MIMF

So a random internet search frenzy prompted by questions on baritone guitar string gauges got me to a brand new subject, for me at least - inharmonicity. It's even hard to spell...

So the concept is that some plucked string instruments, like guitar, can have a string choice for a given note that has it's harmonics mostly closely in tune, or dramatically out of tune. I think the way it works is that a stiffer, heavier gauge string with higher tension will have greater inharmonicity for a given note. I found this quote on this page: http://www.acs.psu.edu/drussell/Demos/S ... ess-B.html

"For a long, thin string (like the E4 string fretted at the nut on the headstock) the inharmonicity is negligible, and the frequencies are almost exactly harmonic (at least as far as the stiffness effects are concerned). For a long thick string, (the low E2 string fretted at the nut on the headstock) the inharmonicity is noticeable for the higher harmonics, but not very noticeable for the lowest frequencies. However, for short, thick string (the low E2 string fretted near the sound hole) the stiffness effects are quite large, and the inharmonicity is easily noticeable even for the first few harmonics."

I found this fascinating, because it solves a conundrum that I have had ever since I built my archtop last year. I first strung it up with what I had in the shop at the time, which were .011 - .050 nickel strings and really liked the sound. I bought into the idea that I had to use medium gauge strings on it, and put them on and hated the sound. It sounded dead and thuddy, got better with light gauge strings, got better again with .012 - .056 tuned down a full tone, in fact it really came to life at that point, and I had no idea why. I also always wondered why an E3 or a G3 played on the sixth string sounded so different compared to the same note played on the fourth or third string. Dull and thuddy compared to vibrant and alive. The idea would seem to be that by reducing the gauge of the string and lowering it's tension you can reduce the inharmonicity, particularly when playing up the neck. I would really love to hear what other people think of this idea.

Edit: Particularly on the idea of scale length relative to inherent inharmonicity (it's still hard to spell). Would a longer scale - say 25.6" compared to 25" - yield less inharmonicity and sound better played up the neck, if string gauges were chosen for the same tension with both scale lengths?

Brian

This is one of the main problems that multi-scale arrangements solve. By increasing the scale length of lower strings, you can use a lighter string gauge and still have even tension across the fretboard, while still keeping the higher strings in at appropriate gauge/tension. Win-win.

Inharmonicity is mostly caused by the stiffness of the strings. For plain strings that's just a function of the diameter, BUT the stiffness goes as the fourth power of the diameter, so small differences in string gauge can make a large change in stiffness. For the wound strings it gets more complicated.

I've got an old program (in BASIC!) that I use to calculate things like string tension. You input stuff like the material and diameter of the string, the length and the pitch, and it outputs the tension and the %T; how close the string is to breaking. For wound strings you specify the core and wrap diameters and materials separately. Thus, you can get a .032" string by wrapping a .016" core with .008" wrap, or a .012" core with .01" wrap. If the core is steel and the wrap is bronze (the program doesn't differentiate between p-bronze and 80/20) the two strings will have equal weight and tension at the same pitch, but the one with the smaller core will be closer to it's breaking tension. Since the stiffness of a wound string once it's up to pitch is all from the core, the smaller core will give less stiffness, and lower inharmonicity. you've got to pay attention to the way the string is built.

All of that assumes round wrap wire. I'm not at all sure that flat wrap works the same way; if it overlaps it could add to the string stiffness. 'Flat top' or 'ground round' strings that start out with round wrap wire and grind off the surface to reduce 'zip' noise should act like round wrap.