Dear Robert
Thank you for putting me back on track. If I understand you
correctly, length plays no role at all. Perhaps the confusion comes
from some lutists considering their 67cm transitional lutes as G
lutes. I have heard this from lutists on a number of occasions. I
assume that a 0,42 string string raised to G (440 Hz diapason) on a
67 cm lute will break far more quickly than on a 60 cm lute. If on
the other hand it is treated as an F lute (or a lower diapason is
chosen) the problem could be avoided, or lessened. This would be a
stress tension question, and not length per se? I think that was what
Edaward Martin was telling me when he said that 67 cms was ideal for
a Baroque lute (71 cms being problematic if you don't lower the
diapason).
Regards
Anthony
Le 10 févr. 07 à 03:36, Robert Clair a écrit :
> From: [EMAIL PROTECTED]
> Subject: Re: re gut strings
> Date: February 9, 2007 8:33:58 AM EST
> To: [email protected]
>
> The technical aspects aspects of this thread have wandered fairly far
> from reality.
>
> First, there is a small language problem: despite their literary
> incestuousness in common usage, "stress" and "strain" mean different
> things.
>
> Stress is force / area, in this case the tension on the string
> divided by its cross sectional area.
>
> Strain is the percentage deformation of an object under stress:
> change in length / length. Strain isn't particularly relevant here.
>
> A given *material* has a breaking stress. When you break something,
> you have to break atomic or molecular bonds to pull the pieces apart.
> This requires a specific amount of force for a given material. If I
> have two strings made out the same material, one thicker than the
> other, I'll have to pull harder on the thicker one to break it
> because I have to break more bonds.
>
> This has an interesting consequence: when you write the equation for
> the pitch (frequency ) of a string in terms of stress rather than
> tension, the diameter of the string disappears. For a given length
> and material, the pitch at which the string breaks doesn't depend on
> the thickness.
>
> True, at a given pitch the thicker string is yanking harder (greater
> tension) on the bridge, but it's the stress not the tension that will
> break it. If you're still unhappy with this, think of it this way -
> the thicker string is under more tension, but that tension is being
> handled by more molecular bonds.
>
> Note that this has nothing to do with the length. The tension in a
> string is the same everywhere along its length. If it weren't it
> would immediately reconfigure itself so that it was. That it feels
> like more tension when you pluck near the bridge is mostly a matter
> of geometry. (Trying to displace the string sideways by some amount
> will have a bigger component of tension perpendicular to the string
> when you're near the bridge. You're also trying to bend the string at
> a sharper angle, so the stiffness of the string material will have a
> greater effect near the bridge.)
>
> As a practical matter, very thin strings are probably more fragile
> because nicks and minor wear and tear take a bigger chunk (as a
> percentage) out of the area of thinner strings. This can make the
> stress at the point of the damage exceed the breaking stress.
>
> Last point (for those whose eyes have not yet glazed over): Most
> lutes have the same length for the fingerboard strings and have the
> first several courses strung in the same material. This means that
> only the chanterelle would ever be near the breaking pitch. Pity your
> friends the baroque harp players who get different pitches by
> keeping tension and diameter (and thus stress) roughly the same and
> varying the length. They can have many strings near their breaking
> pitch. They break lots more strings than we do.
>
> Bob Clair
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> --
>
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