# Does a piano string slowly stretch (creep) over time?

1. Apr 19, 2008

### inkling

Ok, I need some help settling another piano tuner argument.

When a piano string breaks and is replaced with a new one, it takes many
tunings until it becomes stable. It can be brought to the correct pitch, and
will seem to stay there, but in a few days it has dropped in pitch drastically.

The most obvious "folk" explanation for this is that a new string, under load,
actually continues to slowly stretch for quite a while (weeks or even months)

Is this physically possible?
What is the mechanism that accounts for this behavior?

I have heard of something called "creep deformation" but from what I have read,
a solid will not "creep" unless it is around 30% of it's melting point. (I think that
works out to 750 degrees for piano wire.)

Any help?

Kurt

2. Apr 19, 2008

### phlegmy

well i cant tell you exactly why but i can tell you the same phenomenon affects guitar strings, once you put a new set on and start playing you've got about 10mis before you've to tune up again, and then maybe in an hour after that and maybe once more before they stay in tune.

when i first noticed this i put it down to the windings on the peg, which adjusts the tension. i wind the loops of the new strings over eachother so that the first loop is done under relativly little tension, as i wind the peg, the tension keeps increasing but the previous [first] loop is "locked" at that lower tension by the next loop, occasionally it slips as you keep winding and you can hear it slide as well as notice a sudden drop in pitch.

i figure that while playing the strings are tugging at the loops on the peg which slowly relase the trapped low tension loop at the start, lowering the overall tension. then you tune up again, but now the first loop is at a higher tension.

i suppose this is a reasonable guess. to try to avoid it i often tune the string way above its normal pitch then loosen it below its normal pitch and then tighten it again. also when tuning my guitar i almost allway approach the correct pitch from below.

3. Apr 21, 2008

### Andy Resnick

Creep is a real phenomenon. Most materials will creep under tension, regardless of the temperature- piano strings are under quite high tension, IIRC. There is no good theoretical model for why creep happens, or even what it is.

4. Apr 21, 2008

### Oberst Villa

dont know much about material science, but I think one important distinction is between amorph materials and materials with a crystal structure.

amorph materials behave like a fluid in very slow motion, i.e. they may show creep. I think a good example is asphalt, I heard of an long-time experiment where you could see how a lump of asphalt creept downwards during several decades. some people say that the glas in old church windows tends to creep down (over several centuries), with the result that the glass at the bottom of the window is thicker than at the top (but might be an urban myth, dont know)

on the other hand, I think that (at least theoretically) a crystal structure without any impurities should show no creep at all, with all atoms "knowing" their correct place within the crystall lattice.

Last edited: Apr 21, 2008
5. Apr 21, 2008

### chuy

But how about the Floyd Rose bridge? http://en.wikipedia.org/wiki/Floyd_Rose

When you put the string, it doesn't need to wind loops to hold the strings, they hold due to the pressure that exerts the screw. And in the other end of the string also are holding with a screw near the nut. But anyway you need to tune it again because the pitch also come down. Although maybe this effect is lees here than in the other case is.

Last edited: Apr 21, 2008
6. Apr 21, 2008

### Andy Resnick

I don't know if I really know about this stuff, but glass is not a fluid. Obsidian arrowheads remain sharp after thousands of years. The window stuff is an artifact of the manufacturing process.

In fact, the existence of "Bingham fluids" (fluids with a non-zero yield stress) is still debated. Toothpaste is a Bingham fluid (if you think it exists).

Creep is likely due to the migration of dislocations within a material, but I don't know what the state of current research is on that point. I wonder if anyone simply left toothpaste on their toothbrush overnight..... in a humidified environment, of course.

7. Apr 21, 2008

### Atomsk

If I remember from my days of attempting guitar lessons. Guitar and piano strings are very long tightly wound springs. Springs all have different spring constants which is how much force is required to compress or stretch the spring a certain distance (N/m) and if you leave a spring in a strained phase that spring constant will change over time to adjust to the new stress level.

Think of a slinky, you pull it too far or leave it dangling for an extended period of time and it never compresses back to it's original state if set it at rest.

I'm sure there are some details lacking but I'm still a novice in my opinion in the physics world.

8. Apr 21, 2008

### brewnog

This isn't quite true. It's worth mentioning that creep is actually very dependent on temperature, with temperature being a function of the creep rate. Creep is defined as the time-dependent strain of a body over periods of time when subjected to stresses below the material's yield stress. Some materials (like Tungsten) don't suffer from creep until very high temperatures, and most metals require a temperature of at least 30% of their melting temperature before creep will occur.

9. Apr 21, 2008

### Bob3141592

Are these piano strings single strands or cladded in any way, say by another material covering the strand or by another strand being wound around the first? In the latter case, I can see static friction holding back how tightly tensioned the first string could be, then as the string vibrates some of the material held by static friction might give way, allowing the string to relax a bit. I have no idea what might go on in the former case.

10. Apr 21, 2008

### Mapes

This was the case around the middle of the 20th century, but creep is quite well understood today: it is the time-dependent deformation of materials under stress, as brewnog stated.

Inkling, your guess about creep deformation is exactly right. There are several ways creep can occur, and they all involve diffusion. Generally, the bonds between the iron atoms in your piano string occasionally break and re-form due to random thermal energy. Any atomic rearrangement that lets the string be longer is favored because you are pulling on it so hard. Eventually, the lengthening of the string is noticeable.

Creep strictly occurs in all loaded materials above 0K. It is usually negligible in steel at room temperature, but you've found an exception, because the stress is large and the sensitivity of your detector (the human ear) is very good for detecting out-of-tune strings.

One of my professors liked this trick question: which creep mechanism [there are several, including bulk diffusion, grain boundary diffusion, and dislocation climb] is active in material xx at yy°C? The answer is always all of them (they just might be negligible).

11. Apr 21, 2008

### inkling

Thanks for clearing up a tiny corner of my wordview.

[inkling]

12. Apr 21, 2008

### inkling

Ok, I have found a scientific paper that comments on this: (i think)

----
Tensile Stress Relaxation in High-Strength Spring Steel Wire
Sinha UP, Levinson DW
Abstract
Stress relaxation data were obtained in tension tests using the vibrating string technique (measuring the resonance frequency) in spring steel wire of ASTM Grade A 228 (also known as music wire). The steel wire of 0.56 mm diameter had a 0.29% offset tensile yield strength of 1689 MPa. Tests were conducted at low temperatures in the range of 23 to 140�C, and at initial stress levels of up to 75% of the 0.20% offset yield strength of the wire. The test duration was to 4000 h at 23�C and to 100 h at temperatures to 140�C. The test results indicate a faster rate of stress relaxation during the early stage of stress relaxation, and subsequently a slower rate of stress relaxation rate with increasing time, as is usually observed. An empirical equation has been determined that fits the experimental data very well under the given test conditions.

----
Here it is called "relaxation".
How is "relaxation" related to "creep"?

[inkling]

13. Apr 21, 2008

### Mapes

Nice find. Relaxation = creep. A relaxation test usually means that a given strain is applied and the stress is measured over time. The stress is high at first and decays towards zero, which means the frequency decreases, as you've noticed. It's a complement to tests in which a stress is applied and the strain is measured over time.

14. Apr 21, 2008

### inkling

Thanks, but I can't actually take the credit for finding it.
Another piano tech by the name of John Delacour shared
it with me. He has been interested in proof of this happening
for longer that I have, and in fact it is attempting to work
out a way to measure this happening so as to put to rest
the skeptics once and for all.

Do you think this stretch is big enough to be measured
without a scientific lab? How much movement are we
talking about here? Obviously we can hear it, but I'm
not sure we can see it.

[kurt]

15. Apr 22, 2008

### Andy Resnick

While I admit to not being at the forefront of revelant research, I guess we have different criteria for "well understood". I don't consider "understanding" to consist of a definition and isolated non-comparable measurements. For engineering, those may be sufficient. For the design of new materials, it is not.

Creep is a non-linear phenomenon. The phenomenon of 'stress relaxation' and dissipative processes remains an open problem in thermodynamics and mechanics. Constitutive properties are not currently derivable from first principles.

16. Apr 22, 2008

### Mapes

Starting at the information inkling has given (spring steel used in piano wire), a motivated engineer could investigate the creep literature and

- Either find a deformation mechanism map for that alloy and grain size or learn how to perform experiments to construct such a map.
- Using the map, identify the dominant mechanism of creep at room temperature for the load on a piano string, and understand the mechanism on an atomic level.
- By addressing that dominant mechanism, design an alloy that would be less susceptible to creep.

That is what I mean by "well understood." I think the field is farther along that your original comment "There is no good theoretical model for why creep happens, or even what it is." suggests.

To inkling: forget about seeing the stretch, use the resonant frequency! A piano string is a stress relaxation experiment: the strain is set by how much you've tightened the string, and the stress (which is proportional to the frequency) decreases over time.

The simplest model would predict that the frequency decreases in a first-order manner, which means that is follows the equation $F=F_1+F_2 \,\mathrm{exp}(-t/\tau)$ where $F$ is the frequency, $F_1$ and $F_2$ are constants, $t$ is time, and $\tau$ is a characteristic time constant that indicates how long relaxation takes. I would guess $\tau$ is months or years; you guys would know better. This (simplistic but perhaps usable) equation predicts that the frequency starts at $F_1+F_2$ and decays towards $F_1$.

17. May 9, 2008

### ben_gal

Sorry. Yes, it is if u wait long enough.
In old, old houses u can see that the glas is ticker at the bottom.

18. May 9, 2008

### symbolipoint

Have the researchers ignored nylon strings? These also give a drifting pitch after tightening; in fact they also give a drifting pitch after loosening, but in the opposite direction; meaning if you loosen a string but still keep it stretched, the pitch although lowered, drifts back upward. This must be the same general situation for steel strings as for nylon strings.

Curious - do steel and nylon fit the same mathematical model for this pitch drift versus stretching or loosening? Do the pitch drifts for loosening fit a different model than for string tightening?

19. May 10, 2008

### K.J.Healey

Thats because they were made on slanted tables. Glass that is thicker at the bottom has always been thicker at the bottom. It doesn't flow.

20. May 10, 2008

### ben_gal

The Old House

I am not talking about slanted tables.
I remember viziting "The Old House" [maybe the name is not exact] somewhere near Missisipi River on Road 94.
I saw clearly and the guide there, pointed out, the windows I am talking about.