Of reverse headstocks and string tension

guitarz.blogspot.com:

Earlier this month, the post on the Ampeg Scroll Bass legacy provoked an interesting discussion about the so-called "reverse headstock" and its influence on string tension, sound and playability. On this post, I imprudently stated - a common misconception - that the reverse headstock provides better tension to the respective gauges of the strings.

One of our readers, who goes under the moniker dre, provided precious and detailed information to reestablish the one and only truth about this essential topic, and so I've slightly edited his comments for this post.

"The effective string length (ie nut-to-bridge) determines the tension, in concert with string gauge and tuned pitch. If you have two guitars identical scale length, string gauge, and tuning, but different total string lengths, you will still have identical string tension.

Imagine one of those early Les Pauls with the combo bridge/tailpiece: minimal total string length. Then imagine a Firebird with a Bigsby. Longer headstock, more string behind the bridge, maximal total length. Both guitars have the same scale length.

If both have the same strings and are tuned to standard pitch, the strings will still be at the same tension, despite the differences in total string length, because the effective string length is the same, and those 24.75 inches of string between the nut and bridge have to be at the same tension to be at the same pitch.

The real difference created by different total lengths is in the feel of the guitar. All that extra string below the bridge and above the nut on the Firebird's low E string means that the string can be stretched more. If you reach way up and pull that E string across the fretboard (Why? I don't know, you're the one doing it!), that string will be easier to bend than the E string on the Les Paul, because there's less total string to stretch on the Les. Bending a string utilizes the entire length of the string since it can slide through the nut as it stretches. Playing an open note only utilizes the effective length, unless you really hammer it and it stretches a little.

Length, mass, tension. Those are the three determinants of pitch in a string. A guitar's nut and bridge functionally isolate the string between them from the remaining string above the nut and below the bridge, with regard to vibration. The length of string between the nut and the bridge is what vibrates to produce a pitch, and that length has to be at a particular tension in order to do so, depending on the mass of the string. The entire string must be at that same tension, every inch of it, including what's above the nut and below the bridge.

If (I'm estimating here) the .052 low E string on your Les Paul needs 23 pounds of tension to be tuned correctly, then your Firebird's .052 low E string needs 23 pounds to be tuned correctly. You may have more string at 23 pounds of tension, but that 24.75 inch piece of string between the nut and bridge has to be at 23 pounds, and therefore the entire string must be at 23 pounds.

Extra strings at either end of a guitar can be attractive and even musically useful (I am a certified Sonic Youth fan), but it does not change the string tension required to tune to pitch.

Here's a thought experiment that helps visualize the irrelevance of the nut-to-tuner (or saddle-to-anchor) length of string in terms of string tension at pitch. I have forgotten who came up with the basic premise of this visualization, and it was found on some bass forum, so please don't credit it to me.

Okay: Imagine you've got Adrian Vandenberg's secret pearlescent black prototype Peavey 24.5" scale guitar from 1987. It was made with a three-foot-long reversed headstock, which makes the total length of the E string (from tuner to Floyd Rose) 61", assuming half an inch of string from the saddle to the anchor on the Floyd. Don't ask why. Vandenberg was crazy. The custom-made superlong strings cost $500 a set.

You block the Floyd Rose to immobilize it (just to take it out of the equation), loosen the locking nut, and tune up to E. Now you have 61" total string length at a tension at which the 24.5" of speaking length between the saddle and nut play an E. The whole 61" of string is at the same tension from anchor to tuner, yes?

Okay. Now, crank down that locking nut. We don't want to get out of tune while playing the chorus riff from "In the Heat of the Night". When the nut is locked, the entire string is still at the same tension, right? All we did was fix one point on the string so that it can't move. Check to make sure you still have that string tuned to E. What happens when you take your string snips and cut out the string between the nut and the tuner? The speaking string between the saddle and the nut is still 24.5", still tuned to E, and still at the exact same tension.

At the same time, you've removed three feet of string. Now the total length, including the bit between the anchor and the saddle, is 25", less than half what it was, but the tension is still the same. If the tension was lowered when the string was shortened, the string would no longer be tuned to an E. This is fundamental physics. If string of the same speaking length with the same mass is tuned to the same fundamental frequency (and it is the same in every possible parameter in this example, because it is in fact the very same string), it absolutely must be at the same tension. Whether it was 61" or 25" total length, the string had to be at the same tension when tuned to E. When using string mass, length, and tension to determine fundamental frequency, only the vibrating length is relevant.

Please note that I am referring to actual tension, the pulling force of the string. I am not talking about "perceived tension" or "feel" or "slinkiness" or "springiness" or "bendability", all of which seemed to surface in my interweb research, all of which being mistaken for tension. Since every element of a guitar affects feel and sound, surely extra string length beyond the speaking portion somehow subtly affects the feel and sound of a guitar. I'll wager it's a barely perceptible change."

So thank you dre for this extensive contribution (the picture of Adje Vanderberg's signature Peavey guitar is supposed somehow to make all this even more convincing).

Bertram

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