Physics Exam !?

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Listen up fellow geniusses :nerd_face:

Back in 2004 i was working at the Donaueschingen festival setting up Benedict Mason’s
felt | ebb | thus | brink | here | array | telling

A small part of this astounding piece included 4 pair of speakers in each corner of the “room”
fed by portable cd players. Each of the 8 speakers playing a very certain sine wave creating kind of an (literally staggering) accoustic beats “moire” pattern. I’m trying to rebuild this and play around with my small active speakers but i’m missing the frequencies from CD Nr.4

The CDs were named:
green (441,4Hz / 294,3Hz)
purple (490,5Hz / 327Hz)
yellow (407Hz / 305,2Hz)
? ( ? Hz / ? Hz)

most likely CD Nr.4 is blue (vs yellow), because green and purple are complementary. I’m also pretty sure the colors were arranged to face each other like in the color wheel.

Ideas?

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If only we had a physicist in our midst.
It sounds to me (a non-physicist) like a binaural beating phenomenon. A sine wave should be easy enough to produce with freeware of your choice so you might try obvious mathematical approaches. IIRC the third beat to a psycho-acoustical binaural frequency pair is the difference between the two so 337.9 or 272.5 Hz would be possibilities, or better yet set up the 4th speaker directly fed by the active sine source and sweep the frequency. You might find something even cooler than the original “blue” candidate.

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I don’t think you’re looking for a physicist, because physics isn’t going to explain some artist’s choices.

Best I can offer, and it’s pretty bad, is to take a look at the ratios of the known frequencies:

441.4 294.3 490.5 327.0 407.0 305.2
441.4 1.0000 0.6667 1.1112 0.7408 0.9221 0.6914
294.3 1.0000 1.6667 1.1111 1.3829 1.0370
490.5 1.0000 0.6667 0.8298 0.6222
327 1.0000 1.2446 0.9333
407 1.0000 0.7499
305.2 1.0000

Some of these are obviously simple ratios. Some are… not so simple.

441.4 294.3 490.5 327 407 305.2
441.4 1 2/3 10/9 20/27 12/13 9/13
294.3 1 5/3 10/9 18/13 28/27
490.5 1 2/3 39/47 28/45
327 1 56/45 14/15
407 1 3/4
305.2 1

If you can discern a pattern here maybe you can extend it to the two unknown frequencies. But I can’t see a real pattern.

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I think the easiest is to use my laptop, a pd patch and my audio interface. But i must first clear a big enough space to set the speakers up, Today i finished all the cables. And the speakers need a 24V supply with enough juice.

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From the looks of it, im researching musical temperaments. These frequencies look too similar to note values. To add to this theory, there just happens to be 8 values which would align with many standard scales.

Also looking at the values, and it looks like the interval changes are plotted across a sine wave shape. perhaps we can research what these frequencies look like as a fourier series?

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Well, yes, ratios of small integers correspond to consonant musical intervals. 4/3 (2/3 times 2) is a perfect fourth, 5/3 is a major sixth, 10/9 a whole tone, and so on. 39/47, though, or even 9/13, those aren’t common intervals. I suspect that’s the point, that you have some tones making consonances and others making dissonances with prominent beat frequencies.

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Right, im not seeing any temperament that really fits all of these frequencies.
Here are some:

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Thing is, this can literally be a unique experiment. Nobody says it has to be any specific system.

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I’ve got a few more here

 $ ls -l QuantizerModule/software/scl | wc
 5033   45406  324432

Hmm.
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Hmm hmm

The simultaneous use of two equally-tuned pipes, of which one is blown with atmospheric air and the second with another gas, results in two only slightly different tones, called a beat. The function of the methane whistle is based on the fact that the sound when blowing a whistle depends on the speed of sound in the gas. The sound velocities of methane and air differ by about 31%. For a 1% methane-air mixture, the speed of sound is about 1.0031 times as high as in air. If the pipes are tuned to 440 Hz in air, the air-methane pipe has a frequency of 440 Hz × 1.0031 = 441.4 Hz. If two identically tuned pipes are blown by air and an air-methane mixture, the only slightly different tones produce a clearly audible beat.

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Thats fascinating. I was also thinking there was something about the usual sampling frequencies used for audio (44100 Hz).

https://books.google.com/books?id=HCI_CgAAQBAJ&pg=PA120&lpg=PA120&dq=441.4+hz+freq&source=bl&ots=Vo0lLhmadP&sig=ACfU3U3d8hBfWHfUbTX9famew7xmbk5ZoA&hl=en&sa=X&ved=2ahUKEwj7jIPvtMHqAhWDY98KHZdnDngQ6AEwCXoECAoQAQ#v=onepage&q=441.4%20hz%20freq&f=false

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Right now, i have all of these tones generated and synced to the start of the waveforms in my daw. Flstudio has a formula controller thats pretty useful here. Im using it to control the volumes of each waveform. Im thinking this in practice was intended to not be heard all at once, since the head would hear a few louder that it is facing. This would definitely change the effect since the more dissonant freqs can be placed behind the listener.

edit: color coded based on cd color. can confirm those freq pairs are nice sounding harmonies.

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@TrapaNatans I’m wondering if we’re limiting our thinking by only looking at the frequencies. Are there any instructions about where each speaker is to sit, or is it assumed that they are equidistant front the listener at some cross or x arrangement?

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I think we can assume placement by understanding what a human can hear at once, and what sounds good together.

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I tuned the frequencies of each lfo to match the ratios in relation to 441.4 (A ish). I normalized the values between 0…1.

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For those curious what this all sounds like, i have made available what i have done with this:

Just play multiple at the same time.

Individual frequencies:

Combined with LFOs:

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Thank you guys for looking into this. I’m glad to have sparked some interrest.

As already mentioned the sine waves were just a little part of the musical piece.

The audience was seated in circles, around the “sweet spot” like it was a campfire. 48 musicians where playing different instruments in different positions in each of the 12 parts of the performance. They had in ear monitoring each with their own clicktrack. It was a nightmare to set up but the result was fantastic.

Some instruments were custom built, i remember seeing a lot of labels with notes +cent / -cent numbers on them. i’m pretty sure the whole piece is influenced a lot by balinese/javanese gamelan music.

I can’t remember what instruments were played together with the sine waves. But i remember asking the guy where to place the speakers (fostex on mic stands) in the corners of the hall. He said that the positions don’t matter much just the pairs opposing each other so i put one pair in a corner which then defined the location of the other 3 colors.

At first it didn’t work because the guys in the studio mixed the 2 freqeuencies to both left and right. I had to make new CDs on site with my very first laptop separating the frequencies.

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Rehearsals for the second show in Berlin (März Musik Festival 2005)

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If you play some of these simultaneously you get really interesting patterns.
Start playing the first and start the second a few seconds later, then the third a few seconds later and so on …

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I’m not a physicist, but I am a neuroscientist! and I think, given the need to stand in a ‘sweet spot’ between the sound sources @Maxhirez is on the mark with:

If anyone’s unfamiliar, binaural beats are a psychoacoustic phenomenon where if two pure sines are presented to each ear, you perceive a beating pulse at the Hz of the difference between the two tones. Now, the general consensus is that this can only be done with differences of up to around 40hz (though I might be biased in this, as the only time I’ve come across this is to try and synchronized brain oscillations, and we tend to stop looking at anything above 40Hz - this is a contentious point).

Now for some wild speculation:
If you bear this in mind, you’re not looking for a ratio between the frequencies, so much as ratios between the differences of the frequencies? And we know that two sounds from the same source don’t really produce a beat, because they should ideally hit each ear independently, so we’re not interested in the difference between sines on the same CD. Nevertheless, if we imagine you can get an effect from two speakers on the same side but at different angles (front and back), we get some perceived frequencies like:

high tones (400hz+):

	1	2     3
 1	0   34.4  49.1
 2	    0	  83.5  
 3		       0

low tones (290Hz+)
    1	2	 3	
1	0	10.9 32.7	
2		0	 21.8	
3	         0

which musically (with a bit of tuning wiggle room) gives us a C, G and a questionable E (as this 80hz diff is way out of the bounds of what we (or at least, I) think binaural beats can do) in the higher beats, and two Fs and a C in the lower tones. All in, this could give you a very jazzy Fmaj9sus2 chord? however, all in very much sub-bass frequencies. However, given these are perceived tones, as opposed to tones actually stimulated by air pressure on the ear, I have no idea how this would sound/feel/be perceived. As for a wild guess at what CD 4 could be, I imagine you’re looking for a tone between 441.4-490.5, and one within 40hz of the lower set of tones that would give you some more Fs and Cs?

Anyway, this is mostly insomnia speaking but thought I’d give my 2 cents. Binaural beats are quite fun - they seem like hippy madness because people say they can do all sort of mad things, but they actually do ‘work’ a bit in terms of how the modulate brain activity. They’re like sync on an oscillator, but for ya brain.

EDIT - i notice as i posted the 34.4Hz beat is actually a C#, not C, which ruins the nice chord. Ah well, the ideas are still there

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I have a couple of guided meditation recordings that claim to Take advantage of the phenomenon. I have had very pleasant experiences with some of them. Does the idea that brainwaves entrain to the difference between the frequencies so that you could, for example, drop intentionally from alpha/beta to delta/theta for an extended period hold any water, or am I just having the relaxation I expect because I’m open to it?

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Not correct. I don’t know anything about “binaural beating” but you get beats with one ear or two when you have two tones that are (or have strong overtones that are) close together in frequency. That’s the basis of tuning by ear. See Beats. From Physclips for instance.

You’re correct, though, that the beat frequency is the difference of the two frequencies that produce it. However, the frequencies you’re talking about from 10 to 25 or so Hz are pretty much too low to be perceivable as tones as opposed to variations (beats) in the amplitude of the tone corresponding to the average of the two frequencies. I don’t think you’d hear them as a chord. (The lowest note on a piano is 27.5 Hz, and to my ear it’s hard to hear it as a well defined pitch — it’s something like a tone but not readily perceived as the A it’s supposed to be.)

But difference frequencies larger than the 80 Hz limit you talk about can be audible, as a tone rather than beats. It’s called a Tartini tone. Again, this is not a binaural phenomenon. I don’t know how perceptible such tones would be in this situation, but maybe they’re significant.

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