Lazy string bending question

Funkfingers

Fender AVRI Jazzmaster - 10s
Fender AVRI Jaguar - 11s
Squier VM Jaguar HH (Danelectro-style fixed bridge) - 10s

HTH

TADodger

I guess that it is the real life feeling that I am wanting to base it on and, although to some extent subjective, if 9's on a Strat generally feel like 11's on a Jag that is a good starting point. It may only be £6 and 20 minutes, but it seems to me that i may as well be armed with every chance of getting it right first change.

from what has been said, it looks like 12's may be a step too far for my digits so I will fit a set of 11's.

Thanks for the input all.

mart

Musicwolf said:

...
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.
...

Just to follow up on this, I thought a bit about the geometry. If you bend a string by moving it 1/2" sideways at the 12th fret, then on a 24" guitar that increases the speaking length of the string by a factor of just over 1.00085, i.e., an increase of 0.085%. And on a 25.5" guitar it's lower - a hair over 1.00075, i.e., about 0.075%.

(If you bend at a different fret than the 12th then that 1/2" bend increases the length more, but the 12th is the easy one to calculate as it's in the middle).

So how does that 0.085% or 0.075% stretch translate to an increase in pitch? That 1/2" bend raises the pitch by a semitone or so, depending on the string and the guitar, which is about a 6% increase. 

(I can do the maths, it's just the physics I can't handle at all!)

Musicwolf

mart said:

So how does that 0.085% or 0.075% stretch translate to an increase in pitch? That 1/2" bend raises the pitch by a semitone or so, depending on the string and the guitar, which is about a 6% increase.

2 glasses of wine down (and 30 years since my Physics degree) so easier to look up what someone else has already done;

There are numerous mechanical and acoustic properties which heavily influence the resultant pitch from a string bend. Analysis of the physics of string bending suggests that the resultant pitch of a string bent at its midpoint is given by

 

where L is the length of the vibrating element, T is the tension of the string prior to bending, θ  is the bend angle, E is the Young's Modulus of the string material, A is the string cross sectional area and  is the linear density of the string material.

Thus, the pitch is not only dependent on the bend angle, but on material properties of the string such as Young's modulus; this may be interpreted as a measure of the stiffness of the string. The force required to bend a string at its midpoint to a given angle θ is given by

 

It is important to note that the resultant pitch from string bending is not linearly correlated with the bending angle, and so a player's experience and intuition is important for accurate pitch modulation

(I can do the maths, it's just the physics I can't handle at all!)

Physics is just maths with pictures

TADodger

Spent part of the very wet day here in Rugby by giving the Jaguar new strings and a set up. I've gone for 11's and the neck was like a banana, but with a bit of trussed tweaking and slight work on the nut it seems to be set up broadly as fender suggest and to suit my preference.

I haven't messed with neck shims, but I think that the larger strings and Mustang bridge may have made the shims unnecessary. I have tried a tip I saw online to tape one leg of the bridge to stop it rattling. It seems to stop any rattle and as I don't use the term a great deal I will see if it stays or not.

Anyway, now it is done I quick picture albeit not able to get it outside due to the rain. I have to say that it seems a great buy for £320 and some new strings.

https://i.imgur.com/FfnyFTS.jpg