[varsigma (OP)]

I'd like to point out that this weird guitar string thing started out with what I could call a naive algorithm.

It was a used guitar string, it was slightly rusted. I expected the weight itself would break the string if I swung the weight and overstressed the string that way. After many tries I went for as many rotations as I could bother 'storing' in the system by hand, about eighty or so maybe at the height of my enthusiasm, in order to overstress the string. But no breaking string despite hundreds of attempts. I didn't try lifting the weight up and letting it fall, though.

There is something very durable about high tensile steel

[vhfpmr]

There is something very durable about high tensile steel

What's the tension on the string when it's in the guitar? A lot more than your 2.5kg weight at a guess.

[varsigma (OP)]

What's the tension on the string when it's in the guitar? A lot more than your 2.5kg weight at a guess.

I've busted a few steel strings by overwinding them, so that gives you a way to test the durability. At least in one dimension of stress. To make it lab-worthy use a strain gauge; engineer an old guitar somehow.

But I can't help noticing that introducing rotation into the system, makes things more interesting. Although that would be difficult to engineer with an old guitar . . . It is possible to rotate one end of the steel string while the other end is fixed.

Torsion seems to be a more interesting domain than linear stress, for steel guitar strings.

[alancalverd]

Are all guitar strings created equal?

Very far from it. I have skinny "cheese cutter" steel top E strings for a folk acoustic guitar,  all sorts of nylon thicknesses on my classical guitars, heavy steel jazz strings, plastic coated nickel-wound jazz bass lower E's, and the weirdest instrument of all is a bass ukulele  with fat lumps of silicone rubber that oscillate at the same frequency as a tape-wound double bass string four times as long, but still have a useful sustain.

[alancalverd]

There is something very durable about high tensile steel

What's the tension on the string when it's in the guitar? A lot more than your 2.5kg weight at a guess.

D'Addario (manufacturer of instrument strings) quote a range of 6 - 12 kg per  steel  string.

[Bored chemist]

Very far from it. I have skinny "cheese cutter" steel top E strings

I understand it's traditional to say "thank God it's not a G string".

What's the tension on the string when it's in the guitar? A lot more than your 2.5kg weight at a guess.

It's calculable.
https://en.wikipedia.org/wiki/String_vibration#Derivation

[Bored chemist]

the weirdest instrument of all is a bass ukulele... 

I'm not sure that statement requires further qualification.

[alancalverd]

from: vhfpmr on 13/09/2023 12:55:25
What's the tension on the string when it's in the guitar? A lot more than your 2.5kg weight at a guess.

It's calculable.
https://en.wikipedia.org/wiki/String_vibration#Derivation

Reminscent of the Leaning Tower story. The three usual suspects have a barometer. The pilot climbs to the top, measures the air pressure, and calculates the height. The engineer attaches a long piece of string to the barometer and swings it from the top of the tower so it nearly touches the ground, then calculates the height from the period of swing. The cabin steward walks into the ticket office and asks "how high is the tower?"

I refer the hon gent to reply #24 above.

[alancalverd]

from: alancalverd on Yesterday at 17:03:03
the weirdest instrument of all is a bass ukulele...

I'm not sure that statement requires further qualification.

Ask anyone who has played one! Great fun, but it's the size of a violin and the register of a double bass, so every note is a surprise.

[Bored chemist]

every note is a surprise.

I can achieve that effect with a triangle...

[Bored chemist]

from: vhfpmr on 13/09/2023 12:55:25
What's the tension on the string when it's in the guitar? A lot more than your 2.5kg weight at a guess.

It's calculable.
https://en.wikipedia.org/wiki/String_vibration#Derivation

Reminscent of the Leaning Tower story. The three usual suspects have a barometer. The pilot climbs to the top, measures the air pressure, and calculates the height. The engineer attaches a long piece of string to the barometer and swings it from the top of the tower so it nearly touches the ground, then calculates the height from the period of swing. The cabin steward walks into the ticket office and asks "how high is the tower?"

I refer the hon gent to reply #24 above.

Yes, but won't give you the insight that, if you took a high tensile steel wire and annealed it, then strung the guitar (albeit, a long way from tightly) it would give the same fundamental note as before heat treatment.
The stiffness of the string has essentially no effect on pitch.
(Though, even with my "tin ear" I can expect to tell steel strings from nylon. It's as if timbre and pitch are independent.)

[alancalverd]

The stiffness of the string has essentially no effect on pitch.

Instantaneously, true. But IRL the strings creep so you have to retune a classical guitar (with nylon or gut strings) between numbers if the strings are fresh. Steel strings also yield a bit but are easier to stabilise if you have strong fingers - I was taught how by an old dance band pro who reckoned to change a string and stabilise it between numbers. One thing that has improved  in the last 70 years seems to be the durability of steel strings - I used to break one every couple of gigs, and now they seem to last until they are too corroded for comfort. (touch wood! I have a gig tonight!)   

[vhfpmr]

What's the tension on the string when it's in the guitar? A lot more than your 2.5kg weight at a guess.

It's calculable.
https://en.wikipedia.org/wiki/String_vibration#Derivation

It is, but if you don't know the unit weight of the string, it's quicker and easier to measure the tension than measure the weight.

The stiffness of the string has essentially no effect on pitch.

In the specific case of a long, thin guitar string the effect of stiffness is negligible, but in general the stiffness does affect the resonant frequency, by an amount that increases as the L/W ratio, and tension decrease. Consider the case of twanging a ruler on the edge of your desk: there's no tension at all, but it's still resonant.

I did a lot of work on this about 10 years ago in the context of using tone to measure the tension of cycle wheel spokes, prompted by the mention of this website on a cycling forum. To clarify: the tone of the spoke is a very quick, easy and accurate way to match the relative tension from one spoke to another, but the formula cited by Wikipedia and John Allen is as much use as a chocolate teapot for determining the absolute tension, and for for a number of reasons.

The first, (not applicable in the case of guitars) is that a cycle spoke has two resonant frequencies, something that's easy to see if you view the tone with a spectrum analyser. The more dominant one is determined by the distance from the nipple to the first crossover, not the spoke length, and the other by the distance from nipple to second crossover or hub flange, it's not really distinct enough to tell which.

The second is spoke stiffness. I measured this error at around 15% at working tension, increasing to 35% or more at lower tensions.

The next is that the calculation supposes the weight/diameter of the wire is uniform, which in the case of butted spokes, it isn't. Since the frequency is much more sensitive to weight in the centre than at the ends, calculation for a butted spoke on the basis of average weight is much less accurate than using the weight at the centre.

Finally, it's not easy to determine the actual length of the spoke, as the first point of contact with the nipple could be either the bottom of the counterbore or the point of entry, and at the other end, the first point of contact is either the periphery of the spoke hole for inbound spokes or the periphery of the flange for outbound, or more likely, the second crossover.

Having discounted any prospect of using tone to determine tension in situ, I built a test rig using a lever to tension one single test spoke in isolation, in order to determine the practicality independently of the error introduced by the crossovers. The plot below shows the error in the tension determined by tone as a function of tension for a the following wires:

Double butted spoke calculated from average weight
DB spoke calculated from centre weight
Plain gauge spoke
A piece of brake cable (stranded and flexible)
A single strand of gear cable

Also marked is the maximum error I can account for by analysis of the test setup.


Spoke Tension.png (25.01 kB . 672x431 - viewed 110 times)

The difference between a flexible brake cable and the much stiffer spokes is conspicuous.