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

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

Hi Al - you wrote: "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."

Yes, this is exactly what I am saying. All of the harmonic overtones of a sounded frequency are always present in the timbre, so electronic distortion cannot introduce or create new harmonics, it can only distort those already present.

About your last statement: " 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." This is a strange statement. The basic difference in timbre between a flute and a violin, to use your example, is that one is made of metal and one is made of wood, not to mention the fact that their sounds are created in a completely different manner as well. This is obviously the largest factor in the difference in timbre. Without going into the science of it, waves produced by a string behave very differently from waves produced by a tube. A tube with one end closed behaves differently than one open at both ends, and conical and cylindrical tubes behave differently as well. Side holes in the tubes have their effects as well, of course. Not to mention different types of wood or metal alloys used in the instrument's construction, which have very great effect on the timbre.

Another important thing to point out is that although some of these various timbres are more acoustically complex than others, the overtone series for all of them is always the same - it doesn't matter what instrument is creating it.

As a side note, the flute happens to be one of the purest instrumental timbres, and the oboe is one of the most complex. This is the reason that the oboe gives the A to tune the orchestra - it's complex tone is more easily audible.

Last, another word on the audibility of these harmonics. Sometimes, it is possible for the brain to concentrate on an overtone of the tone sounded, if this frequency has already been sounded, so that the ear is aware of it. For instance, if a piano sounds A440Hz, and then the A an octave below (220Hz), it will be easier to attempt to hear the A440 overtone within the sounded A220Hz tone. This takes some training, of course, especially if one wants to try to hear more difficult overtones. There are some people who have claimed to be able to hear as many as 27 different overtones, but the vast majority of researches seriously doubt this claim - 5 or 6 at most, and that for a very highly trained ear indeed. Those types of experiments are fascinating.

Best regards to you as well, Learsfool

"I am unaware of any naturally occuring 'harmonics' in an electrical signal. Only distortion of what ever type."

Harmonic distortion measurement is done by feeding pure fundamental with no overtones (sinewave) and subtracting the same fundamental from the output. Whatever remains are harmonics introduced by electronics that weren't in the original (source) signal. You can call it naturally occuring harmonics (introduced by electronics). Enhancing means adding system produced harmonics to instrument harmonics. System can also introduce harmonics by intermodulation or transient intermodulation. It is also possible for system to introduce frequencies that are not harmonically related to fundamental frequency as it happens often with A/D or D/A conversion with jittery clock.

Instrument might have all overtones but they don't have to be harmonic overtones. Many instruments (like percussion) produce inharmonic overtones. System will alter the sound by adding it's own harmonics.