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Jean-Michel posted a reply in response to my commentary:

http://www.diyaudio.com/forums/multi-way/140190-jean-michel-lecleach-horns-109.html

Jean-Michel Le Cléac'h wrote:

Hello, Romy is totally wrong on that. ( a parte: I hypothesize that Romy's sentence: "why I don't not like Le Cléac'h (La) horns " doesn't find it's origin in any theorical nor technical consideration... please note that one of Romy's reproach against me is that, in his not humble opinion, I don't share enough my own philosophical considerations about what a good sound should be nor I share enough my own ideas about the proper setting up of a complete audio system... ) At high frequency, the waves takes off from the wall of the horn at a shorter distance from the throat than for the lower frequencies, therefore, at HF the roll-back mouth has no effect. At low frequency, the wavefronts leaves the wall of the horn at a large distance from the throat. with an unbaffled tractrix horn this means that the low frequency waves will be partly reflected at the edge of the mouth. Give a look to: http://www.diyaudio.com/forums/attac...s-rollback.png You can see the effect of the reflected waves on the half upper part of the polar graph corresponding to a truncated Le Cléac'h horn. Then, you can see in the lower half of the graph the increased smoothness of the polar graph of the "complete roll-back" Le Cléac'h horn . Then there is the problem of the integration with the bass channel and with the highs. I don't think that the eventual integration problems associated with the increased diameter of the Le Cleac'h horn are of the same importance level than the benefits of the reduction of the reflected and diffracted waves at the mouth. Best regards from Paris, France Jean-Michel Le Cléac'h

Of cause I very much disagree with his concussions. If we accept the Jean-Michel’s assumption that anything beside pressure travels(!) physically across a horn then frequency while they take off from the walls of the horn obey the rules of diffraction - or  bending themselves to the region of geometrical shadow. At HF the bending is “too violent” as the HF slide of the age of the horn, here is what the La-profile works very good providing a smooth transition to decaying HF. BTW, if you look at the shape of my “Water Drop” tweeter then it will be the same La-Profile with negative opening only extended at full 190 degree. BTW, the constant directivity horns are built in the very same way, introducing diffraction edges and they work only at HF.

At LF the wavelength becomes too long and the negative opening not even being recognized. From my photography time I remember that diffraction increases as the diameter of boundary approaches the wavelength. For 2000kH-3000kH and the wavelength of 4 -6 inches the extra 2-4” of La-profile negative opening is working fine. But at 100Hz and wavelength of 135 inch the 2-4” of La-profile negative opening are negligible. You do not need to have special knowledge but just a common sense to understand that as frequency drops the effectiveness of the La-profile negative opening drops as well. BTW as 40Hz and with much more longer wavelength the edge of the horn has no difference at all…

Sure, in response to it the scientific-minded Jean-Michel posts the graph that demonstrates that La-profile at LF has “increased smoothness of the polar graph”. Well, what Jean-Michel forgets however that at LF is not negative opening of his La-profile begin to work but the fact the he has larger baffle around his horn/ If you remember in 30s WE, Klangfilm and other did the same by increasing the forward LF output and smoothing the of-axis response by building small open baffles around the horn mouth.  There is nothing wrong with that approach (for LF only) but you pay by using larger mouths per each channels, larger then it is necessary for given cut off rate.

So, to have a graph is one thing but to interpret the true applied meaning of the graph is a bit other thing. A mouth of horn does act at LF baffle. So, if one wants to do the comparative graph then the max diameters of Tartaric and La-profile hors need to be identical.  I hope everyone understand that it happens then La-profile will have a good half-octave less in profile rate.

Now is the elephant in the room: “I don't think that the eventual integration problems associated with the increased diameter of the Le Cleac'h horn are of the same importance level than the benefits of the reduction of the reflected and diffracted waves at the mouth.” The integration problems associated with the increased diameter is a HUGE problem, really HUGE and if Mr. Le Cléac'h do not spend time to collect graphs, build theories but play with practically of playback then he would not deny it.  The reduction of the reflected and diffracted waves at the mouth is good but in my estimation it is way less important, not to mention that it work ONLY at HF. I personally feel that randomizing mouth edge is way more effective then negative opening and it takes no extra toll of the size of individual channel.

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