You say you want a revolution?

Lybian guitarist urges his buddies on while they smash the state.

Is there a formula for compensation?

For those of you who are new to this, the compensation is the small increment in length added to the string's scale length to compensate for the slight sharpening that occurs each time you press the string down to fret it. As far as an actual formula that predicts what that increment should be, yes, there is a real formula. The late Daniel Haines, physicist at Bell Labs and later a consultant for the CF Martin Organization, gave me the compensation formula he devised, but I don't use it because it is too cumbersome to use. I find that the same compensation of .15" measured at the centerpoint of the saddle works acceptably well for short and long steel string guitar scales (.10 for nylon string guitars). But if you want to try your hand at following the formula here it is for each string:

Where C, as Dan Haines said, "the amount that the saddle half of the string is longer than the nut half of the string" is the compensation, and it's expressed in inches

H is the string height expressed in inches measured at the 12th fret. Notice that it's squared, suggesting that small changes in the string height result in large changes in the compensation required. That's why your guitar goes out of tune as it settles under tension and the strings rise oh-so-slightly off the fingerboard.

E is the constant that represents Young's modulus, or the modulus of elasticity, of the string core material. Steel is 29,000,000. Nylon is around 290,000: roughly 100 times more elastic (or less stiff) than steel.

A is the cross sectional area of the monofilament string or, on wound strings, its core--measured in square inches. That's why steel string saddles are sloped: the thicker strings want more C. On nylon-string guitars its more complicated: the string thickness doesn't go up as neatly and evenly as they do on steel. And since the variation in the inputs of the strings--given the sum of the other factors--is so slight. So that in practice on nylon the variation in total C is so slight among strings that the classic saddle ordinarily doesn't need to be sloped--although in some cases the classic G-strings in some string sets find their intonation improved by notching them back on the saddle. In many cases that can be avoided by using Tynex Gs--(a denser, thus a thinner G), rather than thick Nylon Gs--which can improve the usually notoriously dull and sour G on many classics. Tynex Gs are found on D'addario Composite sets.

L is the vibrating length of the string expressed in inches. You'd use the scale length in this calculation. It's below the line on the formula, so it impacts the compensation requirement inversely. Hence short scales require greater compensation (i.e. mandolin bridges are usually set back as much as 1/4-inch).

T is the tension of the string--at concert pitch--expressed in pounds. Also, because it's below the line on the equation, the lower the tension, the greater the compensation required. Just watch what happens when you drop your low E string to D for dropped-D tuning. Your existing compensation usually becomes insufficient and the floppy low E string goes sharp as you play up the neck. The precise tension of a string is not so easy to find: In order to calculate T you need another formula, found here:

But in order to satisfy that equation, you have to know the precise mass of the string in grams. Got a gram scale? No? That the most accurate way to plug in this number. But if you don't have a gram scale, the next best thing is to go to here. It's a chart which supplies the tensions of the different strings ....  BUT.... on a 25.5" scale guitar. I guess you can approximate what they are on a 24.9 or a 26-inch scale by setting up a proportion. 

So you see the immense hassle. That's why I just rely on the empirical figure of .15" to the midpoint of a saddle that is slanted 1/8 inch in 3 inches? Works fine for me and my fussiest customers.

What the formula is useful for, is to show how the compensation requirement increases in direct proportion to the string height, the modulus of elasticity of the string core material, and the diameter of the string core--but INVERSELY proportional to the string length and tension. So in the equation everything above the line: string height, elasticity, core thickness increases the C while at the same time, everything below the line, on the divisor: length and tension are acting to reduce the compensation required.

So the resultant compensation amount is the result of that  push-pulling of factors. When they are all accounted for the guitar sounds sweet and heavenly. When they are not all accounted for, the guitar sounds soggy and sour. No big deal, huh?

All the rest is sound and fury

Yesterday I read, with delicious pleasure, a transcription of an NPR news report of a recent double-blind listening test--with "seasoned" musicians as the listeners--of two genuine Strad violins, a genuine Guarnerius violin, and three well- and recently-made modern violins. The researcher was an acoustics physicist from France's National Center for Scientific Research. "Everybody wore dark goggles so they couldn't see which violin was which." "No one knew which instrument was which until after the test. That rules out the kind of bias that might creep in when a musician judges an instrument he or she knows is 300 years old and maybe played by someone like Fritz Kreisler." The link is here.

"…of the 17 players who were asked to choose which were old Italians...seven said they couldn't, seven got it wrong, and only three got it right." Most significantly, "When [one] asked the players which violins they'd like to take home, almost two-thirds chose a violin that turned out to be new. She's found the same in tests with other musical instruments. "I haven't found any consistency whatsoever," she says. "Never. People don't agree. They just like different things."

"In fact, the only statistically obvious trend in the choices was that one of the Stradivarius violins was the least favorite, and one of the modern instruments was slightly favored."

I wonder how the last person who paid $3.5 million for a Strad at auction feels about that. Or, for that matter, $200,000 for a prewar D-45. Must shake them up a bit, no?

The test proved to me that the overheated claims I've been hearing over the last 40 years about the source of Strad's "special sound" being mineralized wood buried in swamps for centuries, the "aging" process, or magic varnish recipes that disappeared forever, are total bull-scheisse. The emperor has no clothes.

The inscrutable mythical primacy of scarce Brazilian rosewood and German Spruce is the guitar-world equivalent of this sentimental, often self-serving, fakery. I can add the speculations about crystallizing resins in 100-year spruce to the steaming pile of fake mumbo jumbo. I suspected all this from the beginning. To quote my mentor in guitar acoustics, Tim White, "if you build it to play in tune and play easily, you'll find someone who'll fall in love with it." But that in itself is asking a lot: What really counts is the the individual maker's acquired intuition, commitment and care.

All the rest is sound and fury, signifying nothing.