tumbling dice: experimenter’s lower-mid horns

The best horn is the one that’s with you—to riff on that old saying about cameras—in your room… and stacked on top of other horns. Because while we’re riffing, here is one based on that saying about easter eggs (or computer backups): one horn per channel is not a horn system, two horns is half a horn system, three horns per channel is a horn system.

It all started at the last eTf:

(source: DHTRob, from this photo set)

That Western Electric 15B horn, man, it was something else—together with its WE tweeter and bass bin. I think it was quite an instructive lesson to quite a few people, about getting most of the music together out of a horn. But it was also a lesson why engineers have been trying to cheat physics ever since WE stopped building the 15B: the sheer size of it. Everyone is in awe with this sculpture, even before it plays any tune.

Case in point: I would be fully prepared to go mono if I ever found one of these. But I almost dread finding two of these, and the dilemma of arranging everything in my office around them—well, almost. Now, I can stop dreaming and get on with achieving my goals, see the first sentence of this blogpost.

In the image above, bottom-right, there is the Altec 825 cabinet. Looks relatively small, no? Standing next to it, I was actually shocked how, in absolute terms, modest it size is. I even checked if it was really an 825. And its ‘horn’ is supposed to go down to around 200Hz. ‘It’s really more of a directional baffle’ wrote Greg Boynton about it in sound practices issue 1. That got me thinking.

My Altec valencias are really a combination of a 15" bass-reflex woofer that is asked to go up to 800Hz, and a higher-mid horn that is also asked to cover the treble range. Both of them vary their beamwidth over their over-extended range. The woofer is of course all over the place, from omni down low, through half-space, an then up and ever narrower—half a wavelength of 800Hz is 21,5cm. The radial mid-high horn is 90×40°, up to 3kHz, then it narrows its beam vertically up to 10kHz or so. The valencia description hints at the solution: add a lower-mid (aka mid-bass) horn and a tweeter. This gives me a chance to achieve a modest version of that ultra-fi classic, a full 4-way onken system:

Why not buy or build some (copies of) Altec 825 cabinets and pop in the 416s of the valencias? Woofer + lower-mid horn solved, no? Well, there are several problems with that, but the one that makes it a non-starter for me is that bass and lower mids would be driven by the same amplifier. It takes quite a bit of compromise to achieve the damping factor, power, low frequency response and energy reserve required of a bass amp. All this compromise is not what I want to listen to in the lower mids. The WE 15B lesson shows me to aim for pure bliss in the midrange, even if I have to get it out of two horns (and two amps).

So there I was, december last year, scheming what I could pop on top of the valencias to provide a modest two octaves (200–800Hz) of lower mids. If that sounds like a super-narrow range, don’t forget that in a perfect 4-way speaker system each driver covers 2½ octaves. Possessing few woodworking skills and tools, I was looking for some PA thang to recycle or something, anything, with the right shape to repurpose as a lower-mid horn.

Here is where a little help from my friends started: Dietmar, Bodo, my brother Erwin, Thomas, Wolfgang and Marc.

A chat with Dietmar convinced me that finding some stuff was not that easy and was going to cost thousands. Hmmm, I had to build it myself. He confirmed that a narrow frequency range, constant directivity and a simple, conical horn are a good match. He also confirmed that old-fashioned tube radio drivers would work well on a lower-mid horn.

Back to scheming. Something simple, with straight walls. No mitered joins, please. Scouring the net, I stumbled upon this image:

Interesting, that looks like two drivers firing into each other at a 90° angle, could be done with straight side walls. Top and bottom also attach at 90° angles. In a way, a wooden box that has been cut diagonally. Just a pity about the parallel top + bottom, a recipe for standing waves. That same night, I was trying to fall asleep—but actually still scheming—when intuition delivered an insight…

In 3D space the 90° driver trick can be done with three drivers. Put them in the corner of an open cube; saw off the ‘ears’ sticking out. Result: the crudest conical horn possible. But yeah, conical; constant directivity; no parallel sides; only 90° joints; plane sides to mount drivers. Simple and promising enough to try.

So I built one, from paper, scale 1:10 (millimetre for centimetre, easy):

For 3D, building a cheap and easy model rocks. Iterating without going through the expense of building the real thing is an important part of design. Thus the first paper model was wonderful to get first feeling of how this would pan out. Then over the course of a couple of weeks I made about two dozen more paper models.

Each one showed a problem, provided an insight, or a solution. Some survived only for a coupe of minutes; the next problem of way forward had been found by then. All in all, that saved a lot of wood.

Want to try that out yourself, just to have a look? You can build my final paper model in minutes. Print the pdf below, cut out the squares and cut off the corner show of each; then stick them together with three pieces tape, with the drivers in the common corner:

So now I needed six drivers that could do the job. The day after dreaming up the solution this auction ended:

Mystery drivers. Eight inchers, look the part: old skool, paper cones, goop on accordion surround, vented dust cap, alnico magnets. So I snatched them. I still do not know who made them, nor their specs. If I had to do it all again, I would look for five or six inchers, they would sit tighter in the corner. As long as the resonance frequency is low enough, go for it.

Meanwhile, only a few parameters needed to be decided on before a real build could be attempted:

1. overall size: to be on the safe side with both horn depth and mouth size, I picked 55cm as the size for the cube’s edges;
2. diagonal cut-off: driven by working with the paper models, I picked a diagonal size that makes the horn look on-axis like a nine-petal flower; 0.3473 × 55cm = 19.1cm are the two right-angle sides of the triangle cut-off;
3. driver cutout: I thought that cutting out the full driver circle would effectively shorten the horn length and limit how low it would go; so after some more work with the paper models, I devised how to construct the cutout so that the three drivers combined look like a circle on-axis, and set the apparent size of this circle to that of one driver:

The net effect of this can be seen in the final paper model above; there you can see the vented dust caps of the drivers just peeking out.

Some more basic insight. The angle of the ‘cone’ varies quite a bit, of course. It is 54.75° (from centre axis) along the cube’s edges; it is 35.25° along the diagonal of the cube’s sides. What is remarkable that the angle enclosed by the cube/cone (wall to wall) varies much less: from 90° to 78.5°. This is for instance less than in a 60×60° pyramid horn. There it varies from 60° to the same 78.5°. But no free lunch: the centre axis of that enclosed angle is for the pyramid rock-solid the centre axis of the horn; with our cube/cone it moves in a triangular pattern.

And then I built one (tip from Dietmar, ‘start with one’):

First I got a load of beginner’s tips from my brother Erwin (he is a master carpenter). Then I went out and bought a jigsaw and 16mm blockboard, cut to size (55cm + 16mm rebates). The blockboard is a tip from Thomas; no mdf for me. Both Thomas and Marc urged me to use two big feet to get the horn ‘to stand up’ (I thought I could use one of the cut-off triangles). So I did:

The angle at which the horn must be raised is that 35.25° mentioned before. In practice that is as easy as getting a rectangle of wood with ratio 1 : √2 and cut it across its diagonal. I again used 16mm blockboard, 37×26.2cm. You can see from the screws on the front pic how I spaced them.

Then—drumroll—the first measurement:

The raw response, only a hard cut at 71Hz. Good news: it goes lower than I asked for, down to 158Hz; bad news: That valley exactly centred on 800Hz. I did not expect the high end to be such a struggle. So the hint from my friends was to open up the driver cutouts. I calculated three steps to take it from the initial opening to full-driver-circle cutout. The I performed two of these steps in a row. Now, it looks like this:

And it measures like this (same hard cut at 71Hz):

Good news: it still goes down to 158Hz, no horn-shortening effect; bad news: the situation at 800Hz is marginally worse. This is the kink I mentioned previously and I am stumped at the moment what to do about it. I have experimented with reducing the cutout with various geometries, in an improvised way. Nothing really makes —well, takes—a dent. I still suspect that I did myself no favour creating this combined cutout that look like a circle on-axis; that could work as a uniform effective edge distance to the horn origin.

Although nagging, the kink does not prevent me from integrating the horn with the valencia. Surprisingly, the high and low rolloff of the horn itself is first order. This was verified by using different slopes in the digital x-over and measuring the resulting response. So I am using third order slopes at 158 and 805Hz, and measure fourth order results. A bit of equalisation is needed to flatten out the response, but that is also the case for the two valencia drivers. Here is the response with x-over and eq applied:

I am very pleased with the efficiency of the horn. The drivers themselves did not impress me as particularly efficient, compared to some 93dB/W/m Tesla ovals (same 4 Ohm impedance, so direct comparable on the same tube amp). So I guesstimate 90dB/W/m max, for the mystery drivers. But On the horn! To integrate the lower-mid horn with the Altec horn (806A on 811B), I have to set its level 2dB louder than the Altec. In my experimental setup all drivers are hooked up after the x-over to identical class-D amplifiers (pure voltage amplifiers, gobs of feedback). Because the impedance of the lower-mid horn is different than that of the Altec—12 Ohm vs. 8 Ohm—a correction of 1.75dB is necessary when comparing the two. Thus the lower-mid horn is effectively 0.25dB/W/m less efficient than the Altec horn, which to my best knowledge, is 104dB/W/m.

The whole combo definitely has that clean, effortless horn sound. That effect that you do not realise the volume is really a bit too loud, because the customary distortion increase of ‘normal’ speakers is not there. You only realise when you try to say something, or sing along.

Also impressive is dispersion. Behind the working tables in my office at a distance of a little over three meters from the horn stack, I can move a distance of more than four meters side-to-side and the sound does not change. I am really digging that. ‘Wait,’ you say, ‘did the mid-high horn not also beam?’ Well yeah, vertically. But as long as one is at the same listening height, either sitting anywhere at the tables or pacing all these meters up and down, the sound stays the same.

Overall, integration with the Altec horn was a bit of a nonevent. It just works, quite beautifully. I have spent a lot more time in the last weeks on the general problem of time aligning and the integration of the valencia woofer with the room. Time alignment is now solved and has become a routine task. The woofer will need some more work.

About the name: When Wolfgang visited me and I showed him the paper models, he said: ‘ah, simply the corner of a die.’ And after putting the horn on its feet, the whole thing does look like a die with three dots caught in mid-flight. So now they are called the tumbling dice horns.

Born out of desperation (my woodworking skills; what is available at any price) and the strong will to make it work, the tumbling dice horn has already delivered beyond expectations. It was designed using intuition, some calculations, paper modelling and no software simulation—as a practicing designer I say that there is nothing wrong with that. Of course if you can do, buy or build better, then I can only encourage you to do so—I wish I could. But I am happy I tried this, aiming for 200Hz horn-loaded and ending up a third of an octave below it. If after reading this blogpost you decide to also go for it, than you have made my day.

I will now have to build a second one and that gives me the opportunity to experiment more, starting out with much smaller driver cutouts. And when I got a pair of these finalised, I still have only half a horn system—see first paragraph of this blog post. So there is still some more work to do…

ps: I forgot to mention that Tom Danley’s unity horn designs are of course a factor in this all. They gave me the confidence that one can pull off stunts like this.