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 Post subject: Relative String Lengths
PostPosted: Mon Dec 21, 2009 1:52 am 
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Brazilian Rosewood
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This is most def a harp guitar kind of question, but, not so restricted.

I am finishing up my first harp. Setting the bridge for the 6 string part (normal guitar) is no problem. But the sub-basses are something of a mystery to me. Yes, I built according to plans and so I have a pretty good idea where things go, but I got to wondering about sub-bass string length. In a normal guitar, string length is dictated by scale length and fret spacing (there is a bit of convolution there, but you know what I mean). With harp sub-basses, there are no frets, just strings that stretch from a bone pin to a saddle. Up to six of them in the Dyer model cases. Does one have to worry about relative string lengths? Should one strive to get them to be alike?

Mike


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PostPosted: Mon Dec 21, 2009 4:09 am 
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Brazilian Rosewood
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Mike,

You want them to get longer as you go down the sub-bass strings - which is why the hollow arm peg head is slanted. Then choose the right string gauges to give you the tension you want for the tunings of the sub-bass strings that you want and the vibrating string lengths you have. The "exact" vibrating length is not critical as there are no fretted notes and hence no intonation issues.

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PostPosted: Mon Dec 21, 2009 6:43 pm 
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Go to www.harpguitar.net .. Gregg Miners site .. on there he has the listing for tunings and string guages that the more famous players use.... like my pal Stpehen Bennett ... he even sells them in sets by different manufacturers for the tunings as well ...

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PostPosted: Mon Dec 21, 2009 7:32 pm 
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Brazilian Rosewood
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'Way back when a fellow named Mark Emory Bolles wrote a program to design the strings for harps. He wrote a series of articles in the 'Folk Harp Journal' explaining the reasoning behind good string design, and giving a listing of the program (in BASIC: he wrote it on a TRS-80). He later collected all of his articles and sold them as 'The Harp Makers Notebook'. Extremely useful stuff. He talked a lot about the concepts of 'Tension to Length Ratio' (T/L), and 'Percentage of Tension' (%T).

T/L is mostly about the feel of the strings: too low and they're rubbery, and too high and they're hard. On a harp, when the T/L goes below about 1#/inch of length, it's hard to 'place' your hands well when you pluck the string. If the T/L gets much higher than about 4 (iirc) that's a sign that the string is too thick, and will vibrate more like a bar than a string, with a very inharmonic overtone series. When designing the strings for a harp, or anything else with strings of different lengths, it's really important to have the T/L ratio vary smoothly as you go across the band. A string that's much harder or softer than it's neighbors is hard to play well. Guitars, BTW, typically use T/L ratios of around .7 or so, iirc: easier to fret.

%T is a measure of how close the string is to it's theoretical breaking point. A string of a given material and length will always break at pretty much the same pitch (you can tune thin strings a little higher). The higher the %T of the string, the truer the overtone series, and all else equal, the better the sound. You can't carry 100%T on a string, though: that would not allow you to even wind it around the tuner without breaking. The piano tuner's rule is to run strings at 75%T: high enough to sound good, and low enough so that you don't break too many. The octave G string on a 12 is usually around 80%T, iirc.

On a wound string, you have to use the mass of the windings to compute an equivalent density, but all of the strength comes from the core. That's the point: you can have a thin and flexible core that will allow the higher partials to be nearly harmonic, and enough mass to keep the pitch down to where you want it.

There's one other thing to think about when designing strings: impedance. This is, more or less, a measure of how hard the string is pushing on the bridge. It's fairly easy to calculate the 'characteristic impedance' of a string: it's the square root of the tension times the mass per unit of length. It's often said that, on something like a guitar, the tension on each string should be the same. Actually, if you do that, you'll find the the impedance varies quite a lot from low to high. Usually strings are designed so that the impedances are not too far from equal, and the tension varies a little bit, but not too much. In other word, they compromise.

Guys like Steven Bennet have probably done a lot of experimenting to find string gauges that work, but with a progam like Bolles', you can do the experiments on your computer a lot quicker and cheaper. Most of the harp makers use a program like this, or get their string suppliers to run their harp designs through a similar program.

BTW: what Bennet plays is, in organological terms, a 'zither-guitar'. It has strings that run more or less parallel to the soundboard. On a real harp, the strings pull upward at an appreciable angle. I have yet to see a real harp-guitar.


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PostPosted: Mon Dec 21, 2009 9:30 pm 
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Brazilian Rosewood
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Thanks Alan!

Tony, a clarification on the website: www.harpguitars.net (you left out the "s")

I was perusing the string sets last night. My question was with respect to string length between saddle and nut pin. They do get longer as the one gets to the lower sub-basses. I was wondering why since there are no frets, etc. I think, in Alan's response there is an answer based on tension.

Mike


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PostPosted: Tue Dec 22, 2009 9:14 am 
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Brazilian Rosewood
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Alan,

Interesting stuff. It's a bit ambiguous from your "word formula" - is the string's impedance calculated as:

SQRT(Tension x Mass per unit length)

or:

(SQRT(Tension)) x Mass per unit length

Also do you know where any data is published on the breaking tension for different string types and gauges - the D'Addario site seems to have data on mass per unit length but not breaking tensions.

Thanks again.

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". . . the one thing a machine just can't do is give you character and personalities and sometimes that comes with flaws, but it always comes with humanity" Monty Don talking about hand weaving, "Mastercrafts", Weaving, BBC March 2010


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PostPosted: Tue Dec 22, 2009 11:11 am 
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I think you need to longer string length on the subs as you go lower in pitch otherwise you will likely need gauges so thick to get to a reasonable unfloppy tension, you wont even find them in typical guitar string types.... or they may not also fit the tuner posts ...

Alan .. never seen a real harp guitar as you call it .. then here you go .. Mr Grit Laskin. Canadian museum of Art ... 25 degree bent top ....


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PostPosted: Tue Dec 22, 2009 2:13 pm 
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Brazilian Rosewood
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Thanks for the reminder Tony: I'd forgotten that one! I still have yet to see a 'harp guitar' that's really a HARP guitar.

The formula is sqrt(tension x mass per unit length) It's similar to the formula fro frequency but that's sqrt(tension/mass per unit length). With frequency, raising the tension raises the pitch, but raising the mass lowers it. The impedance goes up when you increase either mass or tension. One autority says that the main effect of increasing the string length is from the higher impedance.


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