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.
