Frequency components that remain fixed when singing a scale

[Swamp Thing]

This clip shows a voice coach demonstrating a 5-note scale and capturing it on a spectrogram. He notes that there is a cluster of frequencies at the high end that remain pretty much fixed, even while the actual sung note traverses the scale, tracked by the first several harmonics.

https://www.youtube.com/clip/UgkxN_M9TPkZv1uJwb3cR6x_PZHeJjUver3l

What might be the physics behind this? In other words, what would be a toy model of a nonlinear oscillator that would demonstrate this effect?

 

[DrClaude]

What might be the physics behind this? In other words, what would be a toy model of a nonlinear oscillator that would demonstrate this effect?

I there really only a single oscillator? Could there be some other source of vibration not linked to the note being sang?

 

[Swamp Thing]

There could well be a separate mechanism at work, but it's probably also in his vocal tract because it carries the same vibrato modulation.

 

[Baluncore]

The harmonics continue up the screen and through that area without change. The harmonics then suddenly disappear. It looks to me like there is a low-pass filter with a sharp cutoff being used there.
Maybe the higher amplitude peaking, near the cutoff, is needed to get the sharp cutoff from a simple Chebyshev filter.

 

[Swamp Thing]

Maybe the higher amplitude peaking, near the cutoff, is needed to get the sharp cutoff from a simple Chebyshev filter.

That would explain the horizontal lines around 9000 - 10000 Hz. But my question is about the part around 3000 Hz. It looked like components around 3000 Hz had frequencies that didn't vary during the recording, while the lower components did follow the scale.

But I have just zoomed into a screenshot and found that that was a sort of optical illusion while watching normally. If I zoom in and carefully trace one single component with my mouse cursor or a pencil, I can see that each line is actually rising and falling in tune with the fundamental.

 

[sophiecentaur]

What might be the physics behind this?

Before coming to a conclusion, take a look at the vertical ('frequency') scale. I was pleased to hear the speaker using the term "overtones" (when he remembered and corrected himself) Without some specific numerical work, we cannot assume that they're harmonics - they're just higher frequencies / modes of oscillation of a three dimensional arrangement of tissue and muscles;

The implied anomalous components are many octaves above the fundamental. That part of the spectrum of produced sound seems to consist of an independent oscillation which is modulated by the main voice sound. This could be due to coupling 'via the power supply' (the energy coming from the breath.) It might be analagous to the Drones on a Bagpipes. High frequency sounds can be produced when whispering wthout any obvious output from the vocal chords.

 

[tech99]

It looks as if the frequency scale is logarithmic so the variations of higher frequencies are compressed.

 

[sophiecentaur]

It looks as if the frequency scale is logarithmic so the variations of higher frequencies are compressed.

Of course; the piano keyboard is logarithmic (Base 2)

 

[SammyS]

It looks as if the frequency scale is logarithmic so the variations of higher frequencies are compressed.

This is an excellent point.

 

[Swamp Thing]

Isn't it precisely because of the log scale that we expect the same vertical variation in terms of semitones, on all harmonics? If the scale had been linear, the jumps from note to note would be even bigger for higher harmonics?

 

[sophiecentaur]

so the variations of higher frequencies are compressed.

The whole thing about our perception of music (any sound actually) is logarithmic. A semitone interval is the twelfth root of two for an equal tempered scale.
However, it's important to be aware that notes on an equal tempered scale do not fall in the same frequency ratios that correspond to a natural scale. This is not a subjective problem because the 'frequency errors' are all part of the musical experience from many regular instruments (and our voices): it's all overtones and not harmonics except from electronic instruments.

 

[tech99]

It looks as if all the harmonics are displayed. So we see something like 200, 400, 600, 800 etc and then 2000, 2200, 2400. As the scale is logarithmic, these higher ones look closer together.

 

[sophiecentaur]

It looks as if all the harmonics are displayed. So we see something like 200, 400, 600, 800 etc and then 2000, 2200, 2400. As the scale is logarithmic, these higher ones look closer together.

There is no chance that the spectrum consists of harmonics. The oscillating system is multidimensional and the modes are not at all likely to be harmonics; they will be overtones. Also those high frequencies are not straightforward mixing products.

 

[tech99]

I tend to think that the vocal chord would be unlikely to be oscillating in overtone and fundamental mode at the same time. It also seems unlikely to me that the vocal chord could oscillating on ten or more overtones simultaneously. When the sound reaches the resonant cavities involved, they can emphasise certain harmonics but cannot create new frequencies. For this reason I feel that we are seeing harmonics.

 

[sophiecentaur]

I feel that we are seeing harmonics.

That would imply that you start here with a simple harmonic oscillator - which the vocal chords are definitely not. There is no reason that the various modes of those raggedy muscles and skin would have a simple set of harmonics. The guy in that video deserves credit for using the term 'overtones' Don't spoil it for him when he tries to get us talking in the right terms. All the overtones can easily independently have their own natural frequency as they have several modes and a power supply in your breath.

Sympathetic oscillations of a set of piano strings (loud pedal down) are a great example of non-harmonics which ring out for seconds . They are all overtones (and undertones) and I'd hope you wouldn't want them to be harmonics.

 

[Swamp Thing]

Sympathetic oscillations of a set of piano strings (loud pedal down) are a great example of non-harmonics which ring out for seconds . They are all overtones (and undertones) and I'd hope you wouldn't want them to be harmonics.

If I remember correctly, these kind of effects are called inharmonic partials, and if done right they add some kind of aesthetic value (richness, brightness whatever) to the sound.

My impression, though, is that those are associated with high-Q multimode resonators like bells, gongs, wineglasses and groups of strings (think of a sitar).

On the other hand, the vocal tract is pretty low Q (it doesn't ring out for seconds ), so even though it has various 3-D resonant modes as you point out, the overall result may be modeled as a pulse generator (vocal cords) feeding a simple filter (upper vocal tract) with 2 or three peaks in its response.

The pulse train, a la Fourier, contains harmonics. And all that the filter can do is boost or suppress different harmonics (not overtones) of the pulse train presented to its input. In a sense, the different peaks of the filter are like overtones, but they don't ring like a gong and so probably won't produce those inharmonic partials.

 

[sophiecentaur]

The pulse train," a la Fourier", contains harmonics.The Fourier transform of a signal is formally over an infinite range of frequencies and over infinite time. You have to be careful analysing a short length of a waveform (e.g.what the Fast Fourier Transform shows. I did try to find some videos of what I'm saying but (of course) the exact thing is hard to find. This link shows a few ms of a human voice but the scope is not synched so the time dependent details are not obvious. I don't have facilities to demonstrate what I mean but the waveforms you can see clearly show a fundamental - but the scope is not locked to it - were it locked, you would see clearly that the wiggles on the trace move along and don;t stick with the fundamental trace. This means that their frequencies are not harmonics. A still photo will not show that so it's easy to assume they are. This link shows a guitar note and the high order variations march over the main trace; they cannot be harmonics.

If I remember correctly, these kind of effects are called inharmonic partials, and if done right they add some kind of aesthetic value (richness, brightness whatever) to the sound.

Exactly. An instrument with none of these sounds completely dull and you can't even identify the instrument from its sound.

On the other hand, the vocal tract is pretty low Q

Very true, so it is not very frequency selective; anything can get through. Imo that's yet another example of evolution getting 'the engineering' just good enough for its purposes. Do you have any reason to assume that only one sustained oscillation is present in the human voice?

 

[Swamp Thing]

Do you have any reason to assume that only one sustained oscillation is present in the human voice?

The video at the top right of the following page shows the kind of thing that some singers have consented to go through "for science"... https://cvtresearch.com/description-and-sound-of-ornamentation/

Thanks to these intrepid volunteers, researchers have been able to measure the airflow and pressure waveforms just above the vocal folds, and found that it is pretty much a "sloppy" pulse train like this:

It is a periodic waveform with a clearly identifiable single fundamental frequency.

https://www.researchgate.net/publication/341523760_The_Mechanics_and_Acoustics_of_the_Singing_Voice

Also see Fig. 8.2 in https://www.researchgate.net/publication/341523760_The_Mechanics_and_Acoustics_of_the_Singing_Voice

It is true that more complex oscillation modes are possible, but those are associated with damaged or disease-affected vocal folds, based on what I've read from this kind of paper (don't remember exactly where).

 

[sophiecentaur]

a "sloppy" pulse train like this:

It's hard ot be sure that the extra frequency components are actually harmonics in one picture with only two peaks. I need some explanation of the three traces. The time and frequency domain parts of the spectrogram are very fuzzy so it's anyone's guess whether the high orders are true harmonics. I can't understand why it's just got to be harmonics when there are so few musical instruments with simple harmonic spectra. If you look at the time domain graph, you would expect any harmonics to track up and down to follow the fundamental. After the third order they stop doing that so how??

I staggered through that paper and it was full of good stuff. I was interested to read the term 'resonances' rather than harmonics.That implies they are aware of how musical instruments produce their sounds. Would you recognise the sound of a Hammond Organ? That early synthesiser mixed harmonically related frequencies , controlled by the 'drawbar'.