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With 9s you’ll have to bend the string halfway to the next county before you’ll get a full tone up...
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Only two things are infinite - the universe, and human stupidity. And I'm not sure about the universe." - Albert Einstein
Just curious.
AFAIK slacker strings need more deflection to bend a note up, which is why classical guitars don't sound out of tune with a high action
The vibrato spring tension works rather like a Bigsby. Thus, it ought to be possible to change to a stiffer spring.
The frequency (pitch) of a vibrating string can be expressed using the formula;
frequency = SQRT ( Tension / Mass per unit length) / String Length
For a given frequency (note) if you keep the Mass per unit length (i.e. string gauge) fixed then for a shorter Length (scale length) you must reduce the Tension. Lower Tension = easier to bend.
Alternatively you can keep T fixed and increase M by using a heavier (thicker) string. This is the reason why some players fit heavier gauge strings to a Gibson (24.75” scale) vs a Fender (25.5” scale) so that they ‘feel’ the same.
When you bend a string then Hooke’s law comes into play. Force = k x where k is a constant (for the particular string) and x is the displacement (bend). The maths gets complicated because you are not stretching the string in a linear fashion, you are bending it sideways (so now you have to build some geometry into the equation). Without working through the maths (‘cos it is a. very early, b. I’ve only had two espressos and I need a third and c. it’s a long time since I did this sort of maths) the net result should be that you need to bend the string ever so slightly less on a shorter scale guitar to achieve the same increase in pitch (I stand to be corrected). In practical terms it is not about distance, it’s about force and bending feels easier (requires less force) on a short scale guitar or with thinner strings or with drop tuning.
In practice other aspects of the guitars construction and set up will alter the 'feel' so sometimes swapping between guitars may not make comparisons quite so straight forward (i.e. you may find one particular neck shape easier to bend than another. Not because the force required to bend is different but because your fingers are at a better angle to impart that force).
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Only two things are infinite - the universe, and human stupidity. And I'm not sure about the universe." - Albert Einstein
@Musicwolf - Thanks for the science behind this but in the bending part you seem to be saying that a short scale should = less bend to achieve any particular pitch change which seems opposite to practice, or, is this showing that for any increase in string size the bend will be slightly less?
I can't guarantee that the maths at this time of the morning but I just tried a practical experiment using a Telecaster (25.5”) and a PRS SE Chris Robertson (24.5”). The PRS has 10’s and the Tele Hybrids so I had to make comparisons on a wound string. Trying to bend a note whilst checking on a rack tuner and then trying to measure with a ruler isn’t going to score well on a Gauge R&R study but it did seem to confirm that there was more displacement required on the longer scale length Telecaster, but it’s slight. The difference in feel is quite noticeable.
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Only two things are infinite - the universe, and human stupidity. And I'm not sure about the universe." - Albert Einstein
Obviously they're a little thicker so your fingertips will need to adjust a tiny bit.
***
The physics question is an interesting one as the the interaction between scale length, total string length, sideways movement to bend a note and sideways force to bend a note is quite complex. I'm fairly sure I could run the numbers for any given string gauge and pitch, but I'm not sure I quite have the energy. I would be interested to know if anyone else has done it properly.
Well this has got me playing around with various guitars and I've just picked up three guitars in quick succession. A PRS Core Studio 22, a PRS S2 semi-hollow and a Patrick Eggle Berlin Pro. All 25" scale length, all strung with EB Hybrids (9 - 46), all in standard tuning. High E string 12th fret bent up to F#.
The two PRS are near as dammit identical geometry, the Eggle has about 3mm less string between nut and peg.
It’s entirely subjective but I can definitely ‘feel’ a difference. It’s not massive but it’s there. In order of ease of bend I would say Eggle > S2 > Core. Worth noting that the Eggle and S2 have been re-strung / fret polish within May, the Core is more than due a change. The Core has the lowest action.
It's not just about the numbers / theory.