# Bending guitar strings

1. Mar 4, 2007

### DannyCov

Hi everybody I’m currently making/coding my own guitar synthesiser and I are interested in creating a 'bend' playing effect. By modifying the tension of guitar strings I presume I will be able to change the rate in which sounds travels in these strings.

From playing guitar myself I thought that if I change the force applied to the string it would change the strings tension. So if I changed the tension I would change the speed, which would in effect change the strings fundamental frequency (so creating the raise in pitch).

These are just my own thoughts; I’m not physicist personally, so I would very grateful if anyone with a grasp behind the theory of this sort of stuff could help me out!
It would be awesome if I could apply this real effect to my own synth!

Cheers Danny

2. Mar 4, 2007

### turbo

The rate of sound propagation in the strings does not change. What changes when you "bend" the strings is the pitch at which the string resonates, similar to what happens if you use the tuning keys to increase or decrease the tension. With a synth, you can also simulate downward bends, similar to dive-bombing with a whammy bar. Have fun.

3. Mar 4, 2007

### DannyCov

Thanks for the reply, do you have any idea of the appopriate equations I should use to create my algorithm? I've now just begun to look into sampled travelling waves as a place to start... hopefully it will lead to something

4. Mar 4, 2007

### turbo

Sorry, I know nothing about programming synths, but having played guitar for over 40 years, I know a little about the physics and practical aspects of playing.

5. Mar 4, 2007

### gabee

Actually, turbo-1, the speed of wave propogation in the string DOES change with tension, according to this equation:

$$v = \sqrt{\frac{F}{\mu}}$$

where v is the wave's velocity, F is the tension in the string, and $\mu$ is the mass-per-unit-length of the string.

The frequency at which the string will vibrate is then determined by the equation

$$v = \lambda f$$

where $\lambda$ is the wavelength of the transverse wave (in this case, the fundamental is DOUBLE the length of the string) and f is the frequency.

If you are just wanting to make a guitar bending sound with a synth, you really don't need any of these equations...however if you are wanting to model the frequency when a string is held at a fret and bent up 1 cm, for example, you can use them.

I suppose you would have to know the force with which the string is being held (this could be determined experimentally by finding the frequency of the wave on the string for a given wavelength and given $\mu$). Once you figure that out, you might find how the tension in the string increases after being bent to a new length. Then, If a string is held at a point x from the bridge and bent up a distance y the mass of that length of string will stay the same and the new length will be $l = \sqrt{x^2 + y^2}$. From there you can find $\mu = m / l$. THEN, with all this knowledge, you can model the frequency the guitar string will create by finding v and using the fact that $f = v / (2l)$. Whew! Good luck. :)

Last edited: Mar 4, 2007
6. Mar 4, 2007

### turbo

I understand that the speed of wave propagation increases as tension increases (which we perceive as an increase in frequency), but the rate of propagation of sound through a medium is proportional to the density of the transmissive medium, is it not? Does increasing the tension on the string increase the density of the material of which the string is constructed?

7. Mar 4, 2007

### gabee

Right, I assumed you had both meant velocity of the wave, since that is what is needed to determine frequency, sorry. ;) turbo-1 is right...the "speed of sound" of longitudinal waves through the string doesn't really matter in this problem; what matters is the velocity of the transverse wave on the string.

Last edited: Mar 4, 2007
8. Mar 5, 2007

### DannyCov

Thanks for the help this definately gives me something to get going with cheers

9. Mar 6, 2007

### billiards

If you can get your synth to sound like a convincing guitar I'd be impressed, even without the string bending effect. Obviously when you bend the string you increase the tension but this won't concern you because all you need to worry about is the change in pitch.

I had a very good physics teacher once who explained the properties of sound at a level beyond which I thought it worked, he was a seismologist so he knew a fair bit about sound waves. He talked about overtones, and the subtle differences between spatial and temporal frequency, and how two waves with different wavelengths could have the same speed and the same frequency (that took me a while to understand as it went against everything I thought I knew about waves), and how all these things and more went into controlling the timbre of sound. You might also want to think about the resonance of the actual body of the guitar and what that might do, how can you model that?

10. Mar 6, 2007

### DannyCov

Im actually investiging the body resonance of acoustic guitars by recording its body response. I have generated an algorithm based on the physics of a string and have had promising results, like you said to get the unique timbre of the instrument is the challenging part. Im looking to use the body response an actual guitar (a recorded wavetable) to possibly drive my algorithm as currently it does sound a little 'tiny' (much like you would hear a clean guitar through an amp) but fingers crossed I can achieve the 'acoustic' sound!

11. Mar 6, 2007

### cesiumfrog

Indeed, care to elaborate?

12. Mar 6, 2007

### DannyCov

13. Mar 6, 2007

### MonstersFromTheId

Facts from an expert on this...

It depends how far you want to take this D, but articulating a synth of any kind with a guitar based interface is VERY hard to do.

Yamaha did about the best job of this many years ago, although it never caught on 'cause - it did require some uniquely specialized playing techniques, it was an expensive interface, and just to set up all the programming properly to respond to the signals output, practically required a PhD in vibrational analysis with a bachelor’s in I.T. and programming.

For one thing the note a guitar emanates is NOT a steady note at all.

When you first pick a note on a guitar it starts out slightly sharp, then settles into it's proper frequency, and although this happens quickly (less than a half second), if this effect isn't accounted for (i.e. you try to use the actual freq of the string to determine what note is supposed to be getting output), you wind up with notes that are sharp, but not by an amount you can simply offset, since it's not at all uniform, since how sharp and for how long varies with about a gazillion variables.

And if you try to add a "delay before reading" function, in order to allow the string to settle into it's proper freq (which is exactly what 99.99% of guitar synths did to overcome this problem), that delay made it REALLY hard to play the instrument, since you had to play as much as a quarter second (an eternity in musical terms) ahead of the beat!

Additionally, playing a really quick series of 64th notes, just plain flat out COULD NOT BE DONE. Play one of those puppies fast, as in "speed metal" fast, or fast enough to pull off most jazz riffs, and what you got was NOT what you played, but instead an all but random series of notes coming out that depended on which note the synth first *figured out* you wanted played, as opposed to which note you actually played first (i.e. the order of notes played got scrambled if you played too fast).

Additionally the frequency spectrum (think FFT graph), varies WILDLY, and in incredibly complex ways, over the time from when a note is first plucked, to when it finally dies away, depending on - how stiff a pick you use, string size and tension, where along the string it was picked, whether or not the meaty part of your palm is grazing the strings near the bridge, and about a hundred other things.

And again, if you can't duplicate those hellishly complex details, your guitar synth sounds EXTREMELY,.. well,.. synthetic (which can actually be a GOOD THING - sometimes, but not if you want it to sound anything like a guitar).

Lastly, MIDI, as a data transmission medium, comes no where NEAR the kind of raw baud rate you'd need to carry ALL the information you'd need to carry in order to accurately duplicate the sounds produced by a stringed instrument when played with the number of subtleties normally associated with a well played guitar. (Great for power chords tho) ;-)

1) They had a set of sensors that you actually picked, mounted on springs, in the area of where the pick-ups would normally be on an electric, that sensed HOW HARD YOU PICKED THE STRINGS.

2) They had a separate set of ultra sonic sensors at the head of the guitar neck (up where the tuning pegs are on most guitars), that sensed where your fingers were placed along the neck (i.e. WHAT NOTE YOU'RE TRYING TO PLAY on each string).

3) They had yet another set of sensors (infar-red I think), to sense HOW FAR YOU WERE BENDING any individual string.

4) Additionally, they had a "WHAMMY BAR", that didn't stretch anything at all, but how hard you pushed on it determined how far the note was "bent".

5) Lastly there were a series of buttons that you could program to change the VOICES being sounded by the synth (to repro things like harmonics, a note damped by your palm, etc).

A few pointers from somebody who spent a lot of time doing this...

1) If you want to emulate a distorted electric guitar, DON'T try to sample a distorted electric guitar.

Instead, sample the electric guitar's output RIGHT FROM THE GUITAR OUTPUT JACK (run a cord directly from the guitar, into a mixing board to pre-amp it enough to sample).

What you want is the "pure", UN-distorted signal the guitar sends TO the amp, to be distorted BY the amp to form the basis of your sampled voices.

Set up your synth to play that UN-distorted signal into your guitar amp, so that you can USE THE AMP TO PRODUCE THE ACTUAL DISTORTION.

Chords sound MUCH more "real" and rich as a result, and you can alter the settings on the amp to vary the distortion without having to store (and set up articulation mapping) for gazillions of different amp settings.

(I used a Marshall JMP-1 to distort the output of my guitar patches, 'cause, well, Marshalls DO sound sweet, but that particular unit allowed you to store any combination of amp settings just as you'd store voice patches with a synth, and to recall whichever "patch" you needed with a foot switch - an invaluable ability when it comes to duplicating live what you did in the studio).

2) Get "coverage" (i.e. sample) the entire neck of your guitar using as many samples and therefore voices as possible. At a minimum 6 strings = 6 samples for first position, 6 strings = 6 samples for 2nd position, etc.

3) Tylenol doesn't rot your stomach quite as fast as aspirin, and Tanqueray gin doesn't give you anywhere near the hangover that cheap BuyRite gin does. Useful things to know since you'll probably find yourself runnin' through quite a bit of both before getting the results you want outta this!

BREAK A LEG MY BROTHER!

14. Mar 6, 2007

### DannyCov

Alright mate ur propably right, im only doing this is a hobby! but thanks

15. Mar 6, 2007

### MonstersFromTheId

P.S. if you get deep into this there's a lot more to cover. Things like the fact that you have to set up, at least the equivilant of ONE VOICE PER STRING, so that when you hit a note on one string, then hit a second note - ON THAT SAME STRING - the first note STOPS playing as the second note starts playing, while still allowing you to play more than one note when sounding more than one string to get chords.

16. Mar 6, 2007

### MonstersFromTheId

P.P.S. - Hey, the best hits often come from "hobbyists" bro! "Hobby" today, hit tomarrow ya know?

17. Mar 6, 2007

### cesiumfrog

DannyCov, you stated that "two waves with different wavelengths could have the same speed and the same frequency". I think that's wrong, i.e., impossible with waves that have a defined frequency (though not necessarilly if you really meant complex signals with different group- versus phase-velocites.. unless the waves are nonlinear..). Can you give any explanation or reference in your support (the link you gave doesn't even mention frequency)?

18. Mar 6, 2007

### Chaos' lil bro Order

We can argue that the wave speed increases if the mass per unit length of the string decreases. This is because it is more difficult to accelerate a massive segment of the string than a light segment. If the tension in the string is Tau and its mass per unit length is u, then

$$v = \sqrt{\frac{Tau}{\mu}}$$

So, increasing tension does not increase the density of the string. Increasing tension decreases the (effective) mass per unit length of the string (root side of the equation) and therefore increases wave speed.

In layman's terms, the thinner the string, the higher the sound. The tenser the string, the thinner it becomes. The tenser the string the higher the sound.

Ref. Physics for Engineers Textbook

Last edited: Mar 6, 2007
19. Mar 7, 2007

### turbo

The effect you describe (if it is even noticeable at all) would be negligible in controlling the pitch of a string. Bending strings = increasing tension to increase the frequency at which the strings resonate.