 The Clarinet BBoard
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Author: pewritylab
Date: 2024-02-06 01:06
Ok, this is going to be long. Turns out I discovered clarinet subharmonics. By playing a note while singing a fifth above that note, the resulting note is an octave deeper. I posted my findings on a clarinet subreddit and the immediate reaction were Tartini tones or combination notes. Basically, your brain creates a difference frequency, which is in the case of a fifth an octave lower (3/2 f – f = f/2) But I wanted to see if the theory holds up to scrutiny and measures the spectrum. If the subharmonic is just in my head, then it shouldn’t be visible on the spectrum… but it was
As a next step, I tried a physics subreddit. As an EE, I am familiar with modulation and realised that playing bith tones at the same time didn’t create just difference frequencies but also sum frequencies according to this trig identity:
cos(f1x)cos(f2x) = 0.5(cos(f1-f2)+cos(f1+f2))
TThe physicists explained this with nonlinearities in the reed mechanics, which also create the harmonics. I am not satisfied with that answer, because if you play quietly, the reed is approximately linear (sinusoidal tone) and yet, the modulation still works.
So I’m trying my luck here, I know that there are some engineers here who know some math. My current theory is this:
Sound is essentially a pressure wave, so the propagation of pressure oscillations. And the propagation happens because air molecules move from areas with low pressure to areas with high pressure. So sound can be thought of as oscillating air velocity instead of oscillating pressure. When you play a note, you basically turn steady airflow into oscillating airflow. Now what if the air velocity increases? Well the loudness increases as well and vice versa. And what if you sing at the same time? In that case, the air velocity is not constant but oscillates sinusoidally (for the sake of simplicity) so the loudness oscillates sinusoidally as well, so you have a product of 2 sine waves => there you go, according to the trig identity mentioned above, this will create a subharmonic cos(f1-f2).
Here are the most important observations about this effect:
1. It is not unique to clarinets - works on any wind instrument (commonly known as Growling on saxophones) and even in flutes but there the sibharmonic happens in the vocal chords
2. It is NOT the Tartini tone / missing fundamental / difference tone. I know it might be tempting to classify it as such, but keep in mind that the Tartini tone is just in your head (caused by some nonlinearity in the hearing apparatus). The subharmonic mentioned here is clearly measurable on a spectrogram.
3. Whistling into the flute does not work. Sure, it produces a beat frequency (linear superposition) and a Tartini tone (illusion in your head), but the subharmonic is not visible on the spectrogram. This suggests to me that the nonlinearity that causes the modulation is somehow in the vocal chords. The problem might be somehow linked to coupled oscillators, but beyond me right now.
4. Instead of singing, it’s possible to play a note into the clarinet from the other side (into the bore) using a tone generator and a speaker. This means that any resonance mumbo jumbo between the mouth cavity and clarinet cavity is out of the game!
What do you think? Is there another explanation for this? Thanks a lot im advance!
Post Edited (2024-02-06 10:18)
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Author: Hunter_100
Date: 2024-02-06 02:22
When players do this accidentally its called a grunt or undertone. It is when the fundamental note is present in the tone even though the register key is open. Sounds like you have come up with your own way of doing this on purpose. I'm not sure this is an accoustic thing though, you can't combine two frequencies to get a lower frequency, the math doesn't work out.
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Author: pewritylab
Date: 2024-02-06 10:17
The math works out perfectly. It's called modulation (multiplication of 2 signals) and the subharmonic is clearly visible on the spectrogram. You can't combine two frequencies if the system is linear. So for example, in air, two frequencies never multiply, just add. A clarinet is controlled by airflow, so changing the airflow leads to multiplication of the two signals.
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Author: Julian ibiza
Date: 2024-02-06 15:14
I'm not refuting your claim pewritylab, and frankly my maths is not great, but I'm having a little trouble with the physics side of it. Wind instruments work based on the principle of " standing waves in an air column ", and the linear movement of the air through them has nothing to do with sound produced ...That is a produced by the oscillation of air molecules between static bands of high and low pressure within the tube ( for a given note that is ).You seem to be saying that the additional element of air flow through the tube is somehow fundamental in the blending of two higher frequencies to creat a lower one.
It all sound very alchemystic, but I'm all ears for a physics based explanation I can get me head round.
Julian Griffiths
Tel. 34 696 798 853
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Author: Philip Caron
Date: 2024-02-06 16:05
Do you have a recording of what you are doing? I think when singers produce subharmonics a similar process is happening. My sporadic clarinet attempts have tended to sound like, well, it's hard to imagine a musical context for the sound.
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Author: pewritylab
Date: 2024-02-06 16:22
Yes, I do! It's in the reddit post I mentioned: https://www.reddit.com/r/Clarinet/comments/184k1g5/how_is_this_technique_called_by_playing_a_note/
Later, I also tried the 4th and 6th, both of which produce two subharmonics below the clarinet frequency (f/3 and 2f/3), the clarinet sounds like a bassoon at that point. Here is the spectrogram which confirms that it's not an illusion: https://imgur.com/a/TKO1CBP
Post Edited (2024-02-06 16:34)
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Author: Luuk ★2017
Date: 2024-02-06 17:03
Attachment: Addition of sine waves.jpg (58k)
Well, the sum of two sinuses, one with a frequency 1,5 times the other, has a periodicity of two times the lowest one. Might it be that simple?
Regards,
Luuk
Philips Symphonic Band
The Netherlands
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Author: pewritylab
Date: 2024-02-06 17:58
No, it's not that simple, that would be the Tartini tone (see my 2nd observation) and it would mean that the subharmonic is in your head, but it's not. The frequency is actually created
Post Edited (2024-02-06 17:59)
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Author: Luuk ★2017
Date: 2024-02-07 17:24
The airwave resulting from the input of two waveforms is not 'in your head', but is the resulting waveform present in the medium (air, in this case). These are called heterodyne waves.
The clue is that the waveform resulting from two or more input sounds may have a lower periodicity than the lowest input wave. And that is the case here.
See https://www.phys.unsw.edu.au/jw/tartini-temperament.html for more info, scroll down to Heterodyne frequencies vs Tartini tones
Regards,
Luuk
Philips Symphonic Band
The Netherlands
Post Edited (2024-02-07 17:26)
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Author: pewritylab
Date: 2024-02-08 00:24
Again, I'm not denying that Tartini notes exist. Sure, it's the reason why you can hear the low frequency even when listening on a smartphone, which can't actually reproduce it.
But it's not the explanation why the subharmonic appears in the spectrogram. When you add two sinusoids, the Fourier Transform will give you 2 peaks at the respective frequencies. But I observe a third peak at the difference frequency.
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