Maybe the OP should have just asked, "how many angels can dance on the head of a pin? "
There are two or three methods of figuring compensation, and as long as you understand what compensation is compensating for, and the relationship between vibrating string length and pitch, then you will be comfortable using any of those methods.
Originally posted by Alex Z
OK. 1 step doesn't work. An octave doesn't work. What the heck works? Are we being evasive here? Try something in the middle. You choose the interval.
The claim is that reducing tension of a string -- the same string -- reduces its stiffness and therefore reducing the compensation needed. Ain't my claim.
Cannot there be some way to test the claim? If not, then it's only a conjecture, without evidence.
Alright, alright. "Simon Says try an interval in the middle."
I am not being evasive, and I think my use of the word "theoretically" more than states that this is conjecture (although lowering tension does, in fact lower the tension and that lower tension does in fact lower the stiffness.
The conjecture, or if you prefer theory, could certainly be tested. It would require some very sensitive equipment, though, due to being such a minute change in compensation. In my opinion, it's not worth the effort because no one would ever hear it.
Vibrating strings are still being looked at by physicists, which perhaps indicates characteristics that are still poorly understood even by science. Then there's the problem of how each individual actually presses his strings down, and how each individual ear perceives the pitch and the overtones produced.
It's quite possible that, as "claimed" above by Johnnycake White, we are approaching the realm of those dancing angels now. Or maybe it's just we devils playing at advocacy.
"The conjecture, or if you prefer theory, could certainly be tested. It would require some very sensitive equipment, though, due to being such a minute change in compensation. In my opinion, it's not worth the effort because no one would ever hear it."
If you've never tested it and don't have any equations to calculate, how do you know it is such a minute change that no one would ever hear it?
Is there a difference between "there is no change" and "I have a theory that there is a change but I know for sure that no one would ever hear it."
A while ago Mr. davidppp and I had an exchange about whether or not the same string at a lower tension would need more compensation, not less. My ears were saying "yes" but the equations were saying "no change in compensation." I couldn't reconcile that, and Mr. d helped out. I think the ear trial was perhaps affected by greater stretching in the slacker string, due to the feel. Mr. d tried it out on some sensitive equipment, and no change was seen, which was predicted by the equations. Ears, equations, and test equipment did not indicate that the lower tension would need less compensation.
If I'm setting a bridge, I'm setting it to be in tune considering the way I play, and so if I'm stretching the higher slack strings more than tuned-up-higher same strings, the fretted note will sound slightly sharper, and then I'll need a bit more more compensation -- but not everyone will.
Hope this helps.
I only have material written by experts and about five decades of hands on experience with piano scales behind my theories. I admit some things are speculative, but they are based upon logical deductions and practical applications. There is still so much information that is not known, and that's readily apparent in this discussion.
I have stated many times in this discussion that not everything is known, and that things don't always give the expected results. I think you have missed that framework, buit I should probably blame myself for not explaning that more thoroughly.
There is one thing I would like to point out, though, that we have all failed to admit to in this discussion. That"thing" being the fact that any string, even with no tension placed upon it, has an inherent stiffness. It also has an inherent elasticity. These factors can also throw ofgf any calculations. Is, for example an .009 string more st6iff at 12 lbs of tension, or is a .010 string more stiff at 11 lbs tension' The determining factorcould be which wire is stiffest before the tension is applied.
The reason I say that the change in compensatiopn should the tension be altered would probably not heard is because the usual amount of compenation is only a matter of a few cents. Let's give that a definite number, say 7 cents of pitch. If one drops the stiffness by two percentage points, the compenstion would in all probability change by no more than that amount. Two percent of the initial 7 cents would amount to a change in compenation to .14 cents in pitch. The human ear supposedly can differentiate tones no closer to each other than 3 cents. .14 cents (or if you prefer .0014 of a semitone) could never be heard by a any currently tested human being, and may not even be discernable with some fairly decent measuring devices. This may not be fact (it's somewhat within th realm of remote possibilities that the stiffness factor might have a gigantic effect on compenation) but it certainly isn't a baseless surmising by a mere wide-eyed, raving lunatic.
Wound strings, as I've stated, get even more complex simply because an extra layer (pun intended) has been added to the equations. The type of wrapping material also has its own stiffness and elasticity, it's own vibrational characteristics (it's helical, whereas the core wire is straight), and also reacts with that core wire, varying both its own and that core's vibrations.
My thoughts might not be yours, but I think we can both agree that compensation is something that is perceived differently by different players and their differnt habits, and that the banjo and its players are not perfect so compensation can't be perfect, either. I can only conclude by saying that although there may be some speculation involved in my thoughts, speculation has led to some investigations that have borne some pretty important discoveries, and the development of some rather sophisticated devices to test those discoveries.
Temper tuning works for me. My strobe tuner has "sweetened" tunings for all my instruments. (and i play 11 string pedal steel) usually a difference of plus or minus (up to) 3 cents
One thing that can illustrate the string stiffness idea is the difference between the bridge saddle on a steel string guitar vs that on a classical (nylon string) guitar.
Nylon strings are not nearly as stiff as steel ones, and have very little change in stiffness between the bass and treble strings, so the bridge saddle is relatively straight—Steel guitar strings keep getting stiffer towards the bass, so the bridge saddle is set at more of an angle—guitar saddles are often slightly compensated as well as it can be done with a saddle that's 1/8" wide.
Exacerbating the issue is the fact that guitars have a whole lot more sustain than banjos do, so notes ring longer and accentuate "off" intonation. Banjos play a lot of rapid fire notes with fast decay, so it's possible to get away with a straight bridge.
When you string a wooden guitar-like instrument that has more sustain with banjo strings, as is the case with a banjo-lute, it's necessary to make the saddle have compensation . The same is true with mandolins.
Here's the bridge saddle on a banjo-lute—not only slanted, but wider to allow for compensation:
Against my better judgement, I'm gonna weigh in on this:
A. Why compensate?
B. How best to compensate.
Two simple rules of physics apply to both:
A. The shortest distance between two points is a straight line. While the strings on a banjo or guitar are indeed straight lines between the bridge and the nut, because of the spacing differences at both points, the treble and bass strings are further distanced than the 3rd string on the banjo and middle strings on a guitar.
Differences in length, however slight=intonation problems. So, how best to compensate for that?
B. Parallel lines can go on to infinity and will never intersect. But the strings on a guitar or banjo are not parallel which means, if they were to be extended beyond the nut, at some point they would all intersect. At that point, the focus, if you were able to place a compass point and draw an arc where the bridge should be, that arc would be the ideal shape for a compensated bridge. That is the idea behind the stair stepped compensated bridges and the "crescent" shaped ones.
On a steel string guitar, the saddle is slanted to compensate for the treble strings, since very few play on the bass strings high enough up the neck where intonation problems are usually manifest. On a nylon stringed/classical guitar, little to no compensation is necessary, since the string spacing at nut and saddle are nearly identical, thus, so is string length.
That's my 2 cents and I'm sticking to it.
I wonder if changing the tuning has been considered. The "standard" tunings of G and C seem, in my mind, to have the most 'slightly- off' tuning problems. I have less trouble with "open" D, A, and D modal, Last Chance and other variations. When playing in a session or small ensemble you sometimes have to 1. use a capo or 2. change tunings AND have more than one banjo (good excuse to acquire more banjos). Fretless banjos and partially fretless banjos can address some of the tuning problems but bring up some others.
I have one banjo, though, that is bang on. So much so that I've considered the possibility that it has supernatural origins.
'Greasy Meat' 29 min
'Dogwood Custom Slothead' 56 min
'Neck blank photos' 2 hrs
'Where to get this part' 2 hrs