What is “warmth” and how do you get it?

Learsfool, as I see it an audio system can introduce harmonics, enhance harmonics, or even reduce harmonics that may be present in the source material.

Harmonics can, and to some degree inevitably will, be introduced by the system in the form of distortion products.

They can be enhanced either by virtue of a frequency response emphasis that happens to occur at a frequency corresponding to some harmonic (multiple) of the fundamental frequency of a note, or by virtue of a frequency response dip that happens to occur at the fundamental frequency, or by virtue of distortion of the fundamental frequency of a note, the distortion products therefore occurring at the same frequencies as harmonics that may be present in the note.

They can be reduced by the converse of those frequency response effects, or by introduction of a distortion product that is out of phase with a harmonic that may be present in the note at the same frequency.

I'm just saying that there is a whole lot more to do with that than amplitudes of individual harmonics within the overall timbre - again, these harmonics are inaudible to far more than 99.9% of us.

I respectfully disagree. My understanding is that timbre and the relative amplitudes of individual harmonics are one and the same.

As I understand it, to cite an example, a violin playing a note whose fundamental frequency is say 1 kHz will produce very audible harmonics at 2 kHz, 3 kHz, and other higher multiples of 1 kHz. A flute playing a note whose fundamental frequency is also 1 kHz will produce very audible harmonics at those same multiples of 1 kHz. The reason that the note produced by the flute will sound different than the note produced by the violin is that the relative amplitudes of those harmonics will be in different proportions.

And, similarly, differences in timbre and tone between two different playings of the same note on the same instrument will be the result of differences in the relative amplitudes of those harmonics, as I understand it.

Best regards,
-- Al

Hi Al - thanks for weighing in on this. However, I think you are incorrect when you say "Harmonics can, and to some degree inevitably will, be INTRODUCED by the system in the form of distortion products." (My emphasis) Your own examples that follow are all examples of what I was speaking of in my previous post - what you call enhancing certain harmonics via distortions (and they are good examples). However, ALL natural harmonics are always present in the natural timbre, so you can't introduce a new overtone that wasn't there before, though you can distort (or even remove) it. This is what I was trying to say in my previous post. If this statement is indeed incorrect, please explain.

One other point - in your violin examples, yes, those overtones are of course part of what make differences in timbre. However, each individual one is indeed indistinguishable from the others to the ears of at least 99.9% of humans. It is not possible to tell which of those overtones are the ones that are different, in your example of two different playings of the same note on the same instrument. If I played the same note twice, at the same volume, on my horn, you would not be able to tell me which individual overtones were affected and how, and this is doing you the credit that you would be able to hear the difference in the timbre between the two at all - a great many audiophiles would not, especially if I tried to the best of my ability to make them exactly the same. And in the same case, it would have to be a VERY bad recording/system indeed that would distort them so much so that most people could hear it. These sorts of differences are MUCH more audible live and at very close range than they are on a recording.

Learsfool, I think you are absolutely correct. I could go on ad nauseum, but suffice it to say that I see only one term when talking about electric signals, 'harmonic distortion', with the word 'distortion' being a noun and 'harmonic' being an adjective modifying it. I am unaware of any naturally occuring 'harmonics' in an electrical signal. Only distortion of what ever type.

FWIW.

Hi Learsfool and Newbee,

ALL natural harmonics are always present in the natural timbre, so you can't introduce a new overtone that wasn't there before.

Let's say that a note includes a frequency component at 1kHz. In response to that 1kHz frequency component, the system may create distortion products at 2kHz, 3kHz, 4kHz, and any and all other multiples of 1kHz that are within the bandwidth of the system.

Let's take the 8th harmonic (8kHz) as an example. Whether the 8kHz distortion component that is created by the system, in response to the 1kHz frequency component of the note, constitutes an INTRODUCTION of a harmonic, or an ENHANCEMENT of a harmonic, depends on whether or not an 8kHz harmonic is already part of the sound that the instrument created.

If you are saying that any note produced by any instrument will naturally and invariably contain frequency components of non-zero amplitude at ALL harmonic multiples of the fundamental (lowest) frequency component of the note (and I don't know whether or not that is true), then yes, that would mean in a literal sense that the system cannot INTRODUCE a harmonic that isn't already there.

However, the system can certainly, as I see it, CREATE a harmonic, as a distortion product of the fundamental frequency of the note, irrespective of the existence of that harmonic in the original signal. If a harmonic already exists in the note at the same frequency as that newly created distortion product, then the natural harmonic and the artificial one would combine in some manner, depending on their phase relationship.

In your violin examples, yes, those overtones are of course part of what make differences in timbre. However, each individual one is indeed indistinguishable from the others to the ears of at least 99.9% of humans. It is not possible to tell which of those overtones are the ones that are different, in your example of two different playings of the same note on the same instrument. If I played the same note twice, at the same volume, on my horn, you would not be able to tell me which individual overtones were affected and how, and this is doing you the credit that you would be able to hear the difference in the timbre between the two at all - a great many audiophiles would not, especially if I tried to the best of my ability to make them exactly the same. And in the same case, it would have to be a VERY bad recording/system indeed that would distort them so much so that most people could hear it. These sorts of differences are MUCH more audible live and at very close range than they are on a recording.

Yes, certainly I would not be able to identify and describe the specific differences in harmonic structure that correspond to the differences in timbre that I may hear, at least without the aid of sophisticated instrumentation. But my point is this: For a note with a given volume, a given fundamental frequency, and what I'll refer to as a given "envelope" (duration, rise, decay, etc.), audible differences in timbre, tone, and even the basic character of the note (e.g., violin vs. flute) are the result of differences in harmonic structure (i.e., the relative amplitudes of each of the harmonics). To the extent that differences in timbre, tone, and the basic character of the note are perceivable, differences in harmonic structure are perceivable.

I don't see how that can be incorrect, because (for a given volume, fundamental frequency, and envelope) I can't envision anything other than differences in harmonic structure that could account for differences in timbre, tone, or the basic character of the note.

Best regards,
-- Al

... For a given volume, fundamental frequency, and envelope I can't envision anything other than differences in harmonic structure that could account for differences in timbre, tone, or the basic character of the note.

Just to be sure it's clear, I should add with respect to this statement that I am referring to the directly heard sound produced by the instrument, apart from hall effects and apart from artifacts of the recording and playback processes.

Best regards,
-- Al