What is Warmth?

Suteetat and Raul are both correct.

Instruments and halls can have warmth of their own. This is natural.

HiFi systems can have warmth too. This is not natural- it is a coloration caused not so much by frequency response errors (as is the common myth) but instead by distortion.

The 2nd order harmonic is the most to blame, and is why SETs are so well-known for a warm sound.

It happens that the ear hears distortion as tonality. In the case of music, where most of the energy is in the bass, you get the upper bass emphasis simply because of the harmonics (in addition to the 2nd, the 3rd and 4th also contribute, although to a much lessor degree).

This is why you can measure the frequency response of two amplifiers on the bench, and while they may measure the same, one will sound warm and the other will not. Its because of distortion, not frequency response variation.

Single-ended circuits in general contribute to the 2nd harmonic. Tubes are often blamed for making more 2nd harmonic, but in reality it has more to do with the topography of the electronics than it does the type of amplifying device. It *is* true however that due to the greater linearity of tubes that you can build single-ended circuits with them and get away with it- this has gone on for many decades and so has contributed to the idea that tubes have more 2nd harmonic. But if that were true, how does that square with tubes being more linear??

Now a system can also sound 'cold' which is caused by distortions that are of a higher ordered nature (and especially the odd harmonics). Any harmonic above the 4th is considered a higher-order harmonic. In addition, the ear uses the 5th, 7th and 9th harmonics to determine how loud a sound is. If these harmonics are messed with by the electronics, the system will sound louder than it really is and it will sound brighter (harsher) as well.

Again this is because the ear interprets distortion as tonality.

This issue is tricky for designers! By picking a certain type of topology you will get a certain distortion signature; that can be modified somewhat by the addition of loop negative feedback. Note that I say modified; 'reduced' is not necessarily correct in all cases.

As an example, if one choses a fully differential topology in which there are no single-ended circuits, the primary distortion component will be found to the 3rd harmonic. If you add feedback to reduce it, other higher harmonics will appear.

Finally one should keep in mind that as much as we are wanting to get to the actual musical experience, the fact is that the closest we can get is to correct reproduction of the recording itself. That recording contains distortions of its own!

Hence the great degree of discussion and debate on this topic...

The definition that Gordon Holt suggests is really quite adequate.

If I understand you correctly, it is not that warm audio equipment have tilted frequency response per se but more that distortion from 2nd harmonic is more pronounced at the bottom end giving illusion to more lower frequency and less at the top, is that correct?

Generally, yes.

I suppose audio equipment is not supposed to add its own signature of harmonics and just play whatever signals that is passed through only.

Right- audio equipment should not editorialize :)

I am curious if you might have an example of equipments that you would consider to be one that is able to tame most of the harmonics created by audio equipment itself. Certain equipment that tends to emphasize clarity and detail that comes with cold, analytical tendency probably has its own set of distortion as well. What would be your closest ideal to neutrality?

Once a bit of electronics has added harmonics (distorted) to the sound there is nothing you can do downstream to correct that (although many people do try, in the name of 'synergy' which in most cases seems to be the act of compounding one distortion with another, although if you were to ask them they would tell you that they are using the 'synergy' to deal with tonal issues). The gear that you are referring to with the 'cold analytical tendency' usually is lacking the lower orders of distortion, but has trace amounts of the higher orders (in particular the 5th, 7th and 9th harmonics). The human ear uses these harmonics to gauge the volume of a sound; IOW we are very sensitive to this type of distortion, so much so that we can often hear it even when our test instruments have trouble measuring it in the noise floor of the amplifier/preamp under test. Audiophiles have terms for such distortion; the phrase 'cold analytical tendency' that you used is an excellent example.