A great deal of Boskian technology is based upon a discovery made in the year 1977 in your timeline, involving the influence of geometry upon patterns of motion. An undergraduate physics student decided to make a carboard model of the simplest projection of the 4D hypercube onto 3-space. It is normally rendered as a small cube inside a large cube, with the corresponding corners connected. He had drawn and then carefully cut out the folding pattern, when he came to a realization: there were two ways to assemble the pieces: the way he had originally intended, and inside-out.
So he put it together inside-out. Instead of the ordinary representation of a hypercube as a cube inside a bigger cube with the corners connected, he got the equivalent of a cube with a truncated pyramid mounted on each of its six faces. He could imagine it as a sort of rotation, where the pyramids would point in and then out and then in, and so on. He showed the model to a friend of his, who simplified it by extending the edges to complete the truncated pyramids.
This was much simpler, and a shape neither had ever seen before. If they had been crystallographers, they would have recognized it as a shape found in nature in crystals of magnetite (loadstone), copper, garnet, lapis lazuli, and other minerals. But they didn’t know that. To them, it was simply something they got by inverting a tesseract (To geometers, it was known as the Rhombic Dodecahedron),
On of the things they noticed while holding the models was that they resonated strongly to music. A loud sound system can easily cause sympathetic vibrations, but this was different. All enclosed volumes of air will resonate to their particular frequencies; an empty bottle is like a tuning fork in that respect. Concert attendees have experienced their chests and lungs resonating to deep bass notes, suffiently amplified.
But while a tuning for crafted for A440 will begin to resonate if a 440 Hz note is played, it will ignore other notes.
A pendulum swings at its resonant frequency; you cannot make it swing faster or slower, only further.
Eventually, a loudspeaker cabinet was constructed in the inverted tesseract shape. To accommodate the woofer, a large baffle plate was needed, so they truncated back one of the pyramid corners to produce a square-truncated rhombic dodecahedron.
When energized, the speaker exceeded expectations. The output was smooth all the way down into the deep bass, and you could crank it up without getting terrible distortion like other speakers made at high volume.
Clearly, something interesting was occurring.
In due course, a patent was applied for. Not a design patent, the kind that seeks to record a novel appearance for a doorknob. A utility patent, which means it is an actual functional improvement on an existing design.
The patent office cited standard literature that said resonance was bad in a speaker. They responded by pointing out that much of the problems with loudspeakers come from the woofer fighting with the box instead of cooperating with it. Standard designs, seeking to minimize interior vibration in loudspeakers, included using thick walls and stuffing the cabinet with sand, fiberglass, or other damping materials.
But the inverted projected tesseract needed none of that. Something about the geometry made it resonate really well, and the result of this was a more cooperative relationship between the woofer and the cabinet, producing clean, omnidirectional sound.
U.S Patent #4,231,446 was awarded on November 4, 1980, the same day Ronald Reagan was elected President of the United States. It was not a complete surprise when the Patent Office decided to stop arguing and granted the patent, because a lot of patent applications are granted; working prototypes are not required except for such things as time travel and antigravity.
Attempts to contact speaker companies did not succeed. The patent languished; an attempt was made to set up small-scale manufacturing, but without adequate capitalization, the enterprise failed.
And then the patent was forgotten.
But not by everyone. Research continued. Although it seemed impossible to book time in an any of the anechoic chambers used by business for loudspeaker testing, technology was providing a workaround, in the form of gear that could use FFT to measure frequency response and distortion without an anechoic chamber. The secret was in controlling the microphone: turning it on to receive sound from the speaker and then turning it off before wall reflections could arrive.
This is a measurement of the frequency response and distortion output of a coaxial driver made by Radian Audio Engineering. It is very good. You can see how low the distortion volume is compared to the main signal.
This is the same driver in an inverted [projected tesseract cabinet. The distortion curves are squashed compared the plot above. The difference is not slight; the IPT distortion is consistently many decibels below that of the standard cabinet loudspeaker.
Another test of loudspeaker performance is called Cumulative Spectral Decay, also called the “waterfall” plot because it tends to look like one. This is a measurement that shows how long it takes the speaker to quiet down after emitting sound. The tendency of boxes to resonate to particular frequencies, called “ringing”, shows up in the waterfall plot.
Here is a comparison of two waterfall plots taken using the exact same Radian driver. First it was put in an ordinary box and a plot was obtained, and then it was removed and put into an IPT and a second plat was obtained.
The plots are similar in the high frequencies, where the tweeter is unaffected by the box geometry because the tweeter is a sealed hornloaded compression driver that does not vent backwaves into the cabinet.
In the low-to mid ranges, however, the difference is immediately obvious. The waterfall plot falls toward you as time progresses. What you want to see in a diagram like this is very low curves at the front — the end of the listening window.
The Radian, in an ordinary box, is still emitting long after the woofer has stopped. You can see this by the height of the curve at the front of the eft-hand plot. When mounted in an IPT cabinet, however, you can see from the graph on the right that the speaker quiets down rapidly.
This is even more remarkable in view of the traditional teaching that cabinet resonance is bad because it will make your box ring at certain frequencies. But even though the IPT cabinet used in this test had thins walls and was highly resonant, it STILL quieted down faster than the standard cabinet.
