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In the Forum: Horn-Loaded Speakers
In the Thread: Bye-Bye, Fane
Post Subject: The tractrix, Newton, Jon Voigt, poor French mathematicians and fishy factsPosted by oxric on: 4/13/2011
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 Romy the Cat wrote:

BTW, I was not kidding about the dual-concentric 8” Fane. They did make a version of Studio 8M with a tweeter in the middle. I have it sitting in my driver storage…

Another BTW: the tractrix curve was not introduced by Brits but by French in 16 century after they study fish moving in water.

The Cat



Romy,

I admit my ignorance when it comes to the dual concentric Fane drivers, I must say the first I heard of the 8M was when I read about your Macondo Acoustic system on your site. Well, I may have some interesting bit of audio trivia for you. Vitavox did produce some ribbon tweeters at some point but I understand they are extremely rare and although I have a friend who is in Paris and finds them very good, I have never encountered them myself. That would complete your set-up rather nicely...

As for the French introducing the tractrix curve, although I have the greatest respect for Claude Perrault (and Huygens), the two French mathematicians you must be referring to (albeit that they were not yet born in the 16th century), it is interesting to note that Claude Perrault felt not up to the task of describing the curve mathematically. He took satisfaction in confiding to Gottfried Leibniz that another French mathematician, Pierre Fermat, had also failed to do so. On the other hand, our good Sir Isaac Newton had solved the problem decades earlier, in 1676!

In any case, the tractrix horn is clearly a british invention, that of the British inventor, Jon Voigt (that is what I was referring to, but I should really have referred to the tractrix horn rather than the tractrix curve). He applied for a patent for the tractrix horns on July 5, 1926 "Improvements in Horns for Acoustic Instruments" which was awarded the following year. see the patent here:

http://v3.espacenet.com/publicationDetails/originalDocument;jsessionid=387C78FE159C8DBF57FCA8D1977AE73A.espacenet_levelx_prod_0?CC=GB&NR=278098A&KC=A&FT=D&date=19271005&DB=&locale

An interesting paper on the early history of horn design:

http://forums.klipsch.com/forums/storage/3/714028/An%20Interview%20with%20PGAH%20Voight%20Part%201.pdf

Anyone interested in this great British inventor might find the following 'memoirs' serialised on the British forum 'pinkfishmedia' of some value:

http://www.pinkfishmedia.net/forum/showthread.php?t=78278

It is obvious that in your system it is not so much the maths which is at issue as the tractrix profile used in acoustical horns which was arrived at in fact in ignorance of the prior work done in that field. Jon Voigt in fact thought that he had invented that equation until he was corrected and told that the tractrix profile was actually an old discovery (or invention arguably).

As for the idea that the original idea originated from observations of fish movement, apart from the fact that this does not appear validated anywhere in terms of historical accuracy, I have difficulty understanding how a curve which is part of the family of curves of pursuit or 'following' (Claude Perrault discussed the problem of dragging a stopwatch by its chain) could relate to the movement of fish in water.


Best regards
Rakesh

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