Sorry for being off topic, but, what about diy-instruments (from experimental fields like einstürzende neubauten etc.), or john cages manipulated piano, or a theremin, or a saw, whineglasses, or even an electric guitar? I‘d consider all of them instruments, as they‘re used as such…
I remember this played on my dad’s system, those big infinitys. The bass was both clearly audible and felt in the stomach 🤩
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I beat like you said I believe. Try it with Audacity. Generate 8 and 12 Hz and see the resulting wave.
OK, I see what you mean, but not why it is relevant.
Extreme example: when you play 3000 Hz and 3001 Hz, the beat frequency is 1 Hz, you see corresponding slow variations in the envelope, but spectrally, there is nothing below 3 kHz, so you don't need a subwoofer.
If beat frequencies do count, then the winner is music that's off key such that there are irrational frequency ratios: 0 Hz beat frequency.
Extreme example: when you play 3000 Hz and 3001 Hz, the beat frequency is 1 Hz, you see corresponding slow variations in the envelope, but spectrally, there is nothing below 3 kHz, so you don't need a subwoofer.
If beat frequencies do count, then the winner is music that's off key such that there are irrational frequency ratios: 0 Hz beat frequency.
You are absolutely 100% correct - but only if everything in the chain is perfectly linear. Beats are just linear superposition. No new frequencies are created.
Everything changes once there is nonlinearity to contend with. Linear superposition only works in a linear system. Once there is nonlinearity, new frequencies are generated.
If you put those two frequencies simultaneously into a nonlinear element, you do indeed generate new frequencies. Every one of the millions of superheterodyne radio receivers made and used on Earth for most of a century, used exactly this method to generate the intermediate frequency (IF).
The new frequency (IF) was generated by feeding the incoming RF frequency, and a second frequency from a local oscillator, through a nonlinear element, such as a vacuum diode, vacuum triode, pentode, semiconductor diode, BJT, JFET, MOSFET, etc.
Modern audio amplifiers are very linear, but loudspeakers aren't, especially when pushed to large cone excursions at low frequencies. I once measured about 18% (!!) third-harmonic distortion from a powerful subwoofer operating below the speaker fundamental resonance frequency.
(Nonlinearity in the transfer function of the spider and surround show up strongly at frequencies below Fs).
I think if you feed, say, a powerful 50 Hz signal and a powerful 65 Hz signal into a woofer, it will indeed create a 15 Hz audio wave.
(Whether that will have enough SPL to be audible in any way, is a different matter.)
The attached image is a little LTSpice simulation, showing what you get if you put 50 Hz and a 65 Hz sine signals into an (intentionally) poorly biased transistor amplifier stage. The FFT shows there is indeed output at 15 Hz, as well as a whole forest of new frequencies due to intermodulation.
-Gnobuddy
Attachments
Remember that with stereo records, vertical stylus excursions do produce output. Vertical excursions of the stylus correspond to the difference signal (between left and right stereo channels. (Horizontal excursions are the mono signal, the sum of L and R.)
Also, there used to be debate about whether huge stylus excursions caused by record warps, could push the phono cartridge into nonlinear operation, which would then modulate the audio signal, and generate subsonic electrical signals.
I've seen record warps so bad that the phono cartridge was practically flung into the air on every rotation of the record. You could literally see the stylus being pumped up and down. That much excursion had to have created lots of subsonic output.
Let's not forget about rumble from turntable bearings. That was quite audible on many affordable turntables, in spite of measures taken to limit deep bass response.
A high-pass filter (aka "rumble filter") to stop all this low-frequency dreck from turntables was pretty much mandatory. Remember switchable rumble filters on the front panel of Hi-Fi record player preamps?
Before the Compact Disc arrived, we never got deep clean bass out of our home audio systems.
The bad-mouthing of CD audio should go down as a disgrace to the human race, just like today's flat-earth insanity.
-Gnobuddy
Of course, hence my question in post #38 what causes the intermodulation between 12 Hz and 8 Hz in a very large pipe organ, if anything.
By the way, the superheterodyne principle is already a bit more than a century old; Lévy filed his patent application in 1917, although it only got popular in the 1930's. https://en.m.wikipedia.org/wiki/Lucien_Lévy Before that, mixers were already used to convert Morse code to audible frequencies (heterodyne but not superheterodyne, Fessenden, 1901, https://en.m.wikipedia.org/wiki/Heterodyne ).
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I don't know for sure that intermodulation exists to a significant degree in this situation. But there are several nonlinearities present, which could potentially create new frequencies through intermodulation:
1) Air itself is no longer linear once pressure fluctuations are sufficiently strong. For example, in the exhaust manifolds of a car engine, the mixing of pressure pulses (very loud sound waves) from the various cylinders is not a linear process.
2) The human ear is not linear at high SPL. A very large pipe organ might get loud enough to cause this effect.
3) If you're listening to a recording of a pipe organ, and not the organ itself, the loudspeaker reproducing the sound is quite nonlinear at frequencies below it's resonance.
At those frequencies, suspension restoring forces are larger than inertial forces due to the cone's mass and acceleration. And suspension restoring forces are quite nonlinear for large voice coil excursions, by design, because the surround and spider attempt to keep the voice coil from jumping out of the magnetic gap entirely.
I once measured about 18 dB of 3rd-harmonic distortion from an 8" subwoofer driven at a frequency below its resonance.
Nifty!
And let's not forget Lev Sergeyevich Termen (aka Leon Theremin) and his eponymous musical instrument, either. It too generated an audible tone by "beating" two RF oscillators tuned to nearly the same frequency.
-Gnobuddy
@Gnobuddy The discussion was about what frequencies are produced by a pipe organ with exceptionally large pipes (see post #34), not by a loudspeaker trying to reproduce its sound or by the ears of someone listening to it, so I think 2) and 3) are irrelevant.
That leaves 1), intermodulation by the air itself. I would expect that to be very small at levels very far below 185 dB SPL per tone (half the atmospheric pressure peak per tone), but there definitely is an asymmetry: the momentary pressure can't go negative.
Besides, there might be something in the hall that starts rattling at the beat frequency and its harmonics when you play the 8 Hz and 12 Hz tones simultaneously.
That leaves 1), intermodulation by the air itself. I would expect that to be very small at levels very far below 185 dB SPL per tone (half the atmospheric pressure peak per tone), but there definitely is an asymmetry: the momentary pressure can't go negative.
Besides, there might be something in the hall that starts rattling at the beat frequency and its harmonics when you play the 8 Hz and 12 Hz tones simultaneously.
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They do go low, but if you think about it, a didgeridoo is far, far shorter than 32-foot organ pipes, never mind some of the even longer monster organs discussed earlier in this thread. Most didgeridoos I've seen pictures off seem to be shorter than the person playing it, i.e., less than six feet or so.
That would mean the lowest frequency from a didgeridoo would be roughly five times higher than that from a 32-foot organ pipe.
-Gnobuddy
Organs, more than any other musical instrument, are capable of enormous SPL at very low frequencies. Ergo, they're more likely to generate intermodulation within the human ear than any other musical instrument.
Your brain can't separate new frequencies generated within your hearing mechanism, from the same frequencies generated externally in the air itself.
IMO it's arguable to claim that the nonlinearity of our ears is irrelevant.
You don't have to get anywhere near 185 dB SPL for air to be appreciably nonlinear.
Remember the adiabatic gas equation:
PxV^r = constant. (r = gamma, which is about 1.4 for air).
This means that for air:
pressure = 1 / (volume raised to the power 1.4).
The equation is intrinsically extremely nonlinear. Compare with triode valves and the famous Langmuir-Child "three-halves" law - air itself is about as nonlinear as a vacuum diode! And a diode is nonlinear enough to be used for rectification (and for deliberate generation of beat frequencies)!
We don't normally notice the extreme nonlinearity of the pressure-volume relationship in air, only because pressure fluctuations at typical SPLs are very, very small. Atmospheric pressure is in the vicinity of 10^5 Pa (101,325 pascals if you're picky), while 0 dB SPL is ten billion times less (2 x 10^-5 Pa).
But I don't think we have to get anywhere near the loudness level at which acoustic peak pressure (peak SPL) is near one-half an atmosphere to expose the nonlinearity, for the same reason you can easily get several percent THD from a single vacuum triode without pushing it to its limits.
We could probably estimate the SPL at which air itself would generate, say, 1% THD, which is about the threshold of audibility.
120 dB SPL gets you 20 pascals of sound pressure, as one example. While 120 dB is "stupid loud", it's frequently exceeded in live music settings.
AFAIK, this nonlinearity can be appreciable in sealed loudspeaker enclosures (the "air spring" isn't actually very linear).
The nonlinear nature of loud sound waves also shows up very strongly inside the exhaust manifolds of any everyday internal combustion engine.
Good point!
-Gnobuddy
The organ concerts I frequently go to don't seem to be excessively loud, but then again, I usually sit at a considerable distance from the organ - unlike the organ player, who actually sits between the small and the large pipes.
It's up to the thread starter to decide on that. If beat frequencies that are not produced by the instruments count, then anything with more than one instrument and an irrational frequency ratio can produce 0 Hz.
No, I don't, but I expected it to be something smoothly non-linear rather than hard clipping. Hence the 'very far below 185 dB SPL per tone' rather than just a bit below 185 dB SPL per tone.
I have an LP of Bach organ music which contains a "Test Track filler" for one track. The Test track is a 16Hz ... then a 12Hz ... then an 8Hz note (NB: an 8Hz note is produced by a 64' long organ pipe! 😎 ).
With my subs, I can hear something when the 16Hz note is played! 🙂 But with the 12Hz tone and the 8Hz tone ... I see the poor cantilever wiggling furiously from side to side ... but hear nothing from the spkrs. 🙁 I'm thinking this is because of the below-20Hz roll-off of my phono stage.
Andy