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

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.

Learsfool - jitter is a form of modulation. It creates in frequency domain sidebands of very low amplitude - still quite audible since not harmonically related to fundamental. This amplitude (order of <-70dB) is proportional to level of fundamental frequency. With many frequencies (music) it becomes many sidebands - hash (noise). This noise is proportional to level of the signal and is zero with no signal - therefore is detectable only as a lack of clarity. Everything affected by noise (clarity and imaging) will be affected by jitter.

By reading this thread and some internet articles I realize that complexity of instruments' sound is something that I will never understand. One article even mentioned that bassoon at low and high notes sounds like two different instruments. In addition to complex harmonics (first five harmonics stronger than fundamental) it has pipe resonances that are getting sharper going up, resulting in "11th resonance hitting 12th harmonic". Incredible complexity - and there is still effect of the hall and technique of the player. One article mentioned interaction between instruments and gave example of two people whistling two frequencies 204Hz and 214Hz. Bystander will hear just one frequency 209Hz (average) with loudness modulated at 10Hz (difference). Orchestra has perhaps many interactions like that but produces nice harmonics. I should read on theory of music to understand it better.

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.

For a bit more background, I'd recommend that you do a bit of reading on the theory and history of electronic synthesizers and speech synthesis. In electronic music composition, this timbral relationship between the fundamental and its harmonics is commonly referred to as "formant", the change of parameters across the duration of a note is called "envelope", and the periodic change within a note is called "modulation". Approximate, crude parallels to acoustic instruments are that formant = timbre, envelope = articulation, and modulation = vibrato.

It is of course possible for analog electronics to generate their own harmonics - this is how analog synthesizers work. I've personally implemented patches on early synthesizers (ARP and Buchla) that can deliver pretty convincing flute, bell, and string sounds. Ironically, it's not so much the timbre/formant that's hard to emulate, rather it's the envelope.

Even earlier, the acoustic principles of building formants are very structured in a thousand or so years of the art of building and tuning pipe organs. Emulation of orchestral instruments became a very common goal - this style of organ-building probably reached its zenith in the very early years of the 20th century with builders such as Willis in the U.K. and E.M. Skinner in the States.

An interesting side note on timbre - I have found it a commonly-held view in vocal and woodwind pedagogy that poor tone production produces a set of overtones that are in fact not in tune with the fundamental, rather they tend to be flat. Although I have not seen any measured evidence to back this up, I tend to agree with it - as the perception of intonation problems as it relates to tone production cannot be corrected simply by raising the pitch. That is, some singers always sound flat, no matter what pitch they're singing.

all of the discussion regarding harmonics is useful and instructive, but does not address the question of whether warmth is a form of coloration. unfortunately, no one has definitively spoken on this subject.

the purpose of the thread , i believe, is the elicitation of suggestions to achieve warmth.

as i have said, without an understanding of what warmth is, the question cannot be answered.

i have proposed an (empirical) concept of warmth as deflections in spl, both positive and nagative, which are audible. as such such a concept would connote that warmth is coloration.

let me give an example.

several posters have mentioned instruments such as the violin and flute, in their discussion of harmonics.

suppose one considers the harpsichord.

if the sound of a harpsichord seems to emphasize the wood body and to some degree, obscures the articulation of the strings, i would say the impression of the sound of the harpsichord would include warmth, as one of the adjectives used. of course, the performer might be responsible for this effect, but that is another question.

i believe the warmth region comprises frequencies below 100, so it would seem that a peak in the region below 100hz (??? how many db) would produce warmth that the poster may be seeking.