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There is a very interesting trick that you can pull with small speakers to make the listener believe that you have this amazing ability to make loud low tones (which is physically impossible below a certain size). You synthesize the overtones of that low tone (which you can reproduce), which will fool the brain into thinking that the low tone itself is present.

Pianos have the same effect for the lowest notes, they will not reproduce the bases directly because the soundboard simply isn't large enough to accommodate the waveform. But the harmonics do fit and again your brain will interpret the harmonics pattern in such a way that they conclude the low tone is actually present.

This is called the 'missing fundamental' and is one of the more interesting psycho acoustic phenomenon.

It works like this: instead of playing A0 directly (27.5Hz) you'd play 110, 137.5, 165, 182.5, 220 etc all the way up to say 2 KHz in diminishing fashion as you go higher. For a piano you'd have to keep track of odd/even harmonics and ensure they are in the right relation to each other to get the right timbre. The brain then is apparently capable of determining the distance between those harmonics and make you believe that you are hearing A0 even though that frequency is not at all present in the output.



Has this been the trick employed by those tiny Bose speakers that got popular in the 90s?

I remember being in some kind of demo truck as a kid, where they were showing a scene of Jurassic Park (from a Laserdisc!) and they had these big speakers left and right in front and small ones behind, and were blasting the audio at pretty high volume so you would think "surely the thick base is coming from those big speakers up front". Then, half way into the demo, they would open up the "speakers" in front of the audience, revealing the surrounding wood to be fake and the actual speakers inside the fake housing being just the same tiny ones as those located in the back.

I remember being very impressed by that demo. By the speakers, but actually even more by that Laserdisc ;-)


The trick the Bose Acoustimass system uses is a form of resonance. While it is proprietary, it is fairly easy to build for yourself. In the 1980s, Popular Science (or Mechanics, I forget which) had a review of these speakers, and they told the "secret":

Take your small bass or midrange speaker (something with large excursion of the speaker diaphragm) and place it between two "tubes" that are in a 3:1 ratio. The tube on the front-side of the speaker should be the longer of the two.

So - grab a cheap 4-5" woofer and a carpet tube. Cut the tube into a 3 foot length and a 1 foot length. Put the woofer between the tubes, sealing it up well, with the front of the woofer firing down the longer tube.

That's it. It actually works well. I built one myself using junk as a kid back the late 1980s, after reading the article. What Bose did was then "fold" the tube so it could easily fit into a box. There is probably a ratio also between the volume of the tubes and the width of the driver, among other things, but the basic idea described above will work rather well. You could even do the folding trick with an actual wood enclosure if you can calculate the lengths and such thru the curves properly.

It's similar to a bass reflex or other ported style speaker, and it scales up and down rather well (see the Bose Wave radio - IIRC, it used either a 2.5" or 3.0" single driver for the bass). The downside is that it doesn't work over a wide range of bass; the bandwidth is somewhat narrow (it is possible to offset this, though, with an EQ and amplifier, to boost those lower frequencies - plus midrange speakers in the "satellites").


The Cheat is showing something on a Laserdisc!

Everything is better on a Laserdisc!

Whatever happened to the Laserdisc?

Laserdisc!

I saw that demo too, though it was in a store and I don't remember a JP scene being used. Bose were always shite at accurate sound reproduction, but great at making things sound good. And nothing noise-cancels like a pair of QuietComforts.


I definitely saw Jurassic Park in that demo. It was specifically that scene in the kitchen with the velociraptors sneaking around, hunting the kids.

But probably they had multiple variants of the demo.


this also happened in 90's drum and bass/jungle when Ed rush started using distorted bass following along the sub bass so you could actually hear bass solo's/breakdowns on small speakers. before that you would have like a 30 minute silence if you did not have proper speakers


Another trick to make a weak boombox sound like it is a lot more powerful is to add an external soundbox. This can be achieved at zero cost by placing the boombox into any receptacle just larger than its size, a bit taller, and like 20-50 cm deeper than the boombox itself, keeping the player inside still near the opening. Wood furniture works really well for this, and floor level is preferable since it would help further bass frequencies.


This will create reverb or sonic “smear”, which may not matter for listening purposes, but technically reduces the timing resolution of notes.


I don't think anybody is under the impression that any of this is about HiFi.


Sure, but I think it’s interesting to point out the trade-off since you can apply the same principle to antenna design.


That's true, this would allow you to build a compromise antenna that works reasonably well over a range of frequencies without being tuned. On a Yagi you could probably achieve that by purposefully varying the distance between the resonators a bit from ideal, correct?


A little more context for those who aren't familiar with how sound works:

Every note an instrument makes is composed of a sine wave at the fundamental frequency of the note plus a number of sine waves at integer multiples of the note, called overtones. The amplitudes of those overtones determine the timbre or sound of a particular instrument. The difference between a guitar playing A2 at 110Hz and clarinet playing A2 is in the relative loudnesses of their different overtones.

So an A2 will be composed of sine waves at 110Hz, 220Hz, 330Hz, 440Hz, 550Hz, 660Hz, 770Hz, and so on. The amplitudes diminish as the overtones go up in frequency and it eventually peters out.

Notes an octave apart are also integer multiples. An A3 is at 220Hz with overtones at 440Hz, 660Hz, 880Hz, etc. As you can see, there are a lot of overlapping overtones. So it seems like you shouldn't be able to fake a lower note by shaving off the fundamental. If you take an A2 and remove the 110Hz fundamental, you're left with 220Hz, 330Hz, 440Hz, 550Hz, 660Hz, 770Hz. That looks quite a lot like an A3.

However, our brains are smart enough to note that there are extra overtones in there that are not integer multiples of A3's fundamental 220Hz. The presence of 330Hz, 550Hz, 770Hz, etc. are enough for our brain to realize there must be a lower fundamental that we aren't hearing that leads to all of these extra overtones. Another great example of how our brains that fill in missing data by perceiving patterns in the data it receives.

This is an important technique in dance music production. On a good sound system, especially in a club, you want the bass to have a deep low fundamental that users can feel in their chest, lower than 100Hz even. But listeners are often using earbuds, in their car, or in other places with smaller speakers that can't reproduce that fundamental. So when doing sound design for the bass, you ensure the note has some overtones above that will still be preserved.

In practice, the user experience in many synthesizers goes in the other direction where they pick a fundamental that is in the reliably audible range and then add in a "sub" oscillator that makes a clean sine tone an octave below.


Is there a demo of this effect online somewhere?

Also, by playing all of the harmonics except one, could the missing harmonic actually be induced somewhere along the way?


For those who are coming from a music background, it's the sound you get when you play a sawtooth synth.




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