How do we get different freqeuncies at the same string length?

What matters is where their hands are on it. The distance between person A’s hand and person B’s hand on the rope is analogous to the nut and saddle.

Where they stand is irrelevent. Where the hands are placed is what sets the length. How tight the pull it is the tension. You can get waves on a rope that is slack

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It’s not how far apart the hands are that matters, it’s the length of the rope between the two hands that matters. That’s the length. On a bass this is fixed

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I guess we can just agree to disagree - I asked twice how to increase tension without moving the people (their hands, their feet, whatever) and without changing the length of the rope, as I don’t understand how tension can change without changing the length, and I don’t really see an answer to that question…

I mean, when you tune the string, you’re changing the length (more or less windings around the peg) in order to increase/decrease tension. The distance from nut to bridge saddle is fixed, but the string length varies with tension.

If you’re explaining why that isn’t true, I guess I’m just not understanding…

I think it’s more a matter of tension over the useable/applicable length (Nut to saddle) that matters. And although length changes a little when adjusting tension (sag) adjusting the tuner doesn’t change the length. The takeoff point is still the same. So in essence you are adjusting tension and not distance.

How does adjusting the tuner not change the string length? Yes, nut to saddle is the same, but a saggy string is longer than a taut string.

And that taut vs saggy is tension. Ergo, tension is related to length.

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This is how I visualize it. By tightening the string even by a small amount you are shortening the length from nut to bridge. It’s what happens when you restring a bass. You start off with a longer string and shorten it as you wind the tuner, no?

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No.

Once the sag is taken out of the string, you get tension. And the length is fixed from the nut to the saddle. Length and tension are two separate properties.

I would suspect under tension the diameter actually changes, but not the length.

The string is physically getting longer, but for the purposes of the wave, it’s the same length, the wave forms in the space from the nut to saddle. The extra length will be from the nut to tuner actually. Nut to saddle is the same

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Well @Wombat-metal is right - two people standing a distance apart, both pulling on the rope can increase the tension by pulling on it harder. The rope may stretch a tiny bit but they won’t have to move closer or further away.

Or maybe a better analogy would be to connect one end of the rope to a wall…

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The takeoff point of the tuner is the same so length is the same. Everything “behind” that point doesn’t matter for “length”

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Me wanna go home :smile:

Yes.
And there are so many variables, this is why there are a lot of places for adjustment.

Think of the slop in a string peg, it will pull the string to a certain focal point, which was drilled into a hole in the head, and placed by hand or cnc machine, to some degreee of accuracy…
Which then aligns itself when; wound up ( the center pin, and places the string along an axis on a plane to the saddle where, etc…

You see, each point of measurement works upon EXACT numbers in the sciene of it all, which is easy to make on a worksheet in perfect math…

But to hand craft, and and machine build, machines even, you can’t reproduce that mathematical accuracy between points A and B to make sure everything is aligned and dead ass balls nuts accurate to pithing a certain degree of accuracy. perfection is unobtainable, so points of adjustment arcaded. …

You see this imperfections stack up in the differences within each fret, and nut, and saddle placement, height, location, etc…
It is probably scientifically possible to exactly create an instrument, for instance a piano, so it has every single part, in every location to within every tolerance, to place perfectly crafted strings and create in the end…

The same music.

Or
Actually, you can, and you can do so in a Keyboard, where it was all scientifically mapped out and perfectly engineered so they in fact don’t need strings anymore at all.

But then you get digital, perfect in every way, but it doesn’t sound as good.

You introduce a whole new set of variables that have to back calculate fo the perfections that go against humanity. :rofl:

To that effect.

If everything lined up perfectly, it would still have some error, and you see this in the set points, AKA bridge saddles, because imperfections stack against each other to create error. and so on and so forth.

When I think of the years in which instruments were invented, and first created, vs the technology and education of today, I am blown away how they ever were able to evolve them to as perfect as they have been for so many years.
And to have all those instruments available in time for for Mozart.
And we said humanity started speeding up, and look at all that they did way the F back then.

Still bringing new found joy and glory to people today. And better for the environment too.

Um…, yeah, on that string, for that string and that string only.
Each string itself has a set of tolerances it is created within. it is more then just a single drawn wire.

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Here is an engineering explanation:
First mode natural frequency of a non-rotating, body like a string, is described by a simple formula which is only dependent upon stiffness and mass.


So, increasing stiffness, increases frequency. Increasing mass, decreases frequency.
Stiffness of an axial element (like a string) is dependent on Young’s modulus (a constant for steel) and tensile stress (tension divided by cross-sectional area).
As you tune the string up, it shortens, which increases the tension and pushes the frequency up. However, the distance between nut and bridge is fixed, so the amplitude of vibration (for a specific initial displacement) is constant.
Lower frequency is achieved by increasing the string diameter (and cross-sectional area) but eventually, making the string thicker means that you cannot pluck it, so it’s better to add mass (not density, the density of string steel is constant). That is why thicker strings have additional windings - they add mass but not stiffness, and thereby drop the frequency of vibration.
Hope that’s clearer than mud.

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Density I don’t believe is a constant between strings… a flat wound and round wound string of the same gauge will tune to a different tension, which implies different density.

Or perhaps mass. But is chrome the same density as steel?

A string is a spring in a sense, no?
So spring constants etc apply between types to yield tension maybe as well.
I don’t know if the density difference in materials make a difference, but the amount of material needed in one metal vs. another maybe different string to string (larger/smaller core vs. wind, etc).
No clue if any or how much of any of these matter.

Strings badged as Chromes are made of stainless steel, but the difference in density between mild and stainless is trivial. The only difference between a flatwound and roundwound string is the finished surface of the windings. So a flatwound string could have less mass (be lighter) because more material has been machined off but the density (mass per unit volume) is the same.

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