MIMF

So, New Topic Tuesday (I know it's actually Wednesday, but I started this post yesterday).

The discussion on archtop bridge string break angle led me to Ken Parker's site, where he discusses a whole lot of things in a rather extensive library of interviews published in a wide variety of places. Man, for a guy who only makes two or three instruments a year he gets a lot of press.

One of this library of interviews includes his ideas on "dynamic tension" - oddly, they are identical to my own, but he actually does something about it, and he gave it a name. The idea is that string length behind the bridge and nut contribute to the dynamic change in tension in a string as the string is played. This I get, and it makes a lot of sense to me - if the string is constrained by the nut and bridge at 25" and is tuned to a pitch, it has a set tension based on the mechanical properties of the string. If the string is stretched, to reach the fret to play a note, the tension is raised, the theoretical pitch of the string is raised, we add compensation at the bridge, nut, or both to adjust the pitch. If the string has say 10" additional length behind the bridge and nut then the added tension from the string stretch to the fret will include the total string length from tuning post to tailpiece, and will be lower than if the string was fully terminated at the bridge and nut (like on a Stratocaster with a tremelo bridge and locks at both the bridge and nut, apparently popular with a certain breed of rock players).

He remarks that in addition to the string length idea dynamic tension is affected by the string break angle at the bridge and nut, apparently the lower the angle the lesser change in dynamic tension. Lower change in dynamic tension has a couple of effects - it should make the strings feel a bit looser to play - if you think about it, your finger doesn't feel the initial tension of the string at all, what it feels is the total tension of the fretted string including the additional tension from the stretch to the fret. It should make bending a string harder - you need to push more to get the same increase in pitch. This one I need to think about - will it make a difference in volume? String vibration is affected by change in tension as the string wobbles about after a pluck, will this change the energy transferred to the bridge from the string? I have no idea.

Parker's discourse discusses string break angle at the bridge and touches on experimental work done to arrive at what he obviously considers an optimum (it looks like around 10 - 15 degrees to me, or pretty normal for an archtop) balance of down-force pre-load on the top and tone production. He also discusses his headstock design. He uses a break angle at the nut of 4 degrees, he says, and uses the six-on-a-side tuner idea to make the string length of the upper strings longer, to reduce their dynamic tension. Neat idea, sez I. I think he means he builds in a headstock angle of 4 degrees, because his actual string break angle is going to be different for every string based on angle to the string post location, but again this actual angle will be minimized for the E4 string, a little greater for the B3, etc. The string break angle for his E2 string is actually quite aggressive.

So, I am planning to build a new neck for my first archtop anyway, which is a hybrid acoustic archtop/solid body electric, and I'm going to incorporate his headstock design concept to experiment with this "dynamic tension" idea and see what happens. I am finding that it's remarkably hard to design a six-on-a-side headstock that isn't horribly derivative of Fender, Parker, et al, but they copied them from turn-of-the-century and earlier designs anyway, so derivative it shall be.

Brian

All this theory seems to assume that there is zero friction of the string sliding through the nut, which obviously can never be achieved. The reality is that there will always be enough friction there to prevent the string from sliding until the string is bent fairly hard. String slide will not happen during normal fretting due to the small amount of string displacement and insufficient extra tension necessary to overcome the initial static friction.

By the way, Ken Parker is quite famous in the lutherie world for his Parker Fly and other innovations. I saw a couple of talks of his at Healdsburgh about 10 years ago and was very impressed by his ideas and presentation.

The thesis seems to be that friction at the nut and saddle doesn't impede the transfer of tension over minuscule changes length due to change in tension. The bridge can certainly rock that thousandth of an inch or so. Is this true? I have no idea. I actually have a lot of sympathy for your friction argument. Ken Parker seems to think so, he is quite definite on the subject. Hofner and Epiphone designed tailpieces that had the string length for the bass strings longer than for the treble strings, the idea being to reduce the amount of compensation required at the bridge. I own examples of both, I should do an experiment...

Page four of this article, btw, for Ken Parker discussing this. https://www.premierguitar.com/articles/ ... ops?page=4

I also appreciated his words on his bridge - when I made the ultra light bridge for my last guitar at 22 grams, I felt at first I was doing something wrong. Same as his, it turns out.

A contrarian point of view: http://www.liutaiomottola.com/myth/perception.htm

This one discusses an experiment by Benedetto that had identical strings tuned to the same pitch on a neck, but with scale lengths varied from 23" to 26". Subjects could not tell the difference in compliance of the strings even though they would have been under pretty large differences in tension. Maybe it doesn't matter, maybe they all had the same total length and that made a difference? Who knows? As soon as you put people's "perception" into the mix, logic flies out the window... I know that I "feel" that I can tell the difference in string compliance (dynamic tension, whatever) if I have the same .010" on my Gibson with 24 5/8" scale and my Fender with 25.5" scale. To me they feel completely different. Far less so on the lower strings, though. They seem so compliant that the change in scale length and tension doesn't matter as much.

Brian

Gore comes to much the same conclusion regarding intonation in his books. Longer after lengths reduce the tension change and require less compensation, according to him.

The after length between the tailpiece and bridge determines how strongly the tailpiece vibrations are coupled to the top. The shorter the after length the tighter the couple, and the more the tailpiece vibrations affect the sound. The strings of the after length themselves can also vibrate, and that can alter the tone too. Lots to think about.

I did not know what to do, so I used Bennetto's tailpiece design where the string attach, but a little shorter in length like Parkers.
My scale 25 5/8" What is a good after length?

'Way back in about '78 or '79, Jim D'Aquisto gave a talk at a GAL convention in Boston. One of the things he said was that he could alter the tone of a guitar a lot depending on what he did with the tailpiece. With all the imponderables it's really hard to say what a 'good' after length would be in general. All you can do is experiment.

I will note that on violins the normal setup has the back string length between the bridge top and the saddle along the front of the tailpiece at1/6 of the vibrating length of the strings. This is a starting point, and makers adjust it all over the place to get the sound they want.

I have one guitar where one or two of the after-strings at the tail are in tune with the played strings when I play in Bb. Creates the most amazing uncontrolled ringing tones. I quite like it! Most people would thread some felt in there and dampen it out.

It's very odd that when you calculate compensation you use the diameter of the core of the wound strings yet when you calculate tension you use the mass of the whole string. I know why, but it's still very odd. I have some thinking to do as this relates to dynamic tension changes. Could it be that change in tension is related more to core string diameter while overall tension is related to mass?

The primary reason for using wraps is to reduce the stiffness of the string and still allow for tuning to a low pitch. The G string problem on Classical guitars is an example of what happens when you don't use a wrap.

For a plain string, the bending stiffness varies as the fourth power of the diameter. Doubling the diameter makes the string sixteen times as stiff. This does two things to the tone: it limits the power in the higher partials, and it shifts all the partials up in pitch, with the higher ones being shifted more. 'Ideal' strings that have no stiffness have an overtone series that it perfectly harmonic and goes on forever. As you go up in pitch the string needs to bend over a shorter length, and a thick string starts to act more like a rod. Eventually, the stiff string can't make the bend at all, so you lose all the partials above that.

Intonation is also a problem with thick strings. We all know that pushing a string down, say, to fret it, increases the tension a bit, and raises the pitch. The amount the tension changes depends on the displacement, the Young's modulus of the string (or the core in a wrapped string), and the cross section area of the string/core. The fatter the string is, all else equal, the greater the tension change when it's displaced. Note, too, that the change in tension does not depend on the initial tension.

Plain nylon G strings (or, for that matter, plain steel ones) have to be thick to get the tension up to more or less the same level as the E and B, otherwise it would be hard to play the guitar. The thick string is hard to stretch, due to the large cross section, so the tension shifts up a lot compared with the thinner E and B. The intonation is off, and small changes in left hand pressure, or a little bit of bend, shifts it. The high bending stiffness also means that there are not so many overtones, and those are shifted upward so that they're not 'harmonic'. This makes the perception of string pitch less secure than it would otherwise be, which contributes to the dull sound of the messed up overtones.

Wrapped strings where successive winds of the wrappings don't touch have the same stiffness and effective cross section as the core, but the mass will be that of the entire string. This allows you to tune them low without undue problems with inharmonic overtones and intonation. The main issues are the 'zip' on the wrap from poor technique when you shift, and the fact that the core is more highly stressed, so it's more likely to break. The zip issue seems to be why Classical players put up with plain Gs.

I have feeling that piano designers (if they still existed) would have something to say about all of this. I know that some upright bass players are constantly fussing with their after string lengths to get the tonality they want to hear. When threaded adjustable tailpiece guts came to be in the 1950s or 60s it must have lead to lots of experimentation on all the violin family.