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

Leersfool, I wrote;
“However, live music is not just primary frequencies but a combination of lots of different overtone frequencies that create harmonic structure, warmth, tone, and timbre."

You repeated this as;
“There are a couple of problems with this. First, there is no such thing, if we are speaking of acoustic instruments, as live music composed only of primary frequencies.”
It sounds like you are in agreement so I don't understand the problem.

Your second point is conflicting. You wrote;
“Second, when a musician alters the color of his sound, this does NOT change the frequency, including the overtones…”

“Now, if the player’s tone is not pure…this CAN (emphasis added) mess with the overtones…musicians sometimes deliberately bend notes on purpose.”

“I am talking about much more subtle changes of timbre. But the main point is that the musician CANNOT (emphasis added) change the natural overtones produced by the frequency being played.”

Conflicting, but I think you may in agreement. Simply, if it sounds different it is. A pure sine wave and a pure square wave with the exact same frequency will have the same pitch, but sound completely different. The frequency only describes the pitch, the waveform describes the sound and all its components i.e., overtones, harmonics, tone, color, warmth, and every other character of the sound all mixed together.

A player can change the ‘sound’ of an instrument depending on how they play it, some instruments more than others, which will change the components of the waveform, but not necessarily the frequency of the waveform. An example is trumpeter using his hand to mute his trumpet, but he could also change his technique i.e., lip position, airflow, etc. to change the sound all at the same frequency. You cannot have a different ‘sound’ without changing the structure of the waveform. Excluding any external factors like room acoustics, these are player induced. It is impossible to change a sound without altering components of the sound and the waveform, so tone, color, warmth, etc. are part of the sound itself.

assuming "benign" acoustics, has anyone attended a concert , especially orchestral or other ,in which instruments were unamplified and used the word "warm" to describe the sound?

naturalness of timbre and warmth are not identical.

warmth represents some relationship between the presence of high and low frequencies.

lower frequencies usually are associated with the perception of warmth, but the 72 posts dealing with the subject, evince some disagreement, so how can advise be given if there is no accepted definition ?

i have defined the term in frequency response characteristics, and yes , i believe warmth is a deviation from neutrality. that is a recording which sounds warm has probably been "equalized" by a recording engineer.

thus i disagree with byron regarding warmth as a coloration. its an opinion consistent with my definition.

Hi Bryon - loved the beginning of your post. :) I think we are actually in agreement here.

@Hifibri - yes, re-reading what I wrote, that is a little confusing, for which I apologize. Basically, this is the part that is the important part: "the main point is that the musician CANNOT (emphasis added) change the natural overtones produced by the frequency being played." In this quote: "Now, if the player’s tone is not pure…this CAN (emphasis added) mess with the overtones…musicians sometimes deliberately bend notes on purpose." the word "overtones" is not what I meant to use - I meant to say frequency, though this is pretty badly worded period.

Without going into a very technical discussion of sound waves and how they are formed inside a brass instrument (to continue your example), a brass player is manipulating frequency and creating different waveLENGTHs when he "buzzes" his lips as the air moves through them and into the instrument. Where this frequency is on the natural harmonic series determines the waveLENGTH. These natural harmonics are of course fixed, as are the resulting overtones in the sound, which are determined by these fixed natural harmonics. It isn't possible for the player to manipulate these. If the player is "lipping" too much or too little, or "blowing" too much or too little, this inefficiency results in the tone becoming unfocused in some way, changing the waveFORM, but it does NOT change the frequency or the waveLENGTH, and therefore does NOT change the harmonic content. The dynamic level, or amplitude, makes subtle changes to the waveFORM, and any subtle "color" changes the musician may make to a note (such as the jazz trumpet player "bending" a pitch) also change the waveFORM, but NOT the harmonic content.

So the point I am leading to here is that changes in "warmth" are NOT related to frequency or harmonics or overtones whatsoever. I hope the above is clear, there is a reason I am a musician and not a writer! So to speak of "warmth" in a system as something to do with frequency response seems wrong to me, and I am trying to understand this association among audiophiles.

This thread has certainly evolved, as might be expected considering the parties who are participating, into a really excellent dialog.

FWIW I must very respectfully say that at this point I agree with Hifibri and I disagree with Learsfool. I see it as follows: Yes, the FREQUENCIES of all of the harmonics are determined unalterably by the fundamental frequency (i.e., the lowest frequency component) of the note that the musician chooses to play. However, wouldn't the individual AMPLITUDES of each of those harmonics, relative to the amplitudes of the other harmonics and to the amplitude of the fundamental, vary depending on the waveform changes you agree can occur?

If not, what would a spectrum analysis of the waveforms indicate is changing? I doubt that extraneous or spurious frequencies are being introduced, that are not harmonically related to the fundamental. What could be changing, that would account for the waveform changes, other than the relative amplitudes of the harmonics and the fundamental?

And if the waveform changes are in fact in the form of alterations of that harmonic structure/balance, then doesn't it stand to reason that there is a relation between "warmth" and harmonic structure/balance?

I do think it is very much an oversimplification, and a common audiophile misconception, to speak of warmth as just being a frequency response that is non-flat in some way. A mid-bass peak, or some similar frequency response emphasis, might contribute to a subjective perception of warmth. But realistic reproduction of timbre, which as I see it correlates with accurate reproduction of the RELATIVE amplitudes of the harmonics and the fundamental of each note, as well as proper time domain performance and ambience reproduction, I envision as being the keys to the PROPER reproduction of warmth.

Best regards,
-- Al

A question and a follow up -- did audiophiles talk about "warmth" prior to the introduction of consumer digital audio? And if they did, does "warmth" mean the same thing in each time period?