Strings of unequal diameter

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Re: Strings of unequal diameter

Postby GrantOlson » Sat Nov 25, 2017 10:08 am

rtroughear wrote:Other than the problem that Lisa points to, of action change at the transition from unwound to wound sections, the non-linear string density is almost certain to produce gross intonation problems. Even if you made a dedicated dulcimer with custom fretting to accommodate the non-linear density, you would probably not be able to duplicate the same density distribution on the next replacement string you put on it. I know from my own experience with ukulele strings that the occasional string turns up which has non-uniform density along its length, and it is impossible to play in tune over the whole fretboard. The only solution is to throw it way and put on another one.


I think what I need to do is buy a couple of strings from the guy Ken recommended. Then I can experiment with how this would behave rather than guessing. What I was thinking is that I would have a tuner on both ends of the instrument so that the location of the joint in the string could be fine-tuned. I'm still not sure if that would fix the intonation but it might be worth trying.
I would still like to try something with a weight like you said. I'm not quite sure what to do though. I did try wrapping some of a steel string onto another steel string. It was not quite an inch of somewhat messy loops. There were strange harmonics in the background, but I found something interesting: when it was right up against the bridge it barely changing the pitch at all, but when I put it close to the middle, (it slides), the pitch went down about a half step. And in between those points it was not gradual but jumped around some.

rtroughear wrote:If you had a multi-segment string of varying mass/length, there would be multiple transitional areas at the joins where there would be different bending stiffnesses which is the reason to do bridge/nut compensation in the first place. So intonation compensation would be even more difficult than a single-density string. You would have to ask yourself -what is gained by doing this?


Robin the Busker wrote:What I can't follow in your posts is what your end goal is? I understand your basic premise that adding weight to a string = making it sound longer (lower pitched) than its VSL but I can't understand why a thicker fully wound string wouldn't do that job better than a partial winding - particularly considering the intonation issues it would throw up when fretting the string.
...
I think that 'starting with the end in mind' is often a good way to approach this type of experimentation. First identify the problem you want to solve - and I'm not sure what that problem is in this case? Is it to make a better sounding dulcimer? If so, what do you mean by that?


You both have wondered why I'm doing all this :D I think partly because I'm curious, and it's kind of a challenge to see how it works and if I can make an instrument like this that would sound good and not weird. I have thought it's a bit strange that I couldn't find any formulas about this situation. There are also many possibilities, such as maybe it would be possible to tune the harmonics, since a string like this would probably have much inharmonicity. However, like it has been pointed out, what would be gained by doing this?
The one thing I have sort of kept in mind is this: some sort of zither that is small and could be easy to travel with. With small strings the frets get close together. I would probably fret at most the first octave and rely on multiple strings for a greater range of notes. The idea is that the thinner part of the string would behave like a bigger string with frets more spread out. This would make it easier to play. Also, it would allow more possibilities, for an instrument of any length, if you were experimenting with a scale of more than 12 notes to the octave. There would be more room for extra frets.
Hopefully this makes sense.
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Re: Strings of unequal diameter

Postby Robin the Busker » Sat Nov 25, 2017 10:38 am

Well you have yourself a theory Grant, so go ahead and test it 8)

I think the natural physics of string vibrations may trip you up though. So here's a question to get to thinking: Why is it that the 8th fret (just an example) on any specific dulcimer sounds a tone (200 cents) higher then the 7th fret no matter what string gauge (thick wound or thin melody) or open string pitch (low A on a baritone to high d on a standard dulcimer) is used fir the string passing over those frets? How would you effect a pitch change between those two frets that is greater than or less than 200 cents? Because that's what you are trying to achieve.

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Re: Strings of unequal diameter

Postby GrantOlson » Sat Nov 25, 2017 12:29 pm

Here's what I know:
For a regular dulcimer looking at the interval between 7th and 8th frets diameter and therefore mass per unit length is a constant. (The same no matter what note you are playing). Tension will always be the same. The wave speed is equal to the square root of tension divided by mass/unit length. That will mean that the wave speed of any note on the string is also a constant. So in that situation you have to variables: frequency and string length, which are proportional. Decrease the length by a certain factor and the frequency increases by the same factor.
What I have yet to test:
I think it would be different for a string of non-uniform density. Let's suppose that the string is wound from the 10th fret to the bridge. If you looked at the length of the string that is thin compared to the length of string that is thick, you would have a ratio. That ratio would be different for fretting at the 7th ant 8th fret. Going from 7 to 8 the length of the thin string would change but not that of the thick. I think that would mean that the 7th and 8th frets would have different overall wave speed. That would change the relationship between length and frequency. There would be some ratio between the two that I think could be predicted by a formula. And if you changed the length of the thick part compared to the thin part, you could change that ratio between length and frequency. For example, if you had a normal string where the interval between the 7th and 8th frets was the normal 200 cents, putting winding on some of the string by the bridge would decrease those 200 cents. Of course, all this is only a theory that seems to make sense to me, but I still have to test it.
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Re: Strings of unequal diameter

Postby strumelia » Sat Nov 25, 2017 1:26 pm

GrantOlson wrote:With small strings the frets get close together. I would probably fret at most the first octave and rely on multiple strings for a greater range of notes. The idea is that the thinner part of the string would behave like a bigger string with frets more spread out. This would make it easier to play.


But the thickness of a string is not what determines or dictates how far apart the frets are. Rather, the shorter the scale, the closer the frets get to each other. Pressing a string down to a fret in effect shortens the scale. Different thickness strings are merely needed to accommodate tuning to different high/low notes at a set scale length. So, I THINK...you couldn[t have a string that was thick at one end and had frets far apart under it, and have the same string then be thin on its other half with frets suddenly close together. I mean, no more than what would occur naturally with a string of all one weight and the frets naturally getting closer together as the scale gets shorter when its fretted.
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Re: Strings of unequal diameter

Postby GrantOlson » Sat Nov 25, 2017 2:56 pm

Remember that this is just my theory and I can't prove any of it :D You are right that for a normal string the thickness does not affect where the frets are placed. I am just guessing that if the string was not a uniform diameter it would affect the frets; but I don't know for sure. And I would agree with you that the frets wouldn't get farther apart up closer to the bridge. In my idea the thick part would not be fretted, only the thin part. Under the thin part I theorize that the frets would be more spread out, and would be closer in the thick part if you put any there.
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Re: Strings of unequal diameter

Postby strumelia » Sat Nov 25, 2017 6:11 pm

In my idea the thick part would not be fretted, only the thin part. Under the thin part I theorize that the frets would be more spread out, and would be closer in the thick part if you put any there.


That's not how things work though. No offense meant, but I'm afraid this plan and theory is not making any sense to me.
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Re: Strings of unequal diameter

Postby GrantOlson » Sat Nov 25, 2017 6:24 pm

No offense taken. I think it will make more sense once I can get a string like this and see how it really works.
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