Drawn in by the Siren’s Song

When I say “siren” what do you think of? Ambulances? Air raids? Sigh. I was afraid you were going to say that. We’ve got work to do.

You see, the siren played an important role in physics and mathematics about 150 years ago. Through the first half of the 1900s, this fine apparatus was trivialized, used for its pure noise-making abilities. During the World Wars, the siren became associated with air raids and bomb shelters: a far cry from its romantic origins. In this article, we’re going to take the siren back for the Muses. I want you to see the siren in a new light: as a fundamental scientific experiment, a musical instrument, and in the end, as a great DIY project — this is Hackaday after all.

Singing Muses, Spinning Disks, Science!

Our story begins in ancient Greece. Sirens, the Muses of the underworld, would sit around on rocky cliffs to lure sailors into shipwrecking into their island with the beauty of their song. Or so the story goes; we weren’t there. Fast-forward nearly two thousand years to Paris in 1819, where Charles Cagniard de la Tour refines a rotating disk with a bunch of holes in it into a fundamental experiment in physics and acoustics.

Photo copyright Smithsonian Institution
Photo copyright Smithsonian Institution

Before the siren, people knew that sound was made of pressure waves in air, and they knew that the frequency of these compression waves was related to the pitch, but they had only relatively imprecise ways to measure it. The siren changed all that because the pitch was easily backed out from the rotational speed of the perforated disk, which could be geared down to something turning slowly enough that it was precisely measurable. This lead to a verification of a number of theories about musical pitch and acoustics, and even an estimation of how fast a mosquito beat its wings (~10,000 times per second). To top it all off, the siren also worked underwater, demonstrating that pitch was all about the frequency of the impulses and not related to the density of the medium through which it traveled, and giving it a poetic name.

Sirens were soon built to test out the mathematical ideas that Joseph Fourier had just formalized, and that we now call Fourier analysis. Again, musicians had been making complex tones by combining pipes of different lengths in an organ — “pulling out the stops” — but they didn’t have data. The siren’s nearly-sinusoidal output, combined with the ease of creating accurate frequency ratios, was one of the important first demonstrations of Fourier synthesis.

And even today, the siren demo is a great hands-on way to convince undergraduates that sound waves are periodic pressure variations, because the big spinning disk and air compressor are large, loud, and visible. In this example, a physics professor gets jiggy, playing “Joy to the World” for his class.

The Sirens’ Children

Which brings us to music: the siren was named for Muses, after all, not physicists. I’m not sure, but I’d guess that the reason we don’t see mainstream musical instruments based on the siren principle is that it’s a serious engineering challenge. Which is not to say that people haven’t tried.

As an alternative to fixed-ratio gearboxes, modern higher-speed stepper or servo motors should be able to play in tune fairly easily, making this a piece of cake in these modern days. siren-orchestraAfter all, who among us hasn’t played the Imperial March on a CNC machine of some kind or other? So we’re a little bit surprised that our web searches came up with only a few examples, and few details.

That said, Dutch artist Rene Bakker seems to be working on an entire siren orchestra, although all we get are glimpses. This Helmholtz double-siren is straight out of a science lab. His servo-driven siren (YouTube link) is the highest-tech and most straightforwardly musical of the bunch, although for sheer visual impact, we like this version of a turn-of-the century Loman organ (PDF):

Similarly, CCRMA students Gina Collecchia, Kevin McElroy, and Dan Somen built up a cool siren organ for a DIY musical instruments class. You can read the documentation and check out their videos of a siren organ prototype or their performance on three siren organs.

Tonewheels: The Siren’s Distant Cousins

While there’s something romantic about making music directly by pushing air out into the room, it’s hard to amplify. And engineering-wise, if you didn’t have a compressor to haul around and a big spinning disk with all that inertia, things would be a lot easier. It turns out that artists and musicians have been making optical tonewheels — the equivalent of the siren’s disk — since the 1920s. This incredibly detailed tonewheel documentary by synthesizer noisemaker Derek Holzer summarizes an incredible amount of history in one webpage. We’ll get back to a simple optical siren in the DIY section below, but in the mean time, here is a sampling of Derek’s (chaotic and terrifying) optical musical madness.

optigan-shot0006On the other side of the artistic spectrum from Derek, but no less cool, is the cheesy musical wonder that is the Optigan. The Optigan uses optical tonewheels that are more like LP records than simple repetitive waveforms, although it has those too. On the left of the instrument is a bank of buttons that play pre-recorded sample backing tracks, and each key on the keyboard plays a separate track on the disk with its own pitch. In principle, each key could play an entirely different sound as well, but they never went that crazy. That said, a lot of musicians have recorded with Optigans, and one fan is putting out new disks right now.

As an aside, encoding sound optically like this is also how the sound track in films worked: a thin strip ran down the side of early “talking” films and the light intensity that shone through onto a photocell produced a variable voltage, which was then amplified to go along with the movie. (See Wikipedia’s entries for Phonofilm and Photophone on your own time if you’re interested.)

Magnetic Tonewheels and the Mighty B3

640px-Tonewheel-p.svgFinally, nearly the same principle is used in the Hammond B3 organ. Each wheel is a disc that resembles a gear with specially-cut non-mating teeth. They pass close to a magnetic pickup that turns the profile of the little wavy teeth into an electric sine wave. Just like the early sound Fourier synthesis experiments, or a pipe organ before that, the output of different wheels can be combined to make a much richer, more interesting timbre.

Keeping nearly one hundred of these spinning tone wheels in sync and running smoothly is no mean feat, even if the sound production method is simple in principle. Hackaday’s own Kristina Panos wrote up a fantastic article on the Hammond organ that includes a video that goes into detail about how they’re made. If you’re a Hammond fan, you should check that out. If you’re not a Hammond fan yet, go listen to some Dr. Lonnie Smith:

DIY Project: The Fan Siren

SFS_handAnd speaking of fans, if you want to build your own “musical” siren, the most accessible design that I know of comes from Dutch electro-punk Gijs Gieskes, whose work we’ve featured on Hackaday going way back. The first project of his that I ever became aware of is the mini Synth fan, which is nothing more than a computer fan whose blades intermittently block light that shines on a photosensor. Yup, it’s a simple siren, with light playing the role of air.

Gijs has a more elaborate version as well, where a microcontroller controls the fan speed and incorporates a small sequencer with MIDI output. But that’s getting ahead of ourselves. Even by itself, the simple fan siren synth is quite playable. You can tap it with your hand or spin it manually. It’s very hands-on. And if you’re handy with the Arduinos, you’ll know where to take it from there. Check Gijs’ site for the (hand-drawn) circuits.

I made one of these, ages ago, and here’s what I came up with. Everything that’s possible to run from the AVR is controlled by the AVR, and four slide pots connected to the ADCs serve as input. In the end, one pot on the far right controls the fan speed and another scales the output volume. The LED is also driven by a PWM signal, and gets brighter and darker (on average) over time. One pot controls the LED PWM frequency (far left) and the other controls the frequency of a triangle wave that modifies the duty cycle — making the LED get brighter or dimmer periodically. Combining all three of these pitches together: fan speed, PWM speed, and the slowly varying duty cycle, makes for a lot of mayhem.

The device is noisy and has glitches galore. I lost the code so long ago that I can’t post it, but it makes some awesome sounds. In the demo video, I first run just the fan synth part and then add in the LED PWM and its modulation. Good times.

Part of the allure of a device like this is how simple it is, but also how easy it is to make it more complicated. Add a second fan? Control the fan speed to play tunes? If you have one of those fancy fans with the built-in tachometer (look for four wires) making a servo control loop should be fairly straightforward. I built a serial port into the device, so I obviously had grand plans.

Whatever you do, don’t resist the song of the sirens! I hope that I’ve pointed you in enough directions that at least something will strike your fancy. If you build anything that spins and makes music, let us know in the comments here, or in the tip line.

31 thoughts on “Drawn in by the Siren’s Song

  1. The diy fan siren could have done without the fan but using the electrical noise straight from a cheap (maybe half burnt out) brushed motor. Put it in series with a speaker and instant crappy speed dependant tone generator.

  2. A couple posts back is Mersenne, a monk who determined the relation of wavelength, frequency, tension, and density (mass) of a string or wire, by using very long wires between fence posts that vibrated slowly enough to count against a heart beat or water clock. Pretty much explained the whole stringed instrument thing in the early 1600’s.

    What is the date of the first experiments with dust in a glass tube and a brass rod? Pull the rod with a rosin rag and get high pitched sound and the dust forms a pattern of the sound wavelength – also measure Young’s Modulus of the metal rod. I understand a HaD post can’t do justice to the history of science. Just about any simple sounding topic is worthy of a major book. It is kinds cool how these simplified stories produce plenty of questions about the details of developments of ideas.

    1. There’s theory and then there’s measurement. I was (hopefully) pretty careful to stick to the latter.

      The physics must have been reasonably well theorized at the time the siren came along. (Didn’t the Greeks observe doubling string length equated to octaves?) And you could extrapolate this, but this is theoretical until you can measure 440 Hz accurately. (The Greeks also thought some kooky stuff about atoms.)

      Anyway, all I know is what I read. And in la Tour’s writeup of the experiment, http://gallica.bnf.fr/ark:/12148/bpt6k65708448/f176.image.langEN, he seems to think that it’s interesting enough that his measurements align with the “theory of Sauveur” that he printed the table on the following page, and complained that he could only get a few octaves out of the thing. And a lot of secondary sources give him credit for the most precise measurements of frequency of vibrations in air. That’s whay I got. That’s what I went with.

      Re: tuning forks and frequency. Boy, do I have a cool video for you: https://www.youtube.com/watch?v=o7A4jyFG7hE Trust me.

      Makes you think that you could draw the slide out at a known speed, and you’d have a frequency measure…

    1. Take it up with the Smithsonian (link in the text). That’s where I got it from.

      My guess: the gimmick with tuning to a siren is that you change the speed and match the tones by ear. I wonder if poor old de la Tour was tuning to an overtone? (Or mis-perceiving octaves, whichever suits.)

      But thanks, because it doesn’t sound right to me either. It’s one of those things where you’re writing, it’s tangential, and you’ve got a credible source, and you don’t think twice about it. In the clear light of day, there’s no way anything that big and biological is moving that fast.

        1. Olavi Sotavalta was a biologist in the mid 20th Century who had perfect pitch and used that remarkable ability to measure wing beat frequency of a large number of flying insects — including several species of mosquito. In 1952 he published his seminal paper Flight-Tone and Wing-Stroke Frequency of Insects and the Dynamics of Insect Flight in Nature [Nature 170, 1057 – 1058 (20 December 1952)]. Yup, his estimates were pretty much in the 400 – 600 Hz range and have later been demonstrated to be quite accurate.

  3. The part on the tonewheels reminds me that, some year ago, my father and I repaired an electrostatic organ of the brand Dereux.
    12 rotating disks are engraved with the waveform of each tone of a real organ.
    Each disk constitutes variable capacitance, which serves to generate the sound signal, after amplification.
    Sadly, we did not take any photo, but the organ is now in use in the local music school.

  4. I moved to Hawaii a few days before the September 11 attacks. Since Oahu has a huge concentration of military bases and personnel, tensions were a bit high. One day in the first week of October I heard THAT SOUND- the one that strikes fear in the heart of anyone from the Cold War era. That siren was louder than anything I’d ever heard, slowly rising and falling and vibrating my bones. I grabbed my dog, my rifle and my emergency bag and ran upstairs to GTFO. As I came up the stairs from the basement apartment, my landlord took one look at me and started laughing. She explained that it was just the monthly tsunami warning test on the first Monday of each month. In hind sight it’s ridiculous and funny, but it was one of the most terrifying 60 seconds of my life.
    Eventually, I came to appreciate the sirens and even went to different parts of the island for a while to see how topology affected the sirens in those areas. They are awesome devices! Thanks for the post and the background info.

  5. Elliot, I compliment you not only on a fine article, but a fine hook paragraph. I brush by a lot of these pieces because I’m typically looking for something else on HaD, but this one definitely grabbed me because I’d never thought of (or seen) the siren as a physics demonstration before.

      1. “can’t stick your finger in”… says who?! :D
        There’s nothing preventing you from fondling a VCO to make squeal, if you use enough voltage, it’ll even have “force feedback” ;-)

  6. Probably worth mentioning is that the old air raid sirens (used in Britain during WW2) and probably most of the sirens used elsewhere are a little different to most of what is described here.

    The air raid sirens were double sided and each side had a different number of slots (frequency) and that cause an inter-modulation distortion or in other words created a much lower frequency component.

    As you probably know from having someone pull up beside your car at some lights and having the doof doof music going – the bass or low frequency component gets into your car and vibrates your bones.

    Air raid sirens were much louder than a car stereo and this low frequency component would rattle doors or your bones miles away.

    It think that has a lot to do with why some people are still traumatized by the sound. The sound alone – even without the threat of eminent bombing – vibrates your tummy and gives the same sensation you have when your confronted high stress or anxiety like the fight or flight sensation that many men experience at times.

    Anyway – power required to create sound pressure level (SPL) is inversely proportional to the frequency so we didn’t have doof doof car stereos until we had the very high powered amps needed to create such a SPL at a low frequency.

    For a air raid siren you have to get the core or mid frequency into the middle of the hearing sensitivity range so ….

    If I pick 3KHz as a ball park figure and make a siren with one gate on one side and two on the other then the average frequency is 1.5 * 60 * the RPM
    that gives –

    Example 1) For RPM=2000*60 => F1 (one gate) 2000Hz – F2 (two gates) 4000Hz – inter modulation (F2-F1) 2000Hz which is *NOT* a very LOW frequency.

    or 20 gates one side and 19 the other

    Example 2) For RPM=150*60 => F1 (19 gates) 2850Hz – F2 (20 gates) 3000Hz – inter modulation (F2 – F1) 150Hz which is the bone vibrating frequency.

    There is of course F1 + F2 which in the second example would be 5850Hz and that doesn’t travel well due to it’s frequency but would be very audible close to the source.

    So the distinctive sound of an *air raid* siren comes from something more complex than what most of these sirens are.

    1. “Our story begins in ancient Greece. Sirens, the Muses of the underworld, would sit around NAKED on rocky cliffs to lure sailors into shipwrecking into their island with the beauty of their song.”

      You forgot the one important part. Among other things, sailors are not particularly attracted to music. They are, however, likely (the probability is proportional to the time they’ve been at sea) to steer directly for a naked woman.

      This also explains why Sirens (the naked kind) are found only in the warm sunny Mediterranean, and not in Arctic or Antarctic waters.

  7. I’m not sure you can have an article about sirens without mentioning this:

    https://en.wikipedia.org/wiki/Chrysler_Air-raid_Siren

    The main purpose of the siren was to warn the public in the event of a nuclear attack by the Soviets during the Cold War. The operator’s job was to start the engine and bring it up to operating speed, then to pull and release the transmission handle to start the wailing signal generation. Of course, the flaw being that the operator needed to stick around in the event of an attack to start the engine :)

      1. I had said: “Good hearing protection”, as this thing was so damn loud. But why didn’t they use some cam-wheel or crank mechanism (directly or electric driven) to modulate the sound? This would not exactly have been high tech.

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