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58 minutes ago, Brad H said:

The tension depends on the mass, not the diameter of the string.    (and string length affects the tension, too)

The Vincenzo Galilei formula, point taken. I'm going off observations from restringing experiments on harpsichords, where sometimes it's advantageous to try different gauges of the same material in order to arrive at the best sound, which is (among other things certainly) a factor of tension. I'm struggling to remember which at the moment, but one renaissance era lute treatise describes the correct diameter for a given course as the one which will hold the desired pitch just without breaking. 

In the harpsichord example, the tension of a red brass bass string of x diameter will not be the same as that of a red brass bass string of y diameter, even though the pitch, length, and density are the same. 

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2 hours ago, Brad H said:

The tension depends on the mass, not the diameter of the string. ..

Not mass.  Mass per unit length.

 

1 hour ago, JacksonMaberry said:

..the tension of a red brass bass string of x diameter will not be the same as that of a red brass bass string of y diameter, even though the pitch, length, and density are the same. 

The densities of your two strings are the same, but the masses per unit length are different, hence they have different tensions.

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23 minutes ago, Brad Dorsey said:

The densities of your two strings are the same, but the masses per unit length are different, hence they have different tensions.

Let us not forget the effects of work hardening and annealing…, not to mention the helix angle and other processing considerations for gut strings.

 

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1 hour ago, Mark Norfleet said:

,,,work hardening...annealing…helix angle and other processing considerations...

These factors are practical considerations that influence the stiffness and internal friction of strings in the real world.  The string equation describes a hypothetical ideal string, which has infinite flexibility and no internal friction.

I’m afraid we’ve gone off topic.

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3 minutes ago, Brad Dorsey said:

These factors are practical considerations that influence the stiffness and internal friction of strings in the real world.  The string equation describes a hypothetical ideal string, which has infinite flexibility and no internal friction.

I’m afraid we’ve gone off topic.

We tend to do that. Mea culpa

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18 minutes ago, Brad Dorsey said:

These factors are practical considerations that influence the stiffness and internal friction of strings in the real world.  The string equation describes a hypothetical ideal string, which has infinite flexibility and no internal friction.

I’m afraid we’ve gone off topic.

That often happens when you go down the rabbit hole.

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I was happily ignoring this thread and will do my best to resume doing so...

I've not read it all, but to respond to one of the OPs questions, I would put a modern style/size bar in it as I think that will give you the greatest chance of having it satisfy the owner or anyone who might play it that has any degree if skill or training.  Presuming you're inclined to invest the time...

For what it's worth I've made more than a handful of "baroque style" modern instruments, "modernized a few previously "baroque" violins and also played/heard a number of Stainers with bass bars that were near the original size and shape, a few with "modern" bars being used as "baroque" and heard one of the relatively unaltered Stainers mentioned above quite a bit and have played and adjusted that same instrument some.  As a bit of an aside to an earlier comment, I don't trust recordings to always accurately represent how an instrument sounds in person.  They can however certainly be entertaining.

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44 minutes ago, Mark Norfleet said:

I was happily ignoring this thread and will do my best to resume doing so...

I've not read it all, but to respond to one of the OPs questions, I would put a modern style/size bar in it as I think that will give you the greatest chance of having it satisfy the owner or anyone who might play it that has any degree if skill or training.  Presuming you're inclined to invest the time...

For what it's worth I've made more than a handful of "baroque style" modern instruments, "modernized a few previously "baroque" violins and also played/heard a number of Stainers with bass bars that were near the original size and shape, a few with "modern" bars being used as "baroque" and heard one of the relatively unaltered Stainers mentioned above quite a bit and have played and adjusted that same instrument some.  As a bit of an aside to an earlier comment, I don't trust recordings to always accurately represent how an instrument sounds in person.  They can however certainly be entertaining.

If you're modernizing original baroque violins you're part of the problem, not the solution

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