Photo 1 Two versions of an extremely simple so-called bass-extender.
Esoterica Electrica columnist and luthier Jol Dantzig has been exploring string-tension myths in recent Premier Guitar articles. Here are some thoughts to add to the discourse.
Dear Jol Dantzig,
Your recent PG articles, "The Doors of Perception" and the follow-up "The String-Tension Follies Experiment, Continued," are an interesting read about string tension, a topic of which your friend Collin Olson of D'Addario said: "There's definitely a lot of confusion out there." He's right, and you're definitely not alone with your doubts, thoughts, and struggles.
Recently a bass builder came up with the idea of how to make a 30" short-scale feel and sound like a 34" long-scale bass. He intended to use a string-through bridge and attach the tailpiece at a place where Floyd-Rose-equipped guitars have those spring-claws to elongate string length. He was about to spend a lot of money on a patent, which he now hopefully saves for something else.
I've discussed this topic in a few earlier columns, but sometimes we might be skeptical about a certain idea and need a different explanation and view angle before we know what's wrong. And since this is even discussed among experienced luthiers, I wanted to shed some light on it.
You mentioned four questions you've been thinking about, and I allow myself to start with my short answers:
1. Does overall string length affect tension?
No.
2. Does string tension really affect tone?
No and yes.
3. Is sustain hampered by pickup magnets?
Yes.
4. Can Eric Johnson tell when my battery is alkaline?
Surely not, but he's free to believe whatever he wants.
With questions #3 and #4 being a very different topic, let's focus on questions #1 and #2.
The issue of string tension has a mathematical answer. This is the formula for a string's tension (T):
Uw= specific weight per length unit of core and winding, L= scale length, f= frequency.
I'm sure you've seen this, but let's put it in words: For a given speaking length of a specific string, tension equals frequency, or the root thereof.
And, less mathematical, if I said that length behind the bridge would add tension, you'd need to tune down to a lesser tension to get back to pitch "f." A classic circulus vitiosus.
Tension (if one-dimensional) is an axial force between two points and is in equilibrium across the whole length of the string between both anchor points, wherever these are. But pitch only depends on its speaking length.
I've discussed this topic in a few earlier columns, but sometimes we might be skeptical about a certain idea and need a different explanation and view angle before we know what's wrong.
Question #2 is a bit more complicated because I think the question should be: Does overall string length affect tone? While tension doesn't affect tone, overall string length can. It's often said that additional string length adds especially to the low end, which once led to the idea of so-called bass-extenders (see "The B-String Extender Myth" [March 2013]).
Two of these "bass-extender" constructions are shown in Photo 1, which to me is not only simple, but debunking at the same time. In physics, it's often helpful to look at the extremes. Assuming adding length worked:
A.) It would be almost impossible to build a good-sounding headless bass, as these sport an extremely short overall string-length.
B.) Using an extra, extra-long string, wound all across the room, would allow one to forever dominate the bass world.
Both outcomes not only sound very unlikely but have been disproven. It's no surprise that you mention two specific instruments that led to the idea of outer string length affecting tension: the upright bass and an archtop guitar or bass.
Photo 2 - This German Fasan archtop bass (built in 1965) has a shallow break angle and long string-length on the left side of the bridge.
Photo courtesy of german-vintage-guitar.com
Both of these are known for their extended string length behind the bridge, sport a separate bridge and tailpiece, and, more importantly, are half or fully acoustic instruments. On an acoustic instrument, you'll want to remove as much weight and stress from the soundboard. The first eases movement of the top, while the latter allows for an even thinner soundboard, moving even more air.
This construction with a very distant bridge and tailpiece is exactly the one where perception chimes in, although I'd prefer to use the term elasticity. Whenever we pluck or bend a string, we apply a force (F) to a given string with an elasticity (E) and diameter (A). According to Hooke's law for a material's elastic behavior:
E and A are constant and so would be the force that needs to be applied for bending a string by ∂l. For a given instrument, l0 is constant—close to the scale length for a headless, and scale length plus the additional length outside the scale, if the string can slip over the bridge once we bend it. When l0 getting bigger, the force needed for the same bend gets smaller and this results in the perception of a softer, more elastic string. Of course, the break angle at both ends of the scale length needs to be rather shallow with low friction to allow for the string's slippage (Photo 2). It's discussed in my PG column "The Break Dance Behind the Bridge" [February 2021].
A final answer to your question about its effect on tone is pretty complex and one I'm also still struggling with. A few of my thoughts on the subject went into the article "Bridge vs. Tone" [March 2021].
Maybe these can give you some ideas to chew on?
Sincerely,
Heiko PG
Instrument makers have always tried to manipulate string length to optimize tone and feel, but how much is myth and how much is science?
Length, gauge, friction, voodoo? Revisiting the mystery of real or perceived string resistance in a science-y way.
In a previous column, I investigated the relationship between overall string length and its resulting tension ["The Doors of Perception," August 2020]. I cobbled together a crude measuring fixture and determined that the length of string beyond the bridge and nut did not affect a string's (linear) tension at a given pitch. After being assailed with comments and emails loaded with physics lessons detailing the math behind my conclusion, I now know that it was folly to assume any other conclusion. The laws of physics state that string tension is determined completely by the active (vibrating) length of the string, the pitch the string is tuned to, and the string's mass. In simple terms, this means that for a given vibrating length, the tighter you pull the string or the heavier the gauge, the more tension it will have. Nothing else, like peghead length or tailpiece position, matters—full stop. Still, the feeling persisted that I could sense a difference on instruments with long lengths of string between the bridge and tailpiece, such as an archtop jazz guitar. I'm not alone.
There have been many seasoned musicians I've known who swear that a flipped 6-in-line headstock tightens up the low strings. They've reported that the strings were tougher to bend and felt stiff. Some of the string manufacturers I spoke to in my research, despite their knowledge of the science behind the materials and construction of guitar strings, offered that there might be a perceived difference. But how could this be? You'd think that if you feel tension, it could be measured, yet my test instrument showed no change. Could there be another force at work, like lateral resistance? It seemed impossible, but it was time to resurrect the string tension fixture to find out.
My string test contraption was originally built to measure the linear tension of strings, but I only had to make a few changes to convert it to quantify lateral resistance. Admittedly, human fingers can detect minuscule changes in pressure, so I wondered if my 20-pound test instrument would have the resolution to pick up any variation. My theory was that if the overall length of a string was longer, there might be a perceivable difference in the force needed to stretch a string to a given interval. I'm counting on the physics majors out there to rush in at this point with the equation that I'm oblivious to.
Perhaps the friction (or lack of same) at the nut and bridge is what we are feeling when a guitar feels easy to play, or, conversely, when we say it fights us.
Nevertheless, my method was to use a pair of .012 plain steel strings and bend them the distance needed to raise the pitch one full step. Each string would have a different overall length despite their identical vibrating length. The full-step bend at the 8th fret position is a lick that all (non-classical) guitarists employ regularly. It's also the figure we often use subconsciously to determine playability when evaluating a guitar. I used this exact move in an attempt to impress Joe Bonamassa while sampling one of his '59 sunbursts. He avoided eye contact.
In my initial tests, I observed that it required a force of 1.8 pounds to raise the pitch one full step, regardless of the total length of the string, as long as the vibrating length remained 25.5". Thinking that perhaps the string's light gauge made any difference too small to measure accurately, I repeated the experiment with a .056 low E string. My test replicated bending the same B note three frets (a step-and-a-half) sharp to D. This is a pretty bold move on a guitar, but I thought maybe I'd see some evidence of difference if I really strangled it. Again, no difference was indicated, as both examples required 4 pounds of pressure to reach the higher note.
Now, I'm sure many of you will be quick to point out that this was a pretty shoddy exercise. I didn't make absolutely certain that the friction at the nut would be equal when extending the length to the tuner. Friction is a factor often brought up when this subject is discussed. Should I have used a ball-bearing roller at the nut? Perhaps the friction (or lack of same) at the nut and bridge is what we're feeling when a guitar feels easy to play, or, conversely, when we say it fights us. What about those players who have that little quivery vibrato that sounds like Joan Baez? Do they feel these forces? As for my research, at this point I was beginning to tire and made myself an espresso.
I'm hopeful someone smarter than me will figure this out and make a YouTube rebuttal. Meanwhile, I'm planning my next test to see if longer scale length is why Eric Clapton "lost" his tone after Cream. Until then, rock on friends!
Boutique luthier Jol Dantzig (cofounder of Hamer Guitars) examines the potential perils of different headstock angles and the balance between performance and ease of construction.
When we think of world-champion guitar breakers, Jimi Hendrix and Kurt Cobain come to mind. But even Pete Townshend can’t hold a candle to the infamous creation known as the guitar stand. Quite possibly responsible for the net worth of 10,000 guitar-repair techs, this venerable device has decapitated even more guitars than UPS and United Airlines combined. So, why are guitars so delicate?
Guitarists blame cords. Or drummers. Critics are swift to point to extreme headstock angles or weaker materials, like mahogany. After all, Leo Fender and company put that quarrel to justice long ago by constructing an industrial-grade, fretted Excalibur from rock maple—with no headstock pitch to boot. Known for durability in combat, the bolt-on maple neck stands as de facto judge and jury for less-robust designs. You’d think guitar makers would have gotten the message by now. I can imagine the advertising bullet points:
· Won’t break when you toss it and miss the couch.
· Strong enough to survive a gig bag.
· Stands up to toppling stands.
· What could be better? Airbags?
Pitched (angled) headstocks can be traced back 15 centuries to the medieval oud and its younger cousin the lute. These had long, thin headstocks raked back at nearly 90 degrees—possibly to facilitate easy reach to their tuning pegs. The guitar as we now know it developed from the Spanish guitar (which evolved from the lute), with the headstock pitch reduced to somewhere between 7 and 17 degrees—or, in the case of Fender, zero. Guitar builders of the last four or five centuries have struck a balance between performance and ease of construction, with Fender taking the prize for the latter.
Let’s take a look at how headstocks are constructed. Part of it is tradition born out of functional design. Head pitch keeps strings in the nut by diverting pressure downward on the nut. The slighter the angle, the less pressure, so each designer must choose how steep to go. The downside of more of an angle is friction that can affect string stretching during tuning, bending, and tremolo use. The benefit is greater transmission of vibration at the nut and reduced dissipation of energy to the headstock. Headstock vibration can also be argued, but that discussion is for another day.
The ways to achieve the pitched angle seen on modern guitars fall into two camps. The first is the scarf joint, seen on traditional classical and flamenco guitars. This is simply cutting the flat neck board on an angle and gluing a flat headstock onto that. The pitch is determined by the cut angle. One variation of this type of headstock—sometimes seen on vintage Martins and other acoustics—uses a “bird’s beak” joint to strengthen things up. The side effect is an attractive diamond-shaped affair on the back of the headstock.
The second type is the fully constructed neck, as seen on instruments like Gibson’s and Gretsch’s. This requires a lot more material that’s cut from expensive, thick boards. The result is a nice, clean look, but it unfortunately provides a shortcut for breakage along the grain line, right at the instrument’s most vulnerable point, where neck and head meet. The cutout channel for a head-end truss-rod adjustment weakens this area even more. Some builders attempt to increase strength by creating a bump (called a volute) at the back of the headstock where it meets the neck shaft, but, in reality, the added material falls below the line of most breaks. The truth is that the volute was a manufacturing shortcut, at least until CNC machining made handblending unnecessary.
The Fender example uses string trees on the higher strings to create the downward angle that the zero-pitch headstock does not. This sometimes results in friction-related tuning issues. For the most part, it’s an inexpensive, slightly inelegant solution. In the win column, the zero-pitch head is a three-birds-with-one-stone example of Fender’s design philosophy. The absence of pitch allows a neck to be made of a single, 1"-thick piece of ordinary and plain (aka cheap) maple, while it dispenses with all the pesky woodworking needed to fashion an angled headstock. The bonus is that the grain of the wood is continuous, which helps prevent breakage. Although not as fancy looking as something like a D’Angelico, I still love it, as does most of the guitar universe.
All said, guitars are not alone in their fragility. Classical instruments like the cello and French horn are vulnerable to damage when mishandled. A 4-foot drop wouldn’t do much for an accordion, either. Playing guitar has become a contact sport, which is probably why the question of outsized durability is discussed at all. To me, it seems slightly comical to expect a multi-thousand-dollar guitar to be toddler-proof. My question isn’t why headstocks break. … It’s why we expect them not to.