Well, what you hear is what you hear.
But you use terms like "warm" & "warmth" in a very individual/personal way--to include not only tonality (bright or dark in terms of elevated or depressed upper frequencies), but also "resonance" and "reverb," which could mean any number of things.
In my experience, terms like "warm," "bright," "peaky," and "bassy" primarily involve tonality, how frequency is conveyed. In that sense, "warm" = depressed treble frequencies; "bright" = elevated treble/upper midrange frequencies; "peaky" could mean elevation of pretty much any frequency; and "bassy" = elevated bass/sub-bass frequencies.
But when you get into resonance and reverb, those terms could refer to soundstaging--ie, how wide, tall, deep the soundstage appears to be; how distinct/separate notes and instruments sound in it; etc. They could also refer to the sound imparted by earcups: their dimensions (ie, lots of space vs very little); whether the earcups are open or closed by design. I suppose those terms could even encompass other phenomena (ie, phase anomalies, channel imbalance, time-smearing of some kind coming from cables, DAC, etc)
Perhaps I'm the only one that thinks differently about this. Maybe everybody but me bundles warmth & brightness together with spacious & reverb. But I don't think so.
To show what I meant: there's a headphone well known to not be "warm" in tonality/frequency, but definitely is spacious in soundstaging & reverberation (Sennheiser HD800).
BTW, you're right about the M Stage being warm; my HPA-1 certainly is. It may be is the warmest component I own. Also bassy. Stock, it's somewhat spacious in sound (fairly wide but also fairly indistinct soundstaging). I upgraded the opamp; the result was far less warmth along with a rather different soundstage--now more pinpoint/focused & centered (narrower), making it easier to "see" different instruments in space--also with a more focused, clear bass.
I don't feel Resonance or reverberation which is literally the cups/housing/drivers vibrating audibly, can be used to describe soundstage
Resonance by the way is synonymous with reverb, "the reinforcement or prolongation of sound by reflection from a surface or by the synchronous vibration of a neighboring object"
reverberation "prolongation of a sound; resonance" the two are interchangeable
every headphone has some decay to it an I like wood back headphone because the cub reverb combined with driver resonance adds a very real sense of warmth, though the drivers them self's resonate, and when they resonate to much you get excessive decay, or the sound audibly hangs around to much after the initial attack, the HD 800 does not have a lot of resonance or reverb, quite the opposite, in fact there are mods to help warm them up or add in some resonance, but here's the amazing thing! Resonance/Reverb are connected with imaging, if you have a LOT of resonance or audible decay you'll find that your imaging may dull, it becomes harder to hear transients or differences between channels because of excessive resonance, think of it as ripples in a body of water. To much resonance and all those ripples come together, which makes a mess, the Eikon has some cup reverb, has some resonance, how ever the driver doesn't resonate excessivelywhich allows it to resolve very well, the drivers lack of excessive resonance allows for more a more accurate image, better sense of left right, backwards, forward, height depth ect... and it's still has some natural warmth or some natural resonance/decay from the cups reverberation
Tonality "the character of a piece of music as determined by the key in which it is played or the relations between the notes of a scale or key" and frequency response are linked. Bright translates to me extra energy up top, dark maybe a little less energy up top, bassy is too much low frequancies, though bassy is vague. Is the frequancy response of the bass very forward/elevated? Or is there a LOT of decay, meaning those low notes hang around after the initial attack, Typically the two are tied together, as the louder the attack is the more audible the decay that follows, it's decay to me translates into warmth. My HE 4 is VERY cold, there's very little decay, and the mids aren't withdrawn in comparison to the bass or highs it just lacks warmth or it lacks decay, which I like but also makes it sound a bit fake
Where as the Eikon again has warmth, the warmth emanates from the resonance of the cups, that cup reverb is why an Open Back like the Grado RS2E has a beautiful warm mid range, despite being an open back
Although again, you can also have a driver that resonnantes a little to much, and adds in a little decay as well, the Focal Elear another open back that's warm, the driver also have some excessive resonance, or a slower decay which is in it's cause creates warmth, another beautiful thing about the elear is it's Distortion is super low
Really it's all connected, too much reverb can hurt imaging, and can remove air, too much audible distortion can also cause the imaging or accurate placement of instruments in the sense of width, depth and height, and some times that distortion can also contribute to warmth or to much decay, it's all connected together, frequency response dictates tonality, but frequency response tied with Cumulative Spectral Decay, total harmonic distortion and impulse response that is what dictates your imaging, the more decay, the more distortion the less impulse response the smaller and more hazy the picture,
So when an amp adds haze, or it adds distortion, decay and dulls impulse response it can be described as warm IMO, and warmth isn't always bad. The HE 4 is TOO fast it's too cold, it sounds fake so it likes a warmer amp, the Eikon on the other hand... is beautiful! Very transparent of what it's plugged into and I personally like it with a hybrid tube, the tube really does imo add to the natural warmth of the Eikon, or how the drivers present the sound, and with the right tube you can introduce just enough distortion to not ruin the CSD or impulse response, but maintain it's amazing imaging and add some more beauty
The Eikon is indeed Spacious, but it's not bright, there is audible reverb which translates into warmth, and the key point is that it's warmth is not excessive, tonality alone doesn't tell the story of how spacious something will sound or how well it will image
That's at least how I understand it, I could be completely wrong but... there's my 2cents
@UntilThen going to a CanJam is an excellent way to figure out what you like best with your Eikon! Let's us know what you try it with
