Audience: Have you done any calculations to find out what changes in temperature and humidity are going to do to relative fret positions? $$X_0 = 650mm$$. Remember, we are trying to fit our data points to our equation in canonical form, which allows us to use standard fret placement, and allows us to calculate a saddle setback and a nut "setforth." The first fret is $$17/18$$ of that distance to the saddle, the second is $$17/18$$ of the first fret distance, or $$(17/18)^2$$ times the total scale length, and so on up to the 12th fret, where the distance to the saddle would be $$(17/18)^{12} \times 650$$. It is very similar to the Rule of 18 in that the octave is divided into 12 regularly-spaced intervals. So we can actually calculate $$\ell'_n$$. You could easily use an entire fingerboard cut well short at the nut end to obtain data for all the frets. We have calculated $$\{X'_n\}$$ for each string, using appropriate values of $$h$$, $$R$$, $$M$$, and $$j$$. Indeed, it was even more complicated before we dropped the higher-order terms. What follows is difficult, and probably will not be fully understood even by the mathematically literate on the first few tries. For the first whole step you had an interval ratio of $$8/9$$, but for the second whole step you had an interval ratio of $$9/10$$. 8 left. My strong suspicion is that nut compensation in steel strings would be beneficial. Shortly thereafter I ran across an article in the Journal of Guitar Acoustics by Bill and Pat Bartolini.2 They describe a method which involved shortening the fingerboard slightly, as did Gilbert's. Notice that the 12th fret is still in the same position as in the hypothetical case. Since both elasticity (stretch) and inharmonicity (stiffness) have tangible effects, any theory about intonation should take both these factors into account. Think about it this way. Use the best tuner you can find to determine the right pitch for whichever note you're looking at. This device has a tuning machine (in this case two) mounted to a $$1/4 \times 20$$ threaded rod, regulated by a wing nut. Graphtech PQ9280C0 TUSQ Fully Compensated Acoustic Guitar Saddle . 1 product ratings - 52mm BONE NUT + pre-cut string slots for CLASSICAL style guitars, 12 product ratings - Graph Tech TUSQ XL Gibson Adjustable Nut (White), 12 product ratings - Durable Ivory Bone Bridge Saddle Nut for 6 String Acoustic Classical Guitar, 1 product ratings - White Bone Bridge Saddle & 50mm Slotted Nut for Classical Guitar. I'll let others pursue it further. Stiffness only. They concluded that for a G string, $$R$$ is about 35 and all the other strings are pretty close to one another at about 26. The typical way of determining saddle setback is to play the 12th fret harmonic and set the saddle so the fretted octave matches that. After a bit more calculus (again Taylor's theorem) we find that. This plan worked fine for one course of strings but when you started putting chords together it began to break down. 10pcs Guitar Bass Real Blank Bone Nut Material 52mmX6mmX9mm Replacement Parts . One of the principal problems that we have to overcome is the fact that open strings do not have this extra stretch, while fretted strings do. Richard McClish: The top of the guitar is a resonator in various ways. To compare his $$\Delta S$$ to mine as I have defined it, it is necessary to use the fingerboard with a BSL of 650mm as a frame of reference. The model does this to increase the fretted string length to compensate for the increase in pitch that results from stretching the string. The setup for classical guitars is basically the same as those for steel strings or electrics, but there are a couple of things you have to take into consideration before you tackle the setup. \$9.49. This is not surprising. Further, it's quite unlikely that you could hear a difference of much less than 0.1MM. What follows now, however, departs from their work. In the end, that stiffness slightly raises the pitch of succeedingly higher overtones. It turns out that we can relate $$\frac{\partial b(L)}{\partial L} \bigg\rvert_{L_0}$$ to $$R$$.