[Eric B]

E/I + S/N (I call them "communication styles", since Keirsey speaks of "concrete/abstract communication")

ES extraverted dominant function, preferred perception function is Sensing (expressive, concrete)
EN extraverted dominant function, preferred perception function is iNtuition (expressive, abstract)
IS introverted dominant function, preferred perception function is Sensing (reserved, concrete)
IN introverted dominant function, preferred perception function is iNtuition (reserved, abstract)

E/I + T/F (I call them "Social image temperaments" because after E and I, we often think of a person as more logical or emotional)

EF extraverted dominant function, preferred judging function is Feeling (ETB: "expressive feelers")
ET extraverted dominant function, preferred judging function is Thinking (ETB: "expressive thinkers")
IF introverted dominant function, preferred judging function is Feeling (ETB: "deep feelers")
IT introverted dominant function, preferred judging function is Thinking (ETB: "deep thinkers")

E/I + J/P ("Sociability Temperaments" --George Frisbie writing in JPT)

EP dominant extraverted perceiving (Bissell: "extraverted eMpiricals" —Jung's "irrationals")
EJ dominant extraverted judging (Bissell: "extraverted Rationals", not to be confused with Keirsey's "Rational")
IP dominant introverted judging/aux. extraverted perceiving (Bissell: "introverted Rationals")
IJ dominant introverted perceiving/aux. extroverted judging (Bissell: "introverted eMpiricals")

S/N + T/F (Original Myers "Temperaments"; preferred function combinations)

SF preferred Sensing and Feeling (Concrete Feeling)
ST preferred Sensing and Thinking (Concrete Thinking)
NF preferred iNtuiting and Feeling (Abstract Feeling; Apollonian/Idealist)
NT preferred iNtuiting and Thinking (Abstract Thinking; Promethean/Rational)

S/N + J/P ("Cognitive Temperaments", "[Janet] Germane Temperaments", "Perceiving attitudes")

SP preferred extraverted Sensing (Dionysian/Artisan)
SJ preferred introverted Sensing (Epimethean/Guardian)
NP preferred extraverted iNtuiting ([Janet] Germane: true Promethean)
NJ preferred introverted iNtuiting (Germane: True Apollonian)

T/F + J/P ("Normative Temperaments", "Judging temperament model", "Judging attitudes")

TJ preferred extraverted Thinking (Bissell: "the most directive")
TP preferred introverted Thinking (Bissell: "the most pragmatic")
FJ preferred extraverted Feeling (Bissell: "the most cooperative")
FP preferred introverted Feeling (Bissell: "the most friendly")

When trying to fogure out how MBTI compared with the FIRO system, and seeing E/I of course, as "expressive", and that both T/F and J/P seemed to be "responsive", I had hoped for a symmetrical correlation. I had heard a suggestion that the "sociability temperaments" (E/I + J/P) were in fact the "real" interaction styles, instead of Beren's asymmetrical model. So then you could have E/I=eI, J/P=wI, S/N=eC, T/F=wC. The standard 16 types table would be divided by perfect horizontal rows representing Inclusion (the Sociability Temperaments) and vertical columns representing Control (the original Myers preferred function "temperaments"). The sociability temperaments would only differ from Berens' model by each style swapping an STP for an SFJ. The former, as an EP or IP becomes "informative", and the latter, as an EJ or IJ becomes "directive"). Still, it didn't fit the more familiar temperaments.
The idea I liked better was E/I + T/F (which I call "social image temperaments"), which would be paired with S/N + J/P (Cognitive Temperaments; used by Germane. There is also an argument that NP and NJ were the "real" "Apollonian" and "Promethean" instead of Keirsey's NF and NT). So having eI=E/I, eC=S/N and swapping the other pairs to wI=T/F and wC=J/P would end up with the styles trading an NFJ for an NTP; yet the former as an EF or IF becoming informative, and the latter as an ET or IT becoming directive. These too did not seem to fit.
So the existing Berens Interaction Styles plus Keirsey temperaments seems the best match for linking with the ancient temperaments (in social and leadership areas, respectively).

It is the addition of a perception scale (S/N) that make the true "temperament" groupings so "asymmetrical" to the MBTI dichotomies. (And S/N does not fit eC as I had wondered, but instead pairs opposite e/w ranges). The way it turns out, is that for Sensors, the Interaction Styles follow ET, IT, EF and IF, and for iNtuitors, they follow EJ, IJ, EP and IP! Just like for S, temperament is J/P, and for N, it is T/F.

Two "asymmetrical" groupings the yielded even higher numbers of difference in a study using EAR data were the "extraverted function" set: SP, NP, TJ, FJ; and also SP, SJ, EN, IN). There's also discussion of a notion of "Mirror Temperaments": ST, SF, NP, NJ.