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In the Forum: Horn-Loaded Speakers
In the Thread: Jessie Dazzle Project
Post Subject: Tractrix vs. Exponential curve for lower frequencies.Posted by Romy the Cat on: 8/6/2007

 guy sergeant wrote:
One issue that I would consider is that the Tractrix profile supposedly does not lend itself aswell to extremely low frequency horns (being too short) as other profiles in particular the Hypex (Salmon) shape.

Yep, it was very predictable, and after post #1 I was wondering how long it would be before post #15 appeared.  It did not take long!

The subject that Guy brought is very complicated, controversial and most likely should upset Jessie as there is not defined answer to it. Let look a slightly deeper into the issue.

There are no doubts in my mind that for MF frequencies no other profiles beside Tractrix must be use (or the negative opening Tractrix – the French one, which is basically is the same). However what we slide down the frequencies then the situation become less one-sided.

When horn touches less than ~300Hz (???) then some people mention some "benefits" of Exponential curve.

This definition of the “benefits” is complicated as I have no definitive judgment on the subject. I personally never was able to conduct the methodologically correct evaluation of the horns, make to be the same rate but featuring Tractrix and Exponential curves. All Exponential horns that I had/heard were serial production rectangular horns, with the typical metal harmonics problems and all Tractrix were custom spherical. Even if I had the same Tractrix and Exponential horn then to make a correct listening assessment is not so simple. The Exponential horn allows itself to be crossed closer to the horn’s cut off, that would make Tractrix and Exponential of the same rate to sound different. Sure, it is possible to cross the identical Tractrix and Exponential, identically imbed them into room and see what happen but I did not do this personally and I do not know anyone who did. I am slowly contemplating, if it worth to pay another $1.5K for a new 250Hz Exponential for my Fundamental Channel to research this subject as I am not completely satisfied with hat my current 250Hz Tractrix does. If some one has 250Hz Round Exponential and can lend it to me for a few weeks it would be wonderful and I would not mind to pay rent.

So, the only people who can shade some light on the subject would be the people who built the horns. Bruce Edgar is unquestionably the most experienced among all and has most qualifications. I consulted with Bruce about it and he feels that Exponential horn of identical rate just has subjectively “more bass”. He however admits that that “more bass” has an idiosyncratic tone in it that does not exist in Tractrix. Here is where the complexity comes…. Do the Exponential horns have “more bass” because they allow to be loaded deeper? Will the Exponential horns offer “more bass” if the bass cut off point will judged not by amplitude but by the “bass cleanliness” that we hear via Tractrix? What is the value of that “idiosyncratic tone of the Exponential horns” and is it possible to USE it beneficially? I personally can advocate the answers to those questions from both sides… and the “right” answer will be only on context of a specific attempt and the specific results.

Now, let look at the Jessie project from the perspective of Tractrix vs. Exponential debate.

The Upper Mid-Range 400Hz Tractrix – that is no question that nothing besides Tractrix must be used.

The Lower Mid-Range 180Hz Tractrix – that might be exponential candidate to get more bass out of S2 lower knee, particularly if Jessie will drop the S2 primary resonance. However, we do not know (and Jessie do not know) where he will low-pass his Lower Mid-Range channel. If it were around 1000Hz (as I do) then the Exponential might be considered, if it will be higher (and there is rational to do it as well) then I would stay with Tractrix. Still, even if Jessie stays with lower low-pass and go Exponential then what will be sound of S2 in that setting? We do know that S2 does in 220H Exponential made by Vitavox, crossed at 500Hz, second order. The Lower knew of that setting is very good. Is it “clean”? Not really. Take that Vitavox-made 220H Exponential and try to talk into it. You will see it has heavy nasal colorations… To cure those nasal colorations the horn should be high-passed heavier… Will this high-passing kill all the “bass benefits” of the Exponential curve? I do not know the answer.
The Upper Bass 115Hz Tractrix. That is another candidate to employ the Exponential “thump” but let look deeper. In the Jessie’s case the Upper Bass will be the only properly implemented Upper Bass that I ever seen. No one, including me, can afford to have 115Hz Tractrix and to cross it at 240Hz. All our horns are fundamentally compromised because we are trying to push more bass out of our horn running them the last “octave down”. Jessie has no need to push the “last drop” from his Upper Bass horn as he has his Mid Bass horns. Well, Jessie’s Upper Bass channel is in a way sonically “unnecessary channel” as his Mid Bass horn can care the Upper Bass Upper signal. What Jessie’s Upper Bass horn does is “anchor” the entire Jessie’s acoustic system. The upper region of Jessie’s Upper Bass channels is directional and if it will be radiate ONLY from horn hangings from the roof then the system (particularly combined with the output of the relatively high-located Lower Mid-Range channel) will have horrible imaging. So, what Upper Bass does, is creates a virtual array of the drivers, lowering the centering radiation point to the ears level. When Jessie’s will finish his horns and will be playing with fine-tuning and integration of channels then turning off the HF and MF channels and playing with high-pass of his Upper Bass horn he will be able to center the vertical image of the system right where the MF will be. Therefore, in context of the Jessie’s system I do not see a lot of need for Upper Bass to have more “Exponential Bass”. Ah, did I mention that Jessie’s Upper Bass Tractrix is ~8 shorter then the Exponential would be?

The Mid Bass 45Hz Tractrix. This is the only candidate that I see in Jessie’s future installation that might be worth to consider to go Exponential as he would need push this horn at it’s bass’s maximum. Unfortunately no one will tell him the right answer in turn of Sound. If I were Jessie and was in front of the decision to make I would probably bother any horn-maker in the World, getting their opinions, getting second, third, fifth, twenty seventh opinions… I would model the competition between Tractrix and Exponential at I would say 300Hz and to see how it works. No one knows anything…. The Exponential will have “more bass” but how right that bass will be?

OK, now somebody will hate me…

As the absolute crazy but the absolutely noblest idea, and considering that it will be LF horn, also considering Jessie experience with molding plasters, I would propose following: figure out the delta between Exponential and Tractrix curve and make the big horn …. in conical shape, I would say 11 straight segments. It will be cheap to do in metal, aluminum for instance. Then inside the belly of the horn (to the each segment) make a detachable insert that will convert the profile of the horn into Exponential, Tractrix or any other imaginable curve. The interesting part is that the plaster insert might be a perfect damper for the frame of the bass horn…

Rgs, Romy the Cat

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