cid said
.....
Are bright strings necessarily loud strings?  

 I guess folks have different interpretations of these terms.  From my own point of view I would say no, "bright" strings are not necessarily "loud" [ they could be but from my viewpoint that's probably more down to the instrument ]

  My own take on "bright" and "dark" is  like this - 

  When a string vibrates, let's say the open A (but it applies to stopped as well), if your A is set to 440 then there is a "fundamental" or 1st harmonic frequency present in the sound of 440Hz.  But, it's not a simple sinusoidal wave, and in actual fact, there will be harmonics created at 2nd, 3rd, 4th, 5th, 6th harmonics and so on - getting ever smaller.  [ So on the open A, you actually have a complex sound consisting of the additive combination of 440Hz, 880Hz, 1320Hz, 1760Hz, 2640Hz and so on at their diminishing levels.... ]

What I regard as "bright" is a string which has a higher presence of the higher harmonics, and a "darker" (possibly I would use "mellower" rather than darker.. but..) string produces less of the higher harmonics - both in number and amplitude - well arguably the number may still be there, but the actual amplitude of the higher harmonics becomes so small as to contribute little to the overall sound.

That, however is only how I classify the term - simply because I can see and understand the physical nature of the sound produced - others will differ in their interpretation of "bright and dark" - and their points of view will be equally valid !!!

So - no - for me - a "bright" string is not necessarily a louder string....