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

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.

Learsfool,

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.

I think that in order for our understandings to converge, what is needed is a description of the differences in spectra that RESULT from the differences you are describing. Although I'm not sure that any of us can provide that without further research. I may try to do some research on that if I get a chance tonight or tomorrow.

If a violin and a flute were to play notes having the same fundamental frequency, the same volume, and the same duration, and if their respective notes as captured by a microphone were fed into a spectrum analyzer (a device which shows the frequency components of a signal, and the amplitudes of each of those components), what would the differences be between the two spectra, that account for their very different sounds? That is the key question, as I see it.

Electronic distortion cannot introduce or create new harmonics, it can only distort those already present.

Although it may not have been your intention, this statement would seem to imply that a distortion component at a given frequency would not be added by the system were it not for the presence in the original sound of a harmonic at that same frequency. Which is not the case, as I and Kijanki (whose post I am in full agreement with) indicated.

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.

Their frequencies are always the same, for a given fundamental frequency. But the amplitudes of each overtone in the series will be very different for different instruments.

The flute happens to be one of the purest instrumental timbres.

Yes, which I think corresponds to its notes having less harmonic content than in the case of most other instruments. I.e., its notes come closer to being a pure sine wave than those produced by other instruments (although of course they are still considerably different than a pure sine wave). Which I think is a basic reason that a flute, when not well recorded and reproduced, can often tend to be "hard" sounding.

Another word on the audibility of these harmonics....

To clarify, I certainly do not assert that individual harmonics are readily perceivable. What I believe is that differences in harmonic structure (the amplitudes of the harmonics, relative to the amplitudes of other harmonics and to the amplitude of the fundamental) are the primary determinant of timbre and tone. Therefore when we perceive differences in timbre and tone, we are perceiving the EFFECTS of differing harmonic structures.

Best regards,
-- Al

Following up on my previous post, I found this excellent writeup:

http://www.phys.unsw.edu.au/jw/sound.spectrum.html

It appears that I was partly right, but not seeing the whole picture. Some excerpts from the writeup:

If you change a sound without changing its loudness or its pitch then you are, by definition, changing its timbre. (Timbre has a negative definition - it is the sum of all the qualities that are different in two different sounds which have the same pitch and the same loudness.) One of the things that determines the timbre is the relative size of the different spectral components....

Let's look between the harmonics. In both of the examples shown above, the spectrum is a continuous, non-zero line, so there is acoustic power at virtually all frequencies. In the case of the flute, this is the breathy or windy sound that is an important part of the characteristic sound of the instrument. In these examples, this broad band component in the spectrum is much weaker than the harmonic components. We shall concentrate below on the harmonic components, but the broad band components are important, too....

Introductory physics text books sometimes give the impression that the spectrum is the dominant contribution to the timbre of an instrument, and that certain spectra are characteristic of particular instruments. With the exception of the closed pipes mentioned above, this is very misleading. Some very general or vague comments can be made about the spectra of different instruments, but it is not possible to look at a harmonic spectrum and say what instrument it comes from. Further, it is quite possible for similar spectra to be produced by instruments that don't sound very similar. For instance, if one were to take a note played by a violin and filter it so that its spectrum were identical to a given spectrum for a trumpet playing the same note, the filtered violin note would still sound like a violin, not like a trumpet.

Here are some general statements about spectra:

* bowed strings and winds have harmonic spectra
* plucked strings have almost harmonic spectra
* tuned percusion have approximately harmonic spectra
* untuned percusion have nonharmonic spectra
* the low register of the clarinet has mainly odd harmonics
* bowed strings have harmonics that decrease relatively slowly with frequency
* brass instruments often have spectra whose harmonics have amplitudes that increase with frequency and then decrease.

To say anything that is much more specific than that is misleading.

The rest of the writeup is quite interesting as well, and even provides a good deal of additional specific discussion concerning the flute.

Best regards,
-- Al

Hi guys - Kijanki, you make a very good point about jitter (and explains yet another reason why digital has never sounded as good as analog for me), and the intermodulation distortions. I guess I thought that jitter had more to do with timing, but I suppose that it would indeed produce harmonic distortion as well.

Al, I do understand now much more where you are coming from, thanks very much! I will have to read up on these types of electronic distortions some more. When I took a graduate level acoustics course, it was geared (as was the very fine textbook which has always been my main reference ever since) to performing musicians and live acoustics, not recordings and electronic equipment. In fact, I am not sure that purely electronic distortions were discussed at all, I will have to look that up. I have never been one to judge audio equipment by the specs, anyway, so these types of things have never held much interest for me. This discussion has certainly got me curious, though!

I will have to check out the article you linked when I have some more time to give it serious attention. Just reading over your quotes from it, it seems like very good info. The text I mentioned goes into great detail about all of those issues mentioned. If you care to look it up, it is entitled The Musician's Guide to Acoustics, by Murray Campbell and Clive Greated, and was published by Schirmer. I do see, getting it out, that the last couple of chapters discuss electronics briefly (I think mostly from the perspective of electronic instruments rather than audio equipment, though), but the book is basically about acoustic instruments and how they behave, and how the room affects them. So my knowledge of acoustics is much more in that line, things that affect live performance rather than recording playback.

What is particularly interesting to me is your discussion of different amplitudes of the harmonics having such a big effect. I am starting to come around, but it would be good to find some info on that in particular. That would certainly seem to be one of the biggest differences between live and recorded sound, then, and probably a much bigger difference than I have thought. Thanks so much for sharing your knowledge - between you and Atmasphere in particular, I have received quite an education on this site.