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The EMG and Expert horns were direct developments of Percy Wilson's "modified exponential" theory, as published in Wilson & Webb: Modern Gramophones and Electrical Reproducers (1929) - here's a scan of the relevant pages.

Marco Gilardetti wrote: Looking at EMG horns, like the one on your profile, it looks to me that they're nor exponential nor tractrix-shaped, but a mix & match of various curves. The first part emerging from the cabinet looks vaguely exponential, but the final flare of the horn seems to have a much less complicated profile: it looks almost like a circular envelope. However, reading about the high reputation that these gramophones have, although their horn is perhaps not theoretically perfect, its shape is good enough to deliver an outstanding sound quality.

The profile photo (Avatar) is somewhat misleading and distorted into a necessarily small space. The attached photos give a better representation of the EMG Oversize horn shape and dimensions.

Perhaps these photos, being EMG and not Expert, should come under a different heading.............?

Orchorsol wrote:The EMG and Expert horns were direct developments of Percy Wilson's "modified exponential" theory, as published in Wilson & Webb: Modern Gramophones and Electrical Reproducers (1929) - here's a scan of the relevant pages.

Thanks for the paper! It seems intentionally written for not being understood, perhaps for reasons of trade secret. As far as I understand, the assumption is that the sound waves may not be planar but spherical, and the usual exponential function used to design a horn is modified accordingly. (Good sense tells me that, under these assumptions, if the throat and mouth are to be kept equal, the "new" horn has to be a bit shallower in the center section and with a more rapid flare rate at the mouth, which is later confirmed). Quite obviously, the "new" formula is still an exponential function, just as the previous one. The author then tries to simplify the new formula a bit, by introducing some approximations. After that, it is concluded that the "new" horn envelope is almost identical to the "old" one, but lies slightly inside of it (which confirms my previous deduction).

Before coming to the new pictures, which are excellent and a marvel to look at, please let me put as a side note that these EMGs are so peculiar that the first time that I've seen a picture of a unit (obviously on the internet - I had never read before about this brand and its peculiarities on books) I thought that it was a mock-up made to fool someone, or one of those stupid internet fakes. Had I find one at a local flea market, I would have probably passed and laughed at it as the ultimate crap-o-phone. You really learn new things every day, and you should never jump to conclusions too quick.

Now, the pictures. It is very, very hard to judge by the shape of a flaring horn wether it is indeed exponential or not. First of all, the exponential function is not a finite curve, but has an infinite length, so only a section of it is used to design real horns in real world (what makes the tractrix curve so appealing to my physicist's eyes is that it is a curve that has a real end on one side, and it's a vertical end, but I'm digressing). So, depending on the parameters fixed for the design, and also on which section of the exponential curve it is used, a truly exponential horn may look indistinguishably similar by (say) a circular or a quadratic one. Even exact measures may hardly reveal the difference. However, it is still my opinion that (at least some of) these oversized horns have an odd, irregular contour. Everything looks quite all right up to the end of the elbow; then the horn axis gets horizontal and the final flare begins. In that point, I seem to see a quite abrubpt change of curvature, and the final flare definitely looks not expanding quick enough. But, as said, exact measures of the cross-sections at progressive points may prove that I'm completely wrong. In any case, should this irregular curvature eventually proven to be true, and should it have deployed intentinally by EMG, it does not come anyway from the "modified exponential" theory, which still is a pure exponential function.

Really fascinating and wonderful to have your scientific input Marco, many thanks indeed!

Don't assume anything from the detail of the external contour - there are local distortions due to the internal metalwork and the transition between supported/unsupported. The interior follows a smooth and accurate curve.

Marco, you might be interested in reading the whole text of Wilson and Webb ?

https://archive.org/details/ModernGramophones1929

You might also perhaps be amused to follow this link...?

http://forum.talkingmachine.info/viewto ... 11&t=15076

Orchorsol wrote:Really fascinating and wonderful to have your scientific input Marco, many thanks indeed!

Don't assume anything from the detail of the external contour - there are local distortions due to the internal metalwork and the transition between supported/unsupported. The interior follows a smooth and accurate curve.

Thanks a lot!
Indeed, just as I completed the above message, I thought that it is the internal shape that has to be considered, which is not necessarily reflected by the external appearance of the horn (unless it is made by - say - metal sheets, which have a constant thickness).

emgcr, thanks for the links. I already have a .pdf of the book waiting to be printed and rebinded, but I didn't understand that the above paper came from it. I also remember having glanced at the repro horns thread in the past, but it's worth reading it again!

If anyone wishes to hear my Expert Senior, directly recorded with my professional microphone, please visit my YouTube channel Expert Senior (two words), or visit Soundcloud posts on Expert78 (one word).

Those are cool horns. They look like they belong on the deck of the Titanic, (that is not meant as an insult, I think they are very cool and I am a sailor, so I am a little jealous).

http://www.ebay.co.uk/itm/EMG-EXPERT-4- ... SwCkZZW2Tg

Just passing this along.