temperament<\/strong>. Without going too much into the details of music theory, imagine having to divide an’octave (the interval between a note and the same note higher or lower) into twelve equal semitones. If we did this with a simple arithmetic division, the guitar would sound out of tune as we go up the fretboard.\n\nInstead, equal temperament mathematically distributes these twelve divisions so that each semitone has the same frequency ratio as the previous one. This ratio è the twelfth root of 2, or approximately 1.0594635. It è a fixed number, a universal constant for all modern fretted instruments.\n\n<\/p> \n\nFrom that ratio derives our “magic number”: 17.81702. This value è the result of 1 divided by (1 – 1\/1.0594635). In practice, it tells us that to find the position of the next fret, we must divide the length of the remaining string by this number. È a constant that enormously simplifies the luthier's life.\n\nThe basic formula for calculating the distance of each fret from the bridge (or rather, from the bridge saddle, the string's contact point) è the following:\n\n<\/p> Key distance \n\nWhere:\n<\/p> \n\nOr, and this is the method I prefer for its practicality in the garage, we can calculate the distance of each fret from the nut<\/em> (or from the zero fret<\/em>) in sequence, or the distance between one key and the next.\n\n<\/p> \n\nBefore doing any calculations, we must decide the scale length<\/strong> (scale length<\/em>) of our guitar. This value, often called scale length<\/strong>, is the distance between the nut (or nut<\/em>) and the bridge saddle (saddle<\/em>). It is the vibrant heart of the instrument and determines the string tension, the timbre and, of course, the fret spacing.\n\nThe most common scale lengths are:\n<\/p> There are no hard and fast rules. You can choose the scale length you prefer, even a non-standard one, but you must be aware of the implications for tension and intonation. The fundamental thing è to be precise to the millimeter in its initial definition, because every subsequent calculation will depend on this value.\n\nA common mistake, which I also made the first few times, è to confuse the total length of the neck with the scale length. The scale length è only the part vibrating<\/em> part of the string. Make sure to measure from the exact point where the string rests on the nut to the point where it rests on the bridge saddle.\n\n<\/p> \n\nNow that we have understood the theory, let's move on to practice. Let's take a common scale length, for example 25.5 inches (647.7 mm)<\/strong>, and let's calculate together the positions of the first frets. We will use the most common and intuitive method for DIY: calculate the distance of each fret from the nut.\n\nFor our calculations, we will use the precise value of 17.81702. Keep a scientific calculator handy or, even better, a good spreadsheet.\n\n<\/p> \n\nOur scale length is 647.7 mm. The nut is the starting point, 0 on our measurement scale.\n\nTo find the distance from the nut to the first fret, we apply the formula:\n\n<\/p> Distance from the nut to fret 1 = Scale length \/ 17.81702<\/strong><\/p> Fret 1 Distance = 647.7 mm \/ 17.81702 ≈ 36.353 mm<\/p> \n\nThis means that the center of the first fret slot must be 36.353 mm from the edge of the nut.\n\n<\/p> \n\nNow, for the second fret, the vibrating string length remaining<\/em> is the scale length minus the distance of the first fret from the nut.\n\n<\/p> Remaining length after fret 1 = Scale length – Distance Fret 1 from the nut = 647.7 – 36.353 = 611.347 mm<\/p> \n\nNow we calculate the distance between the first and second fret:\n\n<\/p> Distance Fret 2 from Fret 1 = Remaining length after fret 1 \/ 17.81702 = 611.347 mm \/ 17.81702 ≈ 34.312 mm<\/p> \n\nSo, the total distance from the nut to the second fret will be:\n\n<\/p> Distance Fret 2 from the nut = Distance Fret 1 from the nut + Distance Fret 2 from Fret 1 = 36.353 mm + 34.312 mm = 70.665 mm<\/p> \n\nSee? Each calculation is based on the length of the string that remains<\/em> from the previous fret. It's an iterative process.\n\n<\/p> \n\nWe repeat the same process for all frets. Here I show you a table with the first frets and then the key frets to give you an idea of how the distances progressively reduce. We will always use a scale length of 647.7 mm.\n\n<\/p> Note the 12th fret: it is exactly half of the scale length (647.7 mm \/ 2 = 323.85 mm). This is a fundamental check. If the 12th fret is not exactly in the middle, something is wrong with the previous calculations.\n\nAnd we continue up to the 22nd fret, which is a common configuration for many guitars:\n\n<\/p> \n\nAs you can see, the distances between the frets progressively decrease as you move away from the nut. This precision is vital. An error of even just 0.1 mm on a fret can affect the intonation, and the effect becomes more evident on higher frets, where the distances are smaller and the percentage error is greater.\n\n<\/p> \n\nWhen you do the calculations, don't round too early. Keep at least 3-4 decimal places for all intermediate calculations. Only at the end, when you have the definitive measurement for each fret, can you round to 2 or 3 decimal places for marking, depending on the precision of your measuring instruments. I usually stop at a hundredth of a millimeter, which is the maximum precision I can achieve with my digital caliper.\n\nA common mistake I made at the beginning was rounding too early, perhaps to the millimeter. This may seem insignificant, but when errors are summed over 22 frets, the guitar ends up sounding out of tune. It's like building a wall: if the first stone is crooked, all subsequent ones will be even more so.\n\n<\/p> \n\nCalculating distances è a great start, but there are other factors that influence the precision of intonation and the playability of the neck. They are not directly related to the calculation of fret distances<\/strong>, but they are aspects that every hobbyist builder should know.\n\n<\/p> \n\nYou will have noticed that the bridge saddles are never perfectly aligned. This is not a manufacturing error, but a necessary feature called compensation<\/strong>. The strings, when pressed on the fret, do not vibrate exactly at the theoretical length. The tension increases slightly, and this causes the note to sound a little higher. To compensate, the string length is slightly extended at the bridge.\n\nEach string needs a slightly different compensation due to its thickness and tension. Thicker strings and wound strings (like the low E) require greater compensation than thinner plain strings. This is why the saddles of a Tune-o-matic bridge or a Stratocaster bridge are individually adjustable.\n\nWhen we calculate the scale length, we do it from the nut to the ideal intonation point of the saddle, which is a point medium<\/em> or theoretical<\/em>. The fine adjustment of intonation will occur After<\/em> when the guitar è assembled and the strings are mounted, by moving the saddles forward or backward. For us who cut the frets, the important thing è that the initial scale length è correct.\n\n<\/p> \n\nSome guitars, especially vintage or more modern designs, use a zero fret<\/strong>, or a fret positioned exactly where the nut is usually located. In this case, the nut only functions as a lateral string spacer, but does not affect the height or the vibrating length of the string.\n\nIf your guitar has a zero fret, the calculation of fret distances becomes even simpler, because the starting point for measuring the scale length is exactly the center of the zero fret itself. You won’t have to worry about nut compensation (which is another thing, but we’ll talk about that another time). For a hobbyist, the zero fret can simplify life a bit.\n\n<\/p> \n\nThe fretboard radius (fretboard radius) is the curvature of the fretboard surface. It does not affect the<\/em>) è the curvature of the fretboard surface. It does not affect the guitar fret distance<\/strong> longitudinal, but it is fundamental for comfort and playability. A smaller radius (e.g. 7.25″) is more curved and typical of vintage guitars, great for chords but less comfortable for bending. A larger radius (e.g. 12″ or 16″) is flatter, ideal for bending and for a modern style.\n\nMany modern guitars use a compound radius<\/em>, where the radius gradually changes from the nut to the bridge, becoming flatter as you go up the fretboard. Although not directly related to the calculation of distances, it è an aspect to consider when designing the neck. A well-matched fretboard with the right radius è a pleasure to play.\n\n<\/p> \n\nFor the more adventurous, there are necks multi-scale<\/strong>, or fanned frets<\/em>. Here, the scale length is not fixed, but varies from string to string. The low strings have a longer scale (for greater definition and tension), while the high strings have a shorter scale (for easier bending).\n\nIn this case, calculating fret distances becomes much more complex, because each string has its own set of distances, and the frets are not parallel to each other, but “fanned”. It is not a project for beginners, but the basic principle of equal temperament remains the same for each individual string. It is an example of how basic mathematics adapts to extreme configurations. I myself have a multi-scale project in the works, but it's not yet time to talk about it.\n\n<\/p> I cannot stress it enough: precision is crucial. An error of 0.1 mm on a single guitar fret distance<\/strong> It may seem negligible, but it adds up. If the first fret is slightly out of place, all subsequent frets will be even more so. The final result will be a guitar that, even if tuned, will sound out of tune in some positions.\n\nI had a guitar with a neck that I had fretted in a hurry, thinking that 'a millimeter more or less doesn't make a difference'. Wrong. When I tried it, every chord sounded slightly 'dead', and solos in the high positions were a nightmare. I had to redo all the work, and believe me, it's much more painful than doing things right the first time.\n\n<\/p> \n\nUnderstanding the formula is fundamental, but manually calculating all the fret distances<\/strong> for 22 or 24 keys, maintaining decimal precision, it is a long, tedious and high-risk job for errors. This is where technology comes in.\n\nFor this reason, here at Biafax we have developed a free Fret Slot Calculator<\/strong>. It's a tool I created precisely because I was tired of doing calculations by hand or looking for Excel sheets online that didn't always work as I wanted.\n\n<\/p> \n\nUsing it is very simple:\n<\/p> \n\nThe calculator will return a detailed table with:\n<\/p> \n\nAll with the highest possible precision, using the exact value of 17.81702 and keeping all necessary decimals. You can print the table and use it as a reference on your workbench.\n\n<\/p> Speed:<\/strong> Get all measurements in a few seconds.<\/p> Precision:<\/strong> You eliminate the risk of manual calculation errors and premature rounding.<\/p> Reliability:<\/strong> Our calculator has been tested and validated on numerous projects. I have used it myself for my necks, and it has never let me down.<\/p> \n\nConsider it a virtual assistant that does the heavy and tedious work, leaving you free to focus on the manual and creative part of your project. È an example of how digital tools can simplify the life of the DIY luthier, making processes accessible to everyone that once required advanced mathematical skills or the purchase of expensive pre-calculated rulers.\n\nOnce you have the fretted neck and the grooves ready, the next step è the installation of the frets themselves, another phase that requires attention and the right tools. But it doesn't end here: once you have the fretted neck, you might want to delve deeper into how to best adjust your guitar. Check out our complete guide on how to modify your guitar<\/a> to optimize every aspect, from action to intonation.\n\n<\/p> \n\nOnce you have your numbers, you need to transfer them to the fretboard. And here, the precision of the tools is as crucial as the precision of the calculations.\n\n<\/p> Precision Digital Caliper:<\/strong> It's your best friend. A good digital caliper allows you to measure with precision to the hundredth of a millimeter. Forget tape measures or school rulers. A decent caliper costs little, and it will pay you back in accuracy and fewer frustrations.<\/p> Precision Carpenter's Square:<\/strong> To draw perfect perpendicular lines on the fretboard. A good square is essential to ensure that the frets are straight and not fanned (unless it's an intentional multi-scale project!).<\/p> Marking Point (Scriber):<\/strong> Much better than a pencil. A fine metal point engraves a thin and precise line, without the variable thickness of a graphite lead. This is fundamental to avoid marking errors.<\/p> Sturdy metal ruler:<\/strong> To be used with the marking point. It must be straight, without flexing, and preferably with a beveled edge for greater precision.<\/p> \n\nI remember trying to use a pencil for the first fretboard. The result? Thick, imprecise lines, and a mess of graphite everywhere. Since then, only a scribing tool. It's a small investment that makes a big difference.\n\n<\/p> \n\nI've made every conceivable mistake, so let me share some of my “lessons learned” to help you avoid the same frustrations.\n\n<\/p> The problem:<\/strong> Measuring the scale length from the wrong point, or not being precise. Perhaps measuring to the edge of the bridge, instead of the center of the theoretical saddle. Or rounding the initial measurement too much.<\/p> Mimmo's lesson:<\/strong> First of all, precisely decide your scale length. If it's 25.5 inches, convert it to millimeters (647.7 mm) and use it with that precision<\/em>. If you use a Tune-o-matic bridge, consider the ideal intonation point of the saddle as a reference for the total scale length, not the outer edge of the bridge. When you mark the nut line, make sure it is your absolute zero point.<\/p> The problem:<\/strong> Rounding intermediate results to a few decimal places or, worse, to the nearest whole millimeter. This introduces progressive errors that accumulate.<\/p> Mimmo's lesson:<\/strong> Use our Fret Slot Calculator! If you absolutely must do the calculations by hand, keep at least 3-4 decimal places for all intermediate steps. Only at the end, when you have the definitive measurement for each fret from the nut, can you round to two decimal places for marking on the fretboard. I've seen guitars that sounded “almost right” for this reason. Don't fall into the same mistake.<\/p> The problem:<\/strong> Using a construction tape measure, a flexible plastic ruler, or a low-quality caliper with poor precision.<\/p> Mimmo's lesson:<\/strong> Invest in a good digital caliper (even an inexpensive one for 20-30 euros is fine, as long as it's precise to a hundredth of a millimeter) and a quality carpenter's square. These are your most important tools at this stage. If the tools are not precise, even perfect calculations will be useless. It's like wanting to make a perfect espresso with a broken moka pot: impossible.<\/p> The problem:<\/strong> Using a thick pencil, drawing crooked or not well-defined lines.<\/p> Mimmo's lesson:<\/strong> Use a scribing tool (scriber) and a straight metal ruler. Engrave a thin, clean line on the fretboard. Be careful to position the ruler exactly on the calculated measurement. I sometimes use a piece of thin adhesive tape to mark the exact point on the ruler before scribing, to have an even clearer visual reference. The line must be deep enough to guide the saw blade, but not so much as to damage the wood.<\/p> The problem:<\/strong> Rushing the process, especially when you are tired or frustrated.<\/p> Mimmo's lesson:<\/strong> Take your time. This is not a job to be rushed. Every measurement, every marking, every cut must be done calmly and carefully. If you feel frustrated, take a break. Go get a coffee, take a walk, and come back with a clear mind. Remember, it's much easier to redo a calculation than to redo an entire neck. Patience is your best friend in lutherie.<\/p> \n\nMany luthiers, especially in the past, used the “rule of 18” (or “rule of 17.817”). In practice, to find the distance of the first fret, you divide the scale length by 17.817. For the second fret, you divide the remaining length by 17.817, and so on. It’s an excellent approximation and a good way to understand the concept, but for maximum precision, our calculator or the complete formula are irreplaceable. The rule of 18 is a practical “shortcut” to get an idea, but not for the final craftsmanship.\n\nFor those who wish to further explore the theory of equal temperament and its application in lutherie, I recommend taking a look at this article by StewMac, one of the most authoritative resources in the field: StewMac Fret Calculator Page<\/a>. It's not just a calculator, but also a reliable source of technical information.\n\n<\/p> \n\nCalculating the guitar fret distance<\/strong> It may seem like a mountain to climb at first, I know. But as you've seen, with the right understanding of the equal temperament formula, the right tools, and a bit of patience, it's an operation within reach of every hobbyist. Don't be intimidated by numbers or the fear of making mistakes.\n\nRemember my story: I too had my moments of frustration, made mistakes, and had to redo things. But it's precisely from these mistakes that you learn the most. And the satisfaction of playing a guitar you built yourself, knowing that every note is in tune because you calculated and cut the frets with precision, is priceless.\n\nSo, arm yourselves with a caliper, our Fret Slot Calculator, and get to work. The next perfect neck could be yours!\n\n<\/p> The rule of 18 is an excellent approximation, useful for understanding the principle or for less critical projects. However, for impeccable intonation, especially on higher frets, it is always better to use the complete formula or a digital calculator that uses the exact value of 17.81702. For a serious project, do not rely solely on approximation.<\/p> Half a millimeter may seem small, but over the entire length of the scale, especially on higher frets where distances are smaller, it can cause perceptible intonation problems. The guitar might sound “out of tune” even if tuned, making the playing experience frustrating. Precision is fundamental, especially on frets subsequent to the error, where inaccuracy accumulates.<\/p> o, the calculated distances refer to the center of the fret slot. The thickness of the fret wire (fret wire<\/em>) is irrelevant for its longitudinal position. It is the position of the contact point<\/em> of the string that matters. What matters is that the slot is cut with the correct width for the fret wire you will use, but this does not affect its position.<\/p>\n\n Related free tool:<\/strong> Fret Slot Calculator<\/a> — calculate online the fret distance of your guitar.<\/p>","protected":false},"excerpt":{"rendered":"The Magic Number: 17.817<\/h3>
= Scale Length \/ (1.0594635 ^
)<\/strong><\/p>\n
The Scale Length: The Basis of Everything<\/h3>
\n
Let's Get to Work: A Practical Step-by-Step Example<\/h2>
Step 1: The Scale Length and the First Measurement<\/h3>
Step 2: On to the Second Fret<\/h3>
Step 3: We Continue Up to the 22° Fret<\/h3>
\n
\n
Practical Tip: Keep the Decimals<\/h3>
Beyond Basic Calculation: Advanced Considerations for a Perfect Neck<\/h2>
Bridge Compensation<\/h3>
The “Zero Fret” (Zero Fret)<\/h3>
The Fretboard Radius (Fretboard Radius)<\/h3>
Multi-scale Necks (Fanned Frets)<\/h3>
Precision is Everything: The Impact of Errors<\/h3>
Your Digital Ally: The Biafax Fret Slot Calculator<\/h2>
How Our Fret Slot Calculator Works<\/h3>
\n
\n
Why Use a Digital Calculator?<\/h3>
Essential Tools for Marking<\/h2>
Common Mistakes and How to Avoid Them (Mimmo's Lessons)<\/h2>
Mistake 1: Wrong Scale Length at the Base<\/h3>
Mistake 2: Excessive Rounding During Calculations<\/h3>
Mistake 3: Imprecise Measuring Tools<\/h3>
Mistake 4: Imprecise Marking on the Fretboard<\/h3>
Mistake 5: Lack of Patience<\/h3>
One last tip: the rule of 18<\/h3>
Conclusion: The Satisfaction of a Job Well Done<\/h2>
FAQ: Common Questions about Fret Distance<\/h3>
Can I use the “rule of 18” for all my projects?<\/h3>
What happens if I miss the position of a fret by half a millimeter?<\/h3>
Do I need to consider the fret thickness when calculating its position?<\/h3>