Why is saxophone growling produced by modulation of the sound waves?

[Daniel Petka]

It is the fundamental.

https://en.wikipedia.org/wiki/Harmonic#Terminology
"But more precisely, the term "harmonic" includes all pitches in a harmonic series (including the fundamental frequency) while the term "overtone" only includes pitches above the fundamental."

Ok fair enough, turns out that most musicians use harmonics and overtones interchangeably. Yeah it's definetly cleaner to separate them like this

 

[sophiecentaur]

Ok fair enough, turns out that most musicians use harmonics and overtones interchangeably.

The two numbers differ by a vital one so never trust a musician. (That can't apply to real musicians, of course.. In the same way, sloppy non-engineer talk is used by non-engineers)

 

[NTL2009]

You need to be more careful referring to harmonics as first, second or third.

If the fundamental is f, then the second harmonic is 2f and is an even harmonic, while the third harmonic is 3f and is an odd harmonic. That means the first harmonic is the fundamental f. ...

Yes, it is confusing between physics/engineering and musicians. Musicians sometimes refer to harmonics as "overtones", where the "first overtone" is the "second harmonic". Harmonic numbers are multiples of the fundamental (the first harmonic), but overtones are counted as starting at the first tone above the fundamental. Geez, now I just found some references (wiki!) that refer to the same numbering for each - that's new to me.

Here's a short video (search the name for more), of singer producing a very low note, apparently by creating a difference frequency from different areas of his vocal chords vibrating at different frequencies. And yes, they refer to them as 'sub-harmonics', but they are musicians. It looks like there is some follow up with scientists, I'll try checking those later to see if there are technical explanations.

 

[NTL2009]

This logic is flawed because then the first harmonic would be the fundamental. We agree that only 2f, 3f, 4f... are the harmonics (multiples of a fundamental), so 2f is the first harmonic, not 3f. But I agree that 2f=second harmonic is easier to hold in your head. The word harmonic in this case is like a synonym to frequency. I mean, some folks count them like this, other folks count them like that, I don't think it's reasonable to argue about how something should be called.

No - as pointed out, the first harmonic IS the fundamental. And 2f is the SECOND harmonic, but musicians call it the FIRST overtone. The physics way is clean - everything is a multiple.

The music way is very, very messy for these conversations - if I play a square wave on my synthesizer, and you should know that a square wave has only odd harmonics, guess what the 'proper' musical way to count these is? Well 3f, being the very first frequency above the fundamental in a square wave is called the FIRST overtone. Because that's what it is! That's the definition of overtones. And the FIFTH harmonic is the SECOND overtone! See how confusing it gets (though it can be useful in musical terms, but keep it there)?

So yes, we should not 'argue' about how something is called - we are having a technical discussion, use the correct technical terms, please!

 

[Tom.G]

Just stumbled across this thread again. It sounds an awful lot like arguing
"How many Angels can dance on the head of a pin?"

 

[sophiecentaur]

Musicians sometimes refer to harmonics as "overtones", where the "first overtone" is the "second harmonic".

Musical instruments, not being ideal systems, tend to produce overtones which relate to modes of oscillation. actual harminics are in a minority. So the musicians are correct in their context and maybe the rest of us should stop feeling righteous in our terminology.

 

[Baluncore]

Musical instruments, not being ideal systems, tend to produce overtones which relate to modes of oscillation. actual harminics are in a minority.

I can see how that may be true for percussion, but what then drives those non-harmonic overtones in other instruments.

 

[sophiecentaur]

Their structure. Even the much quoted guitar has a non-harmonic spectrum, then there’s the trumpet.
This is even more relevant in the attack phase.

 

[Baluncore]

This is even more relevant in the attack phase.

The attack mode is percussion. It is excitation by a step function.

But how relevant is this to the generation of undertones, when two signals meet in the vocal cords?

 

[Baluncore]

Even the much quoted guitar has a non-harmonic spectrum, then there’s the trumpet.

The trumpet is harmonic, but the individual harmonic amplitude is shaped by the transfer function of the tube and the bell.
http://newt.phys.unsw.edu.au/jw/brassacoustics.html#spectrum

 

[NTL2009]

Musical instruments, not being ideal systems, tend to produce overtones which relate to modes of oscillation. actual harminics are in a minority. So the musicians are correct in their context and maybe the rest of us should stop feeling righteous in our terminology.

I'm not sure where this "feeling righteous" comment comes from. I think I acknowledged that the musical approach of thinking in terms of overtones can be useful for certain discussions.

But, as I understand it, the OP was looking for the physics behind what produced the lower frequencies. So I think it best to stick to the proper physics terms for that part of the discussion, and avoid confusion between the two approaches..

 

[sophiecentaur]

The trumpet is harmonic, but the individual harmonic amplitude is shaped by the transfer function of the tube and the bell.
http://newt.phys.unsw.edu.au/jw/brassacoustics.html#spectrum

Did you ever play a trumpet? The bell / conical bore help to get close to harmonic overtones but to play in tune you need to bend / pull the higher notes.
The modes of a real string are affected by the mass of the bridge etc and the shape of the nut and bridge slots. Playing ‘harmonics’ by partial stopping at a point on the string involves choosing a different position than where the fret sits.
My evidence for all my assertions is that Hammond type organs never sound like the name on the tabs. They sound like a Hammond Organ.
If instruments sounded like the model you suggest, musical ensembles would sound boring.

 

[NTL2009]

...
My evidence for all my assertions is that Hammond type organs never sound like the name on the tabs. They sound like a Hammond Organ.
If instruments sounded like the model you suggest, musical ensembles would sound boring.

I don't think he's saying harmonic content is the whole story to how we identify an instrument. The Hammond organ produces a static harmonic content (with the exception of the "Percussion" tab, which adds a quickly decaying tone). The harmonic content of an acoustic instrument varies over time, and with playing technique.

I agree, that in practice, the harmonics of many (most?) instruments are not exact whole multiples. Guitar strings have a stiffness that moves the effective 'end' of the string further in from where the string is physically stopped. And that stiffness affects higher frequencies more - 'compensated' saddles are a means to , ah, em, 'compensate' for this. The higher/stiffer strings are shortened a bit, relative to the low frequency strings. You can see this on just about any guitar, at the 'saddle/bridge' end.

But I think that in most cases, these slight variations from are just accepted, and we still call the harmonic by the whole number that it is approximately equal to. Probably in the same way that when we talk about voltage conversion in a transformer, we don't always add a caveat regarding losses, or slight differences in the winding ratio, unless that is the focus of the discussion, We just mostly say a 2:1 winding ratio provides a 2:1 voltage ratio.

 

[Baluncore]

The origin of growling will not be identified by a discussion of what makes music sound good. It is clouding the physical issue.

But I think that in most cases, these slight variations from are just accepted, and we still call the harmonic by the whole number that it is approximately equal to.

Musical overtones may have non-integer ratios, but the physical harmonics of a distorted sinewave cannot, they must have integer ratios.

Two signals, being mixed together in the non-linear vocal cords, will transfer energy to the real sum and difference frequencies, with numerically correct frequencies.

 

[sophiecentaur]

But I think that in most cases, these slight variations from are just accepted,

You seem to be implying that the 'slight variations' are not a good thing. I would say that they are what distinguishes a 'good' and a 'poor' instrument. I would say that they're highly relevant and making a good violin, for instance, involves being very aware of the non-harmonic nature of the sound it produces. So trying to characterise an instrument using just the term 'harmlonic' is rather pointless.

A point that seems to have been missed in this discussion is that most of the passive filtering (wind instrument tubing, string instrument bodies - and even the vocal chords (when they are not being excited in there relaxatation oscillator mode) is low Q and will not select within a narrow band of any exciting waveform. A waveform full of strange overtones will not be filtered hard enough to be left with a fundamental so the spectrum will be more or less maintained. We certainly do not need to talk in terms of somehow changing overtones into pukkah harmonics; can't be done.

 

[sophiecentaur]

Musical overtones may have non-integer ratios, but the physical harmonics of a distorted sinewave cannot, they must have integer ratios.

That assumes the waveform is a distorted sinewave. If you look at the trace (over time) of most single note sounds (from a real instrument), the high frequency parts do not remain stationary relative to the fundamental; they march along, showing that they are at non-harmonic frequencies. So it is definitely not a simple "distorted sinewave".
The same goes for vocal sounds.

 

[Baluncore]

That assumes the waveform is a distorted sinewave.

Yes, that was the point I was making, but I am interested in clarifying the issue, not clouding the issue.

I want to identify the mechanism where non-linear mixing, transfers real energy to the difference frequency.

 

[sophiecentaur]

Yes, that was the point I was making, but I am interested in clarifying the issue, not clouding the issue.

I want to identify the mechanism where non-linear mixing, transfers real energy to the difference frequency.

Ok, you don’t want to cloud the issue. So use the term ‘waveform’ and don’t make approximations using a simple continuous waveform. If you restrict your analysis to a continuous waveform, repeating at the fundamental rate you really can’t be sure of the results. Inappropriate windowing is responsible for many mistakes.

In the case of ‘growling’ you don’t have simple mixing of tones in a separate passive filter/mixer. Everything interacts within the same system. When do overtones become straightforward harmonics? Can you say how?

 

[Baluncore]

When do overtones become straightforward harmonics? Can you say how?

If by "straightforward harmonics", you actually mean integer harmonics, as in the Fourier representation of a regular waveform, then it will not happen.

That does not preclude one of the many tones, from mixing with another tone, to produce a numerically correct difference frequency. We can ignore all your rogue overtones, to focus only on the sine waves that are present in the analysis, and which generate the difference frequency that is the growl.

This thread needs to get back on topic. Would you prefer it was locked?

 

[sophiecentaur]

if the topic could be discussed using the correct (Physics) terms without confusing shorthand, I’d love to read posts on the topic.

The words ‘sub harmonic’ and ‘harmonic’ should have been discarded very early in the thread, however unless someone can seriously justify them (more than to say they are being used very vaguely.)

You don’t need to threaten the nuclear option.

 

[sophiecentaur]

integer harmonics,

An interesting term and brought in here to maintain the illusion of correctness, maybe. It could make an interesting (?) topic for another post.

 

[NTL2009]

But I think that in most cases, these slight variations from are just accepted,

You seem to be implying that the 'slight variations' are not a good thing. I would say that they are what distinguishes a 'good' and a 'poor' instrument. ....

A point that seems to have been missed in this discussion ...

I'm not trying to make any statement at all (in this thread) about what is 'good' or 'bad' (though I do agree with you in the musical realm).

Maybe I'm misreading this whole thread, but I thought OP was just looking for the physics behind what produces a tone that is lower in frequency than either the clarinet tone or the singing tone? Good or bad aren't a part of that.

 

[sophiecentaur]

Good or bad aren't a part of that.

Of course not. My point was that the model in the attempted explanation is flawed if you assume harmonics and that you can easily detect audibly that departure by the difference between the sound of instruments and simple 'synthesised' sounds.

There should be serious caveats attached when inappropriate terms are used in an explanation. Approximations can be relevant and need to be justified properly - or at least mentioned.