Well, the title says it all 
I have relatively little trouble bending the B and G strings by one step, but the high E always feels like hard work - even at the 12th fret (easiest place to do a bend because the string has the most āflopā).
Currently using 9-42s on 25.5 scale guitars.
Is this normal? Do I just need to setup my guitar better? Should I give up guitar? 
(no, Iām not giving up guitar donāt worry!)
In the Malmsteen world, thereās a need to achieve a 1.5 step bend on the 21st fret fairly regularly. Using a .008 high E makes a difference for bending, unsurprisingly. But I find I need to keep extra high Es around because Iāll break two or three of them inside of a single set of stringsā life span. Not sure if this is useful to you but my main point is that 8s are something to consider.
Ha, the nasty 1.5 bend!
Thereās one in āThe Curse of Castle Dragonā by Paul Gilbert, and I must have broken 10 x (high E strings) on it while trying to record my cover
(Also, I never understood why YJM doesnāt just ask Fender to build him a 22-fret)
Well, this is a lot of fun.
I asked years ago about this and someone told me there is more tension on the outer strings, but Iāve never been able to verify this.
The reality is that I can do 2-tone bends in the B and G strings but there is no way Iām doing that on the high e-string. There has to be some explanation behind this beyond individual skill as it seems to be a recurring question on the internet.
In saying this, I donāt think you should have ātroubleā doing 1-tone bends around the 12th fret, definitely not beyond the 12th as the string doesnāt have as much tension.
The gauge shouldnāt be a problem. 9ās are widely used and considered soft.
I had a smaller scale guitar before and now I have a 25. I feel there is more tension on the high e-string than before. Iāve snapped the high e-string twice in a month doing a 1.5-tone bend on the 10th fret (from d to f), which I could do before without much trouble. There must be something there, too.
Probably the 8ās will help you and so will tuning down if you are in standard tuning but ultimately you should be able to do at least the 1-tone bend. Do you feel you donāt reach the full tone? Does it hurt? Do you ever warm up for bending exercises? (I used to do pentatonic in bends to reach the next legal note, it was good practice, but Iād suggest doing the minor/major scale to avoid tendinitis).
I have some difficulty on my more played out guitars, how are you frets looking?
thank you all for the responses!
I can even reach the 1.5 bend but it feels like itās infinitely more work than on the G and B. Yes Iād say that If I had a piece with a lot of 1-tone bends on the high E itād definitely hurt fairly soon.
I have to confess that I never do any traditional āwarmupsā anymore - I just directly play the piece of music I want to play / record / practice. If that contains a bend that Iām not doing properly, I may repeat it a few times and try some adjustments until it feels/sounds decent. Very often, this means that I may avoid beinding the high E string altogether, and just move stuff to the B string if possible.
Pretty poorly on pretty much all my guitars 
I need to get some proper setups done but Covid19 said ānopeā.
PS, I just thought about this:
Shouldnāt the 12th fret be the easiest to bend for all strings? My reasoning is that at the 12th you have the āsame amount of stringā left and right of the fretted note.
I think itās always going to be more work than on the 2nd and 3rd string. Thereās G.Govanās bending masterclass on youtube and on his first video heāll play around bending up to 3.5 tones I believe but he didnāt do all those extreme bends on the high e string, I think even he will recognise the limits of the strings.
Itās worth trying on a different guitar just to confirm your suspicions. Just donāt hurt yourself.
I suppose youāre right but I always thought the distance between notes after the 12th fret is shorter and I feel the bending distance is shorter, too, but I may be playing this by ear so donāt quote me.
Good point! The physics may not be as simple as I thought
The high E diggs into my fingers more because itās so thin.
I find itās easier to bend on my guitar with 11s. I assume itās due to the pressure being more evenly distributed.
I also think that theres little room for adjustment with the high E because itās right near the edge and if you fiddle to much to get a better grip it can slide off the fret. Also because theres not much fretboard behind the fingers you have to come at it at a steeper angle. Where as most the others you can get far more horizontal in angle.
Just trying to bend the other strings with a steep or more vertical angle also feels akward. So I think that might be the main issue?
I think if youāre having trouble, itās likely more to do with this than other factors. It probably means you donāt get to push the string with the same area of your fingertip that you do for other strings.
And the distance from the string to the edge of the fingerboard isnāt necessarily the same with every guitar design. And occasionaly, small variances in manufacturing can result in either the bridge not being ideally positioned, or the neck not being aligned perfectly in the neck pocket. I know Iāve picked up some guitars in a music store that had less fretboard āmarginā than others.
The first thing I do when I try out a guitar Iām thinking about buying is put it under my chin like a violin (not completely literally, but that gives you the basic idea) to see how the strings and the edges of the fingerboard line up.
Position of the nut or the nut slots could be another variable, but it seems like that would be harder to get wrong unless somebody is cutting the nut slots by hand.
In any event, on a guitar you own, you could experiment with either slightly changing the position of the nut, or using a narrower-spaced nut to see if that makes you happier. Some bridges allow you to adjust the spacing at the bridge, but I think most of them have the saddles lined up in āgroovesā now. Depending on the bridge design, it might be reasonable to swap in another bridge with narrower spacing.
Before modding your gutiar, the simple non-pandemic way to test whether some guitars bend easier for you than others would be to go to a music store and try doing bends on a bunch of different guitars to see if you have the same difficulty on all of them. String gauge is a potential variable there too (though I think 9s are pretty standard on strat-like guitars at least), but you should also be able to visually inspect the amount of fingerboard margin.
Just never bend and slide instead, problem solved.
But seriously, does it feel like it hurts or it physically hard?
Abstract:
The physics seems pretty straightforward to me.
Analysis:
The tension of a guitar string is a function of length L (inches), weight per linear distance W (lbs/inch), and frequency (Hz): T = 4*W*L^2*F^2/386.4 = S*F^2, with S being roughly constant for a given string and fret [1]. (Iāll ignore the small change in length that comes from bending and fretting, and focus on tension as the dominant variable.) Then the force required for bending is dT = 2T*dF/F. Since dF = F*(2^(n/12) - 1) for bends of n half-steps, we get dT = 2T*(2^(n/12) - 1), meaning that the force required to bend a given interval is proportional to the tension of the unbent string. I donāt think the bending distance (lateral deviation of the string) matters too much as far as effort is concerned.
The tension of each string is often published by the manufacturers. A quick scan of several manufacturersā tables for various gauges [2,3,4,5] indicates that there are no hard and fast rules about which strings have the highest tension, but DāAddario EXL120ās at 25.5" and standard tuning look like this:
The force felt on the fingertips is just the along-string component of dT, so 2*dT*sin(alpha) where alpha is the angle in radians between the bent and unbent string. The factor of two is because we are increasing the tension on both sides of the string (11th fret to nut and 12th fret to bridge) and those two lengths are almost equal.
When we move away from the 12th fret, our approximation for the force felt on our fingertips becomes dT*(alpha + tan(beta)). When weāre close to the nut, the angle at the nut end (beta) is larger than alpha and the tangent term dominates. Closer to the bridge, the opposite is true. So jlopez is correct, the higher up the neck you go, the less force is required for the same amount of pitch change. This effect is pretty consistent across strings. So it remains true that the amount of force required to bend a string is proportional to the unbent tension of the string.
Weāre assuming a double-locking nut for simplicity. If the nut or bridge allows the string to slide, then the distance required for bending to a given pitch will increase, though the force wonāt be too affected, and our results will still hold.
Discussion:
While itās true in these results that the high-E string does take more force to bend than the B-string, the G-string takes even more force, and the lower strings take even more than that, since itās all just dependent on the unbent tension, but I always find that the thicker strings give much more pitch response for a given amount of bending āeffortā. I assume this is because thicker strings give lower pressure due to greater surface area contact with your fingertip. There also may be a psychological effect: thicker strings seem to sustain longer and I think I end up squeezing thinner strings harder when I bend in a misguided attempt to get more sustain from them. I also tend to agree with the leverage arguments mentioned above. Technique seems to matter, too. Bending with forearm rotation rather than finger extension makes a lot of difference in terms of how hard it feels like Iām working for a bend.
Also, if you can bend hard enough to break your strings, then it doesnāt seem like force is the limiting factor.
Conclusion:
None to speak of. The reason bending is harder at low frets is explained, but the reason the high E string feels more difficult to bend is still just a guess. This was fun, though.
Also:
Oops. Sorry.
References
Dear @induction, many thanks for choosing our journal.
While the science in your manuscript appears solid, we are puzzled by your choice of units. What are there inches/lbs that you speak of?
Until your manuscript is converted into SI units, I am afraid we wonāt be able to process it further.
Sincerely,
Jimi Pickslanto,
Editor in Chief
Physica Guitarristica Scripta
Jokes aside that was a great post, thank you
Pretty straightforward.
Amazing level of detail in that answer, mate, thanks for the input. But to the layman the word straightforward has a different meaning!
This may well be true on paper but I can easily bend the G-string 1.5 tones or more without as much effort or fear of breaking the string. So tension might be a smaller factor than we give it credit for.
Loved the sense of humour! Keep it up.
Not sure how helpful I can be but hereās my experienceā¦ back when I was into SRV there was a tune where I broke a few high E strings on the same lick at the fret on the same day! I think by the 4th string the issue went away, this was a while ago but I suspect I changed my technique from holding the sting down and sliding to just pushing the string up from under. Now Iām on a YJM strat and the scallops make it a non-issue, but again with the scallops, itās even easier to apply more pressure along the fret then down onto the fret, granted at all times Iāve tuned a half step down. Iām travelling and donāt have my guitars with me, so this is really me just thinking about it.
Think itās just judo, apply pressure at the right points
edit: and vector I should say!
This is interesting, Iāve noticed I often bend and even vibrato with my thumb not touching the neck. I guess Iām using more forearm rotation (edit: more of an up and down motion than rotation) ! Never thought about it, but I suspected itās something I had to look into eventually. Great post!
Iāve broken a couple of strings by pinching the string against the edge of a fret while bending. Apparently itās quite usual to pull down the string a bit right before the bend comes and it is possible this is responsible for a lot of the breaks.
Cool replies all! I never realised how scalloped frets could allow you to get the fingers in a better position for pushing/pulling the string. Makes sense!
Also @jllopez you were totally right, bending feels easier in the higher frets (beyond the 12th). So my initial theory (just looking at string length on both sides) was definitely wrong / oversimplified.
This is an interesting question @Pepepicks66! I paid more attention to it and the real problem is not the force I need to apply, but the fact that I feel like my nails start to want to separate from the skin of the finger - if that makes sense? Again, with 1-tone bends this is only a problem on the high E.
The angle with which my fingers approach the string may definitely be a factor!
Yep, high-E is hard to bend for me. In most data Iāve seen E and G strings have more or less similar tension (B-string usually has lower tension). which is interesting.
Iāve just tried to do a whole tone bend on both strings, and results are as follows:
Basically, the angle neccesary to change the pitch depends on many factors, such as tesnion force, Youngās modulus, and cross-section etc. While tension force and Youngās modulus for E and G strings are more or less similar, cross sections are not.
Letās take a simple formula:
cos phi ā (Tk^2 - EA) / (T - EA),
where phi - angle neccesary to make a bend,
T - tension force,
E - Youngās modulus for a string
A - string crosssection
k - koefficient of frequency change (ā1.122 times for a wholetone)
I use 0.009 vs 0.016 strings as reference string diameters. I assumed tension and Youngās modulus for both strings similar (60N and 170GPa respectively).
For this data I get angles ~3.8Ā° and ~2.2Ā°, i.e. E-string requires more angle to achieve the same bending (theoretically). For a 650mm guitar scale-length it gives us:
325tan(3.8) ā 21.6mm shift
325tan(2.2) ā 12.5mm shift.
(325mm for a 12th fret which is half of scale-length)
Though I used a lot of simplifications the result is in agreement with my experiment and my overall feelings ))
