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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The Clarinet BBoard
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