I have a question about frequency analysis in music. If I load a virtual instrument such as a piano VST and play just one note, say an A 440, my understanding of the harmonic series is that upper harmonics would show up on a frequency analyzer. However, there is one concept I am not understanding. A frequency analyzer shows additional frequencies BELOW the fundamental frequency. Can somebody explain to me what these frequencies are and how / if they relate to harmonics. Thank you so much in advance!

 

Yes, they are coming from the characteristics of an instrument. In this case the "hitting a key-sound".
Cut it out and hear which sound is disappearing.

 

a oscillator cannot go from rest to your frequency (for A440) without any amplitude. you are seeing the oscillator speed up and create lower frequency sound.

 

The tiger is correct, and this is made somewhat worse by the interaction of that phenomena and the piano's own resonator (the big heavy cast metal harp frame inside the piano) which moves enough air but because of it's mass vibrates at an interval relative to it's mass/shape/composition and the total energy of the initial transient and decay. Recordings generally exaggerate this as well as add their own sub-harmonic.

You can see the amplitude of the resonator's vibrations even in oscilloscopes using transducers to tune a piano rather than microphones and it's generally lower in amplitude and more complex than the FFT provided.

 

Either acoustic noises or compression/saturation artifacts.

 

Speaking from the perspective of a student learning digital signal processing, it's actually three things happening at once.

First of all, a piano is an acoustic instrument. There's more happening than just the sound of the string vibrating. This includes both the instrument itself, and the microphone's noise floor, as well as any other equipment that has been used in the recording signal chain.

Second, your analyzer is "lying". The way it works is by using FFT (Fast Fourier Transform), and the "quality" setting (the numbers that you can change in spectrum analyzers) lets you pick a compromise. If you want to see more resolution, as in a less smooth and more detailed graph, you wait until you get more samples. This gets you more frequency bins (yes that's the technical term), at the expense of the meter being slower to respond (basically, kinda like latency). If you use less bins, you get a faster response (as seen in the Waves analyzer you posted) but they connect the dots where there's no information, to give you a smooth graph. There's nothing inbetween the peaks you see on your graph, the lines are there just so you can see easier.

Third, your analyzer is also lying in another way. Because it is not synchronized to a point right at zero, it just works every X number of samples. Say every 1024 samples. It just grabs the next 1024 samples, it might start above or below zero, as well as end above or below zero. This way you end up with a sudden jump from one point to the other in the waveform, and sudden jump equals high frequency glitches.

Not only that, but also you end up analyzing the same fragment of time multiple times - you always need some overlap between the pieces of audio that you analyze. So you could end up with more at a certain frequency than there really is.

To avoid that, they're using what's called a window function. That's the Hanning, Hamming, Blackman, etc options that you see in your analyzer settings. It's a glorified fade in and fade out, different options have different strengths and weaknesses. It is basically doing this:



And on each screen update you see the result of just one window being analyzed. By using a windowing function, you remove this overlap from your analysis, but as a byproduct there's "bleed" from the frequency bin where you have data, to other bins close to it. So even a sine wave won't be just a single peak, but a bell shape, just like in a EQ. Try it, generate a pure sine wave and you'll see it has "frequencies lower than a fundamental".

This is not a bug, it's basically limits of maths and physics that make spectrum analyzers not a 100% representation of what's actually happening. It is possible to do it "perfectly", or at least more precise, but then it's not possible to do so in real-time - you'd have to load a WAV file in a program, wait a minute, and then you'd see your analyzer.

Hope this shines some light to the issue.

 

@Qrchack Quick question, have you seen the FabFilter Pro-Q 3 analyzer?
You don't need to answer that.
Tho indeed now when I think of it, OP's spectre does look like a large FFT window.

 

Yes, I have. And you're completely wrong. Look no further than FabFilter Pro-Q 3 Manual:

Also, from Waves PAZ manual:

While I'm not familiar with wavelet techniques, I am familiar with what FFT offers and how it compares to their claims here:

Here's a quote from documentation of some IRCAM software, widely known experts in the field:

That means at a window size of 1024 we're already better than the default setting of PAZ (which I presume was posted above). At 2048 we'd be at 10Hz, which is the best setting PAZ offers, and anything beyond that is better than that.

It would also have 1024 frequency bins, or bands, vs PAZ's "up to 68 bands". PAZ is not a precise spectrum analyzer, it was clearly meant to help you tune a graphical EQ, and not be a precise measurement tool.

 

Last edited: Mar 15, 2022

Because it is using a windowing function (fade in/out) as mentioned. The side effect of that is the fact that you see stuff at 300, 600Hz, not just at 440Hz. That's literally what I've been talking about.

The point is there is nothing at 300 and 600Hz there. It's the analyzer being not a perfect measurement tool, because it has compromises that make it possible to analyze in real time.

 

That moment when you explain things how they are and you get a "disagree" from some ignorant peasant because he can't understand what you said because he got just F-s his entire highschool. But hey, democracy

 

thanks for taking the time to teach us

 

He JUST WANNA DOWNLOAD. No time for all that science bs

 

there is also something like subharmonics, undertones

 

Double-checked and I did indeed say "large FFT window" (－‸ლ) That's what frustration does to you, huh. You start saying the words your brain short circuited on instead of what you want to.
@Qrchack I know all that. I'm not a DSP engineer, but I got Master's in applied maths. My degrees are irrelevant beyond that point tho.
First off, Pro-Q does all the stuff you said is "impossible in real time". Apparently window pops aren't an issue for them ¯\_(ツ)_/¯
Furthermore, the slopes on left and right of a test tone in SPAN aren't window pops either. Assuming such phenomena is even present, they should be dependent on window size (also depending on samplerate, the sound spectrum, phase, yadda yadda), and go lower in spectrum the higher the resolution is. This isn't happening tho. if you wanna know why, look closely at the graph you've attached to your first post.
What OP sees is definitely a low resolution FFT analysis, but also something in the lows, because it wouldn't've been a peak below the fundamental.
And that's one, or both, of the following:
1) Acoustic noise, as you yourself pointed out.
2) Artifacts born from nonlinear processing. Namely intermodulation from asymmetric distortion.
I wish you a success in your studies, despite your attitude. Maybe you won't pick a stupid fight next time once you know more.

Oh, and I won't comment on those two idiots judgement-happy interlocutors.

 

Last edited: Mar 15, 2022

Technically I agree pretty much with all you've said.
But I wonder if the artifacts caused by windowing can be so high. Seem to high for me.
Though if it's a snapshot at the moment, say for instance, that hit-key noise included in the sample sounds the highest...

 

BTW, welcome to the forum @RonnieSpectrum .
As you can see, we're nice guys. Mostly

 

@RonnieSpectrum jumped straight into the deep end I see

But yeah I always chalked those frequencies to acoustic noise, the rest of this was an interesting read!