Monofilament length to note ratio?

This may be an obvious question, but I am trying to understand with a given string diameter what the length will allow for tuning. For instance an akonting uses the same width string at different lengths to achieve three dramatically different notes.

I have tried googling to find a formula or chart but have had no luck. Any thoughts/advice?

Thanks!
Ben

There are many threads on this here, but usually under the subject of tension.

D'addario has a string tension calculator which can be used to model the behavior of different strings under different scale lengths or tunings:

http://web.daddario.com/StringTensionPro/

It's set up to work with their product line, but there's enough options among their products that you can get a really good idea for how strings work in general. Any time I'm building something new (in terms of string style, scale length, tuning, etc) I spend some time using this calculator to understand how it will work. It's very helpful when trying to compare different scale lengths, or when wondering what gauge strings to use for a new project.

The theory of monofilament wires which applies to steel bronze, nylon etc is related to cross sectional density strength and length was established for harps but applies to other chordophones like guitars banjos and ukuleles.
http://www.sligoharps.com/string.html

There is also a lot of discussion on the matter in the cigarboxnation.com forum because they fiddle around a lot with different strings and scale lengths.

Thanks! This is all very helpful!

I'm not sure what you're looking for. It comes down to a combination of size, density, tension, length, and note you want. Here is Cluze's formula. He explains this in a couple of different threads here.

It’s a fair question. I’m trying to build this https://www.etsy.com/listing/892641...allery-1-3&from_market_listing_grid_organic=1 (well really this https://www.youtube.com/watch?v=f-i49gCjNbQ but it’s a video so hard to see)
But without knowing specifics regarding string type, scale length et al. They tend to be very variable and reportedly forgiving to make but I would at least like to gather what info I can ahead of time.

If you haven't already found this, Aquila has a conversion table for various string types at different sizes.
It's at https://aquilacorde.com/wp-content/uploads/2019/09/conversion.pdf

Perhaps it can help get you closer to what you need.

Every time I see one of these threads, I think it would be simpler if manufacturers specified, say, the weight of 10 metres of string in grams.

Piecomics said:

It’s a fair question. I’m trying to build this https://www.etsy.com/listing/892641...allery-1-3&from_market_listing_grid_organic=1 (well really this https://www.youtube.com/watch?v=f-i49gCjNbQ but it’s a video so hard to see)
But without knowing specifics regarding string type, scale length et al. They tend to be very variable and reportedly forgiving to make but I would at least like to gather what info I can ahead of time.

Click to expand...

Because of the physics of strings there is a range of tensions at which it works nicely, roughly 5 semitones or so. Below that it sounds muddy and won't intonate well, above that it might snap.

You can use this to estimate starting gauges for your strings by using your knowledge of other instruments. The instrument in the video looks to have around a 17 inch scale, which is the scale of a tenor uke. If that's what you decide to build, work out what notes each string is tuned to and find the closest equivalents (within 2 or 3 semitones) from a tenor set. Use those strings for your first set.

Once you've strung it up and played it you can decide if each string is about right, too floppy or too taut, and then go up or down a gauge for that string on your next set.

Here's a worked out example for my baritone uke which I wanted to tune in 5ths, GDAE. I reckon its 19 inch scale is the equivalent of a classical guitar capoed at the 4th fret, so my choices were:

G - guitar 6th (E, up 3 semitones)
D - guitar 4th (A, up 5 semitones)
A - guitar 3rd (G, up 2 semitones)
E - Guitar 1st (E, no change)

In theory the D should be a little too taut, but it's not too bad. Still, when I re-string I'll use a string one gauge thinner than the guitar A.

The E plays better than I expected, but I could do with a string one gauge thicker next time.

If I'd wanted to get the tensions more even across the strings then I could have bought two sets of cheap classical guitar strings, one light, one heavy, and used the best strings from each set according to my mental calculations (which would be, the light set=the heavy set tuned down one fret).