Subjective Impressions (pre-measurement)
OK here's the deal: how these will sound will be dependent upon the recording. The K812 remind me of the HD700 and K550. Allow me to explain. The K812 has an overall warmth. By that I mean there is a slight broad elevation centered over the high bass area. (I tend to isolate regions when I describe tonal characteristics). However there seems to be shrillness, harshness, a bit of glare, a bit sibilance - a sign of a peak in the lower treble area. Not too unlike the HD800, but it seems higher up and more peaky on the K550 K812.
The K812 is like in HD700 in the sense that with the right recording, it can take on a warmish tone. For example, k.d. Lang's All You Can Eat and Natalie Merchant's Tigerlity, two albums which are on the bassy and laid back side, sound pretty OK on the K812. With the wrong recording (and we are not necessarily talking about bad recordings either because these two I am amount to mention sound perfectly fine on my speakers and other headphones), the K812 can be grating in the treble. Examples of such "wrong" recordings are Talking Heads (200X? remaster) Naive Melody and Cassadee Pope's Not Over You.
Is the K812 as nasty as the HD700 when things are off? No, but the K812 can certainly be "difficult". I can also see lots of other folks not having an issue with the K812 because the broad high bass elevation can help mask the treble irregularities.
I've attached some screenshots of the spectrum analyzer when the snare drum hits on these tracks. The exception would be the Not Over You recording which was snapshot of a harmonic of Ms. Pope's voice. Note that on the two recordings which work well with the K812 (k.d lang and N. Merchant), the lower treble region around 7-8k is 5-10db more laid back than the tracks that don't (C. Pope and Talking Heads)
The K812 is like the K550 in the sense that it has the same kind of timbre and soft bass of the K550. It's sort of like an open K550, but with better technicalities in terms of resolving ability. Sadly, I don't think it offers that much more clarity.
P.S. One thing I did notice is that the K550 tends to fall apart at higher volumes. The treble peculiarities get worse.