Jussi wrote: ↑
Fri Sep 22, 2017 3:06 pm
Thus, the most harmonic string is as thin as possible, as long as possible and under as high tension as possible.
Interestingly though - and let's see if I have this right.
If the string is longer, it actually has to have more tension on it right?
So, in other words, a Les Paul with a shorter scale length (let's pretend it's the 1st fret's worth) tuned to E has to have a lower tension than a Strat with a longer scale length. IOW, if you "add a fret's worth of length" to the neck, at the same overall tension the string's going to have to be tighter to be the same pitch.
But, if I'm correct, a thinner string will have LESS tension on it tuned to the same pitch than a thicker string. For example, tuning a B string to an E pitch is going to have a lot more tension than an E string.
So don't these two counteract each other?
If so, the trick is to find which thickness has the highest tension at the lowest diameter.
Looking at the link: http://www.daddario.com/upload/tension_chart_13934.pdf
For an E string at 9, the tension is 13.1 (lbs per square inch I think).
Then at 10, it's 16.2. That's an increase of 3.1
11 is 19.6, so that's a 3.4 increase.
a 12 is 23.3 so that's a 3.7 increase.
So which is the more favorable ratio? We want more tension, but, we want thin-ness. So it actually sounds like the 9 or 8 0 it's a 2.5 increase from 8 to 9 - or do I have that backwards? The bigger increase per unit of thickness is better?
In practice there are many other factors which also have an influence as well as obvious constraints on things like string length, radius and tension. I've measured harmonics which deviate both above and below the mathematical model, often on the same day!
Our Piano Tuner has a piano tuner that measures overtones - it actually allows him to store presets for various pianos - so each and every piano is different - this allows him to do precise stretch tuning for each instrument - he recalls the memory and tunes based on that (making adjustments of course).
I imagine there are many factors...
As an interesting aside, bowed instruments don’t suffer this form of inharmonicity as energy is constantly being supplied to the system via the bow and gets distributed perfectly harmonically (though there are other imperfections which lead to imperfect harmonics)
Yes, I had heard this. I believe it's possible this may have contributed at least in part for the strings becoming the "core" of the orchestra - they played "in tune with themselves" which makes it easier for all of the members to tune to each other, and since they have not frets, can further refine to other temperaments as well.
As far as we're concerned - yes, I would believe how you pluck the string, and where, and how old it is is going to cause it to vary, as well manufacturing imperfections.
One thing I noticed with the plain G - the "warble" became more obvious to me as I kept moving to thicker and thicker gauges. I probably also became more attuned to it though...(and your other solutions - this has been a problem for me for decades - I've been through many brands of strings over the years).
I guess I'm at the point where I wonder if moving up to a 12 on the high E would give me more, or less inharmonicity, or, if moving back down to a 10, or even a 9 would improve it.
I'm also saddled (pun intended) with the issue of string to string balance and breakage - The B at the current tension is "floppy" - easy to bend a step and a half - but the high E is tough to bend that far at all. So a 10 or 9 would improve that, but, I'd be more likely to break it (which is why I went to 11s to begin with). That said, I once put a 19 wound G on, and broke it almost immediately - I think becuase it was SO much tension.
Also, the B as is is looser - under less tension because of its size (14) and doesn't warble, so I wonder if the High E being thinner would benefit.
But then I'll break it.............