Injecting 2nd order THD into the audio stream to bring "warmth"

[audio_engr]

First, all instrumental and voice sounds that musicians make include harmonics. If there were no harmonics every note produced would be a pure sine wave and every voice and instrument would sound the same. Harmonics occur at exact multiples of the fundamental pitch so instruments and voices produce odd and even harmonics in differing proportions which is why each instrument and voice has its own tonal character. Musicians can make their voice or instrument sound warm or edgy by the way they sing or play the note. The musician has control over the harmonics that are part of the sound they produce.

Second, what we normally think of as a "warm" sound is a sound which drops slowly in level in the high frequencies as frequency rises. This is the kind of sound we get naturally in good concert halls where there's a bit of room gain in the bass frequencies and the high frequencies are absorbed increasingly by air in the room as the frequency rises. The room gain at low frequencies boosts all low frequencies, both fundamentals and harmonics, though a little bit unevenly depending on frequency (less as frequency rises and the room gain fades) and room modes (standing waves) boost or cut both fundamentals and harmonics at the frequencies at which they occur. High frequency absorption in air simply increases as frequency increases and doesn't distinguish between fundamentals or harmonics but the highest fundamental produced by a musical instrument is somewhere around the 8 kHz mark and everything above that is fundamentals so basically absorption in air largely just increasingly rolls off the level of the harmonics increasingly as frequency rises and it doesn't distinguish between odd and even order harmonics. The same frequency can be an odd order harmonic for one fundamental and an even order harmonic for another fundamental and the amount that frequency is absorbed by air in a space will be the same regardless of whether it's an odd or even order harmonic.

So, what happens if you add 2nd order THD. You boost a particular harmonic, one that is more harmonious to our ears than some of the higher order harmonics, and that adds a pleasing richness to the sound which may make the sound "warmer" to us but it's doing something slightly different to what a musician does to make their notes sound "warm" or what room acoustics does to the sound to produce a "warm" sound. "Warmth" of sound in music isn't a simple single characteristic, it's made of of a few different things. A musician will play a note differently in one room to the way they play it in another room in order to produce a similar tonal colour in both rooms because they can hear what the room is doing to the sound they produce so they adjust the sound they produce in order to get the sound they want in that particular room. In our homes we play with things like bass and treble controls, speaker toe in, acoustic treatments, electronic room correction, and the like in order to get our systems to deliver the kind of sound we like and want to hear. Boosting 2nd order harmonics is just another thing we can do in the range of a whole lot of things we can do to change the sound our systems produce.

It's not going to be a magic bullet. No single thing we can do is a magic bullet that will work for all music. Some recordings sound a lot warmer than others and boosting 2nd order harmonics might be too much of a "good thing" while some recordings can sound dry and the same amount of added 2nd order harmonics may be just the right thing for you but you can make the sound "warmer" or "drier" in other ways as well.

If you boost the low frequencies with the bass tone control you will increase the level of all of the fundamentals and harmonics that the musician chose to produce that  were captured on the recording and the music should sound warmer. It doesn't take a large boost of the tone control to get a noticeable affect. If you decrease the high frequencies with the treble tone control, you roll off all of the harmonics the musician chose to produce which  were captured by the recording and the music should sound warmer. Again only a small roll off may be needed to produce a noticeable effect. You can do both together if that's what you like.

You could also simply try sitting a little further away from your speakers and adjusting toe in a little in order to roll the highs off a little and sitting further away from your speakers will put you closer to a wall and increasing your proximity to the wall will make the bass a bit richer and stronger as you get closer to the wall and that will produce a warmer sound.

You don't have to buy a fancy device or software to make the sound you hear a little warmer. There's a lot of simple things  you can do right now with the speakers and amp you have and your listening position which will make the sound you hear a bit warmer and you can do it for free without adding distortion and probably a bit of noise along the way from the operation of the software and/or the device adding a bit of 2nd order distortion.

Addition: a warm sound isn't always a good thing. People often say that music sounds warm or sweet or rich or something else but only some music does. Other music is intended to sound harsh or edgy or dry or something else. Making music that is supposed to sound harsh or edgy sound warm loses the character of that music just as much as music that is supposed to sound warm and sweet loses its character if it sounds dry and edgy. Be very wary of thinking that adding a particular sort of colouration to the sound is always going to be a good thing because it isn't. Not all music is supposed to sound warm, or happy or joyful or anything. Music is made to express the moods and feelings that human beings have and there's music that expresses every one of those different moods and feelings that we have from time to time. Adding a dash of warmth or happiness or edginess or whatever to everything actually makes some music worse, and it probably makes as much music worse as it makes better. Go easy with what you want to do, however you want to season your music. A little seasoning can go a very long way.

+1 ... Excellent post & totally in agreement ...