First, I don't debate posts because DavidRavenMoon made the post. Let's be clear on that. I have nothing for or against you in particular, aside from admiring some of the basses you've made, appreciating many of the posts you've made, and recognizing one or two inaccuracies you've stated.
I do sometimes debate posts, regardless of the poster, if I feel an inaccurate statement has been stated as truth, and I know that I can set it straight, and that I have verifiable proof behind me.
Second, I do not post opinions as facts, with little to back them up. I always attempt to delineate my opinion from fact in any situation where I feel there might be a question as to which I might be expressing. Hopefully, I recognise those situations most of the time.
I have done many pages of derivations in order to analyze some of the ideas I've put forth, and have both shared the derivations and have invited, even courted, peer review. Further, I've accepted the review, and corrected any errors, gladly.
To the best of my ability, I am not ever trying to present an opinion as a fact. If anything, I make a rather excessive use of "IMO"s and "IME"s and "I think"s and "possibly"s in order to intentionally differentiate.
Finally, getting past the defense of the ad hominem, and to the actual issue at hand.
I think the confusion here comes from the difference between mass and gauge. I have no doubt that, for example, a TI of the same gauge as a D'Addario tunes up to the same pitch at a lower tension. This would be due to the TI being a truly lighter string, despite being the same gauge.
Gauge is simply a measure of the outer diameter of a string. Despite it commonly being interchanged with "weight," it is only a loose indicator of the weight of the string, or of its unit weight (as seen in the standard string equation), which is the weight per per length (i.e. ounces per foot).
Ideally, the term "heavier gauge" would be stricken from the language. It is somewhere between misleading and false. "Larger gauge" is an accurate concept, and "heavier" is a different concept.
There are several reasons why two strings of the same gauge would have different weights (and therefore would tune up at different tensions). The most relevant (IMO), and likely to be causal in this case (fact) are:
a) Concept: Material differences. Differences in materials used, each material having a different density, resulting in different weight strings.
Application: Two strings of the exact same construction, regarding all dimensions (wire sizes, helix angles, etc.), but of different materials, will result in strings of different weights, despite their being the same gauge. So, for example, a pure nickel wrap string will be at a different tension from a SS wrap string when tuned up, because they have different weights.
b) Concept: Construction differences. Given similar materials, and similar outer diameters, the string weight can be varied according to how it is put together.
Application: The most obvious construction change is probably (Do I need an IMO here? I did say "probably," didn't I?) variation in the wire sizes in each wrap, and variation in the number of wraps applied. There are many recipes to reach the same OD (outer diameter). But, perhaps less obvious, but of at least equal importance, is the winding angle. As a wrap wire is applied, it is wound in a helix. In so doing, a little bit of air gap is left between each successive winding. (If there were no gap, the coils would contact, and the string would act pretty much as a solid rod because it would be rather inflexible.) The amount of air is crucial in determining the final weight per foot of the string. For example, if you lay on a .017" wrap wire with a .004" gap, as compared to laying on a .017" wire with a .0005" gap, you will cover each foot of string with fewer rotations/wraps (because you'll get further down the string, sooner), and will therefore have a lighter string because less wrap wire was used. And, at the same time, the OD will be virtually unchanged.
A real-world example of this was a string comparison I once read, between two sets of flats (I think it was BP magazine a few years back). Both were the same gauge, same materials, but A was looser and B was higher in tension. Did this make A easier on the the hands? No, quite the contrary: A had its final, flat wire applied very loosely, with a gap (IIRC) nearly half the width of the flat wire, while B was nearly touching itself on each wrap. The result was that A was lighter, and therefor tuned up at a lower tension; but was horrible to do slides on because it felt so rough. B felt really smooth, and was easier on the hands despite the higher tension (which had resulted from it being a heavier string, despite the similar OD).
c)Concept: combinations of construction and material.
Application: An example would be the strings made by TI (and perhaps others) that use a steel core and steel or nickel or Ni-plated steel, but which use an in-between layer of nylon fiber. These strings build up a significant portion of their OD as nylon, which is a lot lower in density than steel or nickel, and results in a lightweight string that still has a large gauge, which will tune up at relatively low tension because of the light weight.
Another property that affects our perceptions is flexibility. Two strings may be the same mass, and therefore will tune up at the same tension; but if one is more flexible (which can be accomplished by variations in construction, including but not limited to core sizing, wrap sizing, wrap temper, wrap spacing/helix angle, and core or wrap tension during wrapping), the more flexible string will be called "lower tension" by many people because it feels softer or less stiff. IME.
As a matter of fact, core size has been shown by experience and by theoretical derivation to affect how much the tension goes up as you pull the string sideways to pluck it. A smaller core string increases less in tension, and so may feel looser as you pluck; but it does not affect the tension of the string as it vibrates (except in a very complex and minimal manner) or is at rest.
As far as backing up the arguments, the basic string equation and its derivation are in virtually every first-year college physics text; further, the equation in the form I cited in my earlier post was drawn directly from D'Addario's literature; and further, I (and thousands of other college students) have actually done experiments that confirm the equation.
I do sometimes debate posts, regardless of the poster, if I feel an inaccurate statement has been stated as truth, and I know that I can set it straight, and that I have verifiable proof behind me.
Second, I do not post opinions as facts, with little to back them up. I always attempt to delineate my opinion from fact in any situation where I feel there might be a question as to which I might be expressing. Hopefully, I recognise those situations most of the time.
I have done many pages of derivations in order to analyze some of the ideas I've put forth, and have both shared the derivations and have invited, even courted, peer review. Further, I've accepted the review, and corrected any errors, gladly.
To the best of my ability, I am not ever trying to present an opinion as a fact. If anything, I make a rather excessive use of "IMO"s and "IME"s and "I think"s and "possibly"s in order to intentionally differentiate.
Finally, getting past the defense of the ad hominem, and to the actual issue at hand.
I think the confusion here comes from the difference between mass and gauge. I have no doubt that, for example, a TI of the same gauge as a D'Addario tunes up to the same pitch at a lower tension. This would be due to the TI being a truly lighter string, despite being the same gauge.
Gauge is simply a measure of the outer diameter of a string. Despite it commonly being interchanged with "weight," it is only a loose indicator of the weight of the string, or of its unit weight (as seen in the standard string equation), which is the weight per per length (i.e. ounces per foot).
Ideally, the term "heavier gauge" would be stricken from the language. It is somewhere between misleading and false. "Larger gauge" is an accurate concept, and "heavier" is a different concept.
There are several reasons why two strings of the same gauge would have different weights (and therefore would tune up at different tensions). The most relevant (IMO), and likely to be causal in this case (fact) are:
a) Concept: Material differences. Differences in materials used, each material having a different density, resulting in different weight strings.
Application: Two strings of the exact same construction, regarding all dimensions (wire sizes, helix angles, etc.), but of different materials, will result in strings of different weights, despite their being the same gauge. So, for example, a pure nickel wrap string will be at a different tension from a SS wrap string when tuned up, because they have different weights.
b) Concept: Construction differences. Given similar materials, and similar outer diameters, the string weight can be varied according to how it is put together.
Application: The most obvious construction change is probably (Do I need an IMO here? I did say "probably," didn't I?) variation in the wire sizes in each wrap, and variation in the number of wraps applied. There are many recipes to reach the same OD (outer diameter). But, perhaps less obvious, but of at least equal importance, is the winding angle. As a wrap wire is applied, it is wound in a helix. In so doing, a little bit of air gap is left between each successive winding. (If there were no gap, the coils would contact, and the string would act pretty much as a solid rod because it would be rather inflexible.) The amount of air is crucial in determining the final weight per foot of the string. For example, if you lay on a .017" wrap wire with a .004" gap, as compared to laying on a .017" wire with a .0005" gap, you will cover each foot of string with fewer rotations/wraps (because you'll get further down the string, sooner), and will therefore have a lighter string because less wrap wire was used. And, at the same time, the OD will be virtually unchanged.
A real-world example of this was a string comparison I once read, between two sets of flats (I think it was BP magazine a few years back). Both were the same gauge, same materials, but A was looser and B was higher in tension. Did this make A easier on the the hands? No, quite the contrary: A had its final, flat wire applied very loosely, with a gap (IIRC) nearly half the width of the flat wire, while B was nearly touching itself on each wrap. The result was that A was lighter, and therefor tuned up at a lower tension; but was horrible to do slides on because it felt so rough. B felt really smooth, and was easier on the hands despite the higher tension (which had resulted from it being a heavier string, despite the similar OD).
c)Concept: combinations of construction and material.
Application: An example would be the strings made by TI (and perhaps others) that use a steel core and steel or nickel or Ni-plated steel, but which use an in-between layer of nylon fiber. These strings build up a significant portion of their OD as nylon, which is a lot lower in density than steel or nickel, and results in a lightweight string that still has a large gauge, which will tune up at relatively low tension because of the light weight.
Another property that affects our perceptions is flexibility. Two strings may be the same mass, and therefore will tune up at the same tension; but if one is more flexible (which can be accomplished by variations in construction, including but not limited to core sizing, wrap sizing, wrap temper, wrap spacing/helix angle, and core or wrap tension during wrapping), the more flexible string will be called "lower tension" by many people because it feels softer or less stiff. IME.
As a matter of fact, core size has been shown by experience and by theoretical derivation to affect how much the tension goes up as you pull the string sideways to pluck it. A smaller core string increases less in tension, and so may feel looser as you pluck; but it does not affect the tension of the string as it vibrates (except in a very complex and minimal manner) or is at rest.
As far as backing up the arguments, the basic string equation and its derivation are in virtually every first-year college physics text; further, the equation in the form I cited in my earlier post was drawn directly from D'Addario's literature; and further, I (and thousands of other college students) have actually done experiments that confirm the equation.
