scale lenght question

[ken cierp]

Here's Cumpiano's up date -- his method is to use the center of the finger-board and the center of the saddle slot, that point equals scale length + .15 measured from the nut ---- no matter what scale you are using and no matter where the neck attaches to the body (12th 14th or even 13th fret) This ball park method seems to work adequately for most.


How do I compensate a scale other than the one in the book?

There is no simple and practical way to calculate the precise figure for the location of the saddle midpoint for any given scale, because there are too many factors that add to--or subtract from--the compensation requirement. So the luthier has little choice other than locating the saddle midpoint according to a process which is purely empirical, or in other words, relying on a quantity that has been confirmed by prior experience.

The experience of this luthier is that the .15-inch figure for the saddle midpoint compensation increment is successful for any of the modern guitar scale lengths, from 24.9 to 25.7.

This may be unsatisfying for a technically-minded person to learn, because one would reasonably expect that there must be a single and unique figure that should be calculable for any given value of scale length distance.

This uncertainty has bedeviled luthiers for literally hundreds of years. The reason why no practical way of determining compensation with mathematical precision has ever been developed, is that luthiers are not physicists or mathematicians.

There exists, however, a formula which was proposed to me by a highly respected physicist, before he passed away several years ago. The formula takes into account most, but not all, the variables that affect the compensation requirement for any given string. Unfortunately, the formula requires a great deal of data acquisition in order to plug in the numbers in the right places. So for any given guitar, the formula is pretty much useless to the luthier for practical reasons. But that is not to say that much can't be learned from it.

The formula reads as follows:



where:

C is the compensation, or more accurately--given that the 12th fret divides the scale length precisely in half--it is the amount the saddle-half of the scale is longer than the nut half.
H is the string's height over the twelfth fret
E is the Modulus of Elasticity of the string's core material (a constant which differs for each material, obtainable from a Properties of Materials textbook)
A is the cross-sectional area of the string if it is monofilament; or of the string's core if it is wound.
L is the length of the scale
T is the tension of the string when raised to concert pitch.

I once plugged in the data for an actual string during a experimentation session, and the formula indeed predicted a value that corresponded closely to a midpoint distance of .15", but it took me several days to acquire the necessary information. When I reported this to the physicist, he warned me not to rely on the formula until I had accumulated a voluminous amount of data. Needless to say, I had to drop the project, and return to my empirical figure, .15.

The formula predicts that the compensation requirement:

increases as the cross section of the string increases, the elasticity decreases (the modulus is an inverse figure)--and due to the fact that the height value is squared--increases rapidly with any small increase of string height.
decreases with the increase of the string length and the string tension.
In discussing this with yet another physicist recently he pointed out that, in terms of pure precision, the resulting value of C will only be true to obtain zero pitch distortion when the fret is pressed at the 12th fret. Indeed, the distance H is not constant over every fret, but increases slowly from the first to the 20th. So the formula is accurate only at the 12th fret. But then, that is how us luthiers verify the accuracy of the bridge's placement: by pressing down on the 12th fret and comparing the given pitch to the 12th fret harmonic, which is our test standard.

[stevem]

say what?---ok, I'll stick to the double plus .15"

Thank you for that bit of wisdom- tho I may not need that amount of precision!

Steve

[Ron Belanger]

If you want the correct intonation you do need that amount of precision.

[Eric_K]

Note that the formula includes string material and string size.
So, if set the intonation perfectly for one set of strings it will be off with a different set.

Eric