Based upon what I read in the article associated with the link, I think it's still a secret. The article didn't make a lot of sense to me. I'm suspicious that the writer either didn't understand Mr. Politzer's analysis or he didn't know how to explain it.
It seems to me that what a listener hears from a banjo is a function of the interaction of the membrane in the ear and the sound pressure wave created primarily by the vibration of the head of the banjo.
The writer dwells mostly on the peculiar vibration characteristics of the strings caused by the interaction of the the head, the bridge and the tail piece. Then at the end of the piece, he states:
"But what of other stringed instruments where the bridge moves relative to the fixed ends of the string like the banjo? These include the violin and the mandolin but they do not produce a metallic ring.
Politzer says this is because the soundboard on these instruments is made of wood and so does not move nearly as much as the membrane on a banjo. Indeed, he points out that if the membrane on a banjo is replaced with the wood, the quintessential banjo features disappears."
Based upon that statement, I think most readers would logically conclude that the banjo head is the component of the instrument that is the quintessential element responsible for the characteristic sound of the instrument. If Mr. Politzer's analysis is correct, the peculiar vibration characteristics of the strings certainly must be affecting the way the head vibrates, but it is the head, not the strings that directly creates the sound pressure waves.
Very interesting article. Thanks for posting it. I suspect that the explanation offered in the article is just one of many reasons why a banjo sounds the way that it does. Others being:
A banjo sound's distinctive "pop" is probably due to the very short rise time of the volume of its audible sound air pressure wave, which is caused by its large but very light (low inertia) banjo head under high tension.
A banjo sound's timbre which sounds like a mixture of something metallic and something wood because that is what it is. (If it looks like a duck and quacks like a duck,...)
The wonderfully clear, brilliant, immensely pleasing sound of some banjos (think pre-war Gibson Mastertone) is due to the strong presence of harmonics (high frequency multiples of the basic frequency of notes played), just as is true with a fine violin, plus the absence of sound absorbing materials. (Can anybody tell me why Elvis covered one of his guitars with leather?)