On their names:
It must be said that the Fire spirits themselves do alter the spelling of these names, and the most usual difference is the change from Paraketi to Parakati and Paraseg to Paraseje and saji. This I have experienced to emphasize certain aspects of these spirits and I find it goes in accordance with the letteressences of Patricia Shaffer. The word Seg have I always got translated as bad, awful and similar things and I see the main root here is the SG as also is found in the word for Earth; Caosg. Keti, Kati or even Ketil is translated to the Good brother. That means that one can expect some teaching of basic enochian moral from these two. Zam means war or fight, doi-snake, ma-falling, maon - door, but I am not entirely convinced on the latter. The three first have also confused me withe regards on their names meaning, but Pa-i-on is at least a phrase meaning Being is made. It is very obvious that his name does stand out as something different as he has not got any R in his prefix. This I heard very early in the translation work to be caused by that Pa-i-on is not his true name, his true constitution is of an art that cannot get named.
It is also worth noting that the central governor in the Aethyr LIN : Paraoan is a name made in this pattern.
Runar.

On their structure
In Call 6, the EM are described as "mighty in the firmament of waters". Water here, as well as in Call 5, the ACAM call, the corresponding OX cube, and also in numerous other systems, refers to the turning from the causal to mental plane. In Kabalistic terms this would refer to the region bounded by sephiroth 2-5, the region of Daath. The EM relate to the process of the supernals sending forth Daath as their child and its then influencing the lower sephiroth. This same process is described in the Stanzas of Dzyan (in H.P. Blavatsky's The Secret Doctrine), especially stanza 3.
Here, the "firmament of waters" is referred to by both water symbolism and the symbol of the egg. The divine thought, mahat, corresponds to the supernals.
The first group seem to correspond to active versions of Kether- Chokmah-Binah, more or less, and are the subject of DOzmt. PA-I-ON is the same as the unmanifest version of Fohat in the stanzas, the CLA being the manifest version. PERIO is associated with the opening of passages through the veil over the Earth (see OS and OL). PERIO is responsible for overseeing the lower six EM.
The second group is responsible for Daath as child of the supernals. PARAMAON is responsible for the formation of this out of the supernals. PERDOI, who is the same as OEAOHOO the Younger, the Blazing Dragon of Wisdom of stanza III:7, translates what is projected from above into energies capable of acting below. PARAMA is responsible for these being implemented and oversees the lower three EM.
The third group is responsible for implementing these energies. PARAZAM chooses whether they will be implemented by PARAKETI or PARASEG. PARAKETI implements things in a balanced way, PARASEG is a destructive way. The three groups are able to function in the spaces between the groups of NI; PERIAK, PA-I-ON, and PERIO being between the first and second groups with PERIAK closer to the first and PERIO closer to the second; the second group of EM between the second and third NI groups similarly; and the third group of EM between the third and fourth NI groups similarly.

-Dean

See also the zodiackal aspects of the EM.

Analysis of the names by Patricia and Dean.

Eight of the EM names begin with either PER or PARA, both roots related to the word for fire. PER can be read as "establish willful motion", PARA as a combination of PAR, the word for "in them", as "to fix or establish to remain that motivation" and ARA as "the source-waves of beginning arising from the Root of Motion", giving the idea of establishing a motivation which is the source of beginnings. The beings whose names start with PER seem to act directly, whereas the ones whose names start with PARA seem to inspire others to action

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PERIAK:
to establish willful or intentional motion to energize the beginning of creation; to set into purposeful motion the energy to begin causing or creating; to establish deliberate or intentional change in energies is the beginning of creation; to set purposeful motivational energies as the beginning of causation.

Pe = the Angelic title for the letter transliterated as the English "B" (Choice): to establish (in all dimensions of space and time) the will; to establish or set [for a] purpose; to set or place willfully or intentionally; to establish by will, or willfully, deliberately. + (er) = to will to move or change; willing or willful movement; the will to move or change; the purpose of movement, differences; for the purpose of change; the purpose of emotions; willful or deliberate motion or change, the will in motion; ® (per) = to establish willful or intentional motion; to set into purposeful motion; to establish deliberate change; to establish [place or set ][for] the purpose [of, for, or by] emotions; + (ri) = movement is; to move, change or be motivated by energy; to be emotionally energized or enabled; changeability, variety, ® (eri) = to will or intend to motivate ability; purposeful motivational energy; to intentionally change the energy [of]; + (ia) = the energy source; energy "is" the origin or source, energy is the beginning, the enabler of beginnings; able to begin, the energy or ability to begin: can begin; "is" enabled or energized at or from the beginning; to energize or enable a beginning; able to refresh or renew; ® (ria) = to move or motivate the energy or ability to begin or be renewed; to change the energy of beginning; to motivate or change the ability begun; the emotional or motivational energy to begin; + (ac) = the source or original cause; to begin to make or cause; to begin because; ® (iac) = to energize the beginning of creation; the energy to begin causing or creating.

PA-I-ON:
This name is read as three words, PA establishing a source, I pure energy, and ON becoming self or becoming within. These relate respectively to PA-I-ON combined with PERIAK, PA-I-ON in himself, and PA-I-ON combined with PERIO. The ON is related to the ON in PARAMAON and is best read as becoming self here but as becoming within (the waters) in PARAMAON because PA-I-ON functions within the realm of divine thought and PARAMAON within the waters.

PERIO:
to establish deliberate or purposeful motion to energize being and enable becoming.

Pe = the Angelic title for the letter transliterated as the English "B" (Choice): to establish (in all dimensions of space and time) the will; to establish or set [for a] purpose; to set or place willfully or intentionally; to establish by will, or willfully, deliberately. + (er) = to will to move or change; willing or willful movement; the will to move or change; the purpose of movement, differences; for the purpose of change; the purpose of emotions; willful or deliberate motion or change, the will in motion; + (per) = to establish ["by choice" is implied by Pe] willful or intentional motion; to set into purposeful motion; to establish deliberate change; to establish [place or set ][for] the purpose [of, for, or by] motivation [e.g., via emotions]; + (ri) = movement is; to move, change or be motivated by energy; to be emotionally energized or enabled; changeability, variety; + (eri) = to will or intend to motivate ability; purposeful motivational energy; to intentionally change the energy [of]; + (io) = the energy of being; to energize or enable to become; the ability to become; [whatever] "is" able to become (or evolve); + (rio) = to move or change the ability of being-becoming; the motivational energy of [a] being; what moves or motivates enables to become; variability or changeability of being[s]-becoming;

PARAMAON:
To fix or establish to remain a motivation as source of beginnings emerging from divine mind becoming within (the waters)

PAR = "in them": to fix or establish to remain that emotion or motivation; "in them" there remains that emotion or motivation; + (ara) = Significant Triad showing the source-waves of beginning arising from the Root of Motion; all beginnings arise from motion, change; that which moves or motivates anew; that which renews or refreshes (eg., as through the emotions). that which changes, that which awakens, that which motivates anew; + (ram) = to move to refresh or renew the knowledge; emotion which triggers the memory; to be taught or reminded of; + (ama) = the mind (and what it knows) as the source of all beginnings, the Mind that began all, to renew or refresh the memory of all; + (mao) = the mind of the original Being; the memory of the source or origin of all being; to remember the beginner of all being; the mind begins to evolve, memory begins to come to be; all that was known will again be remembered through becoming; + (aon) = the source of Being-Becoming is within the self; to begin to become within the self; the source of Being within each self; to renew or refresh the being-becoming or evolution within the self.

PERDOI:
To establish willful motion which moves potential to become diverse energies

(per) = to establish willful or intentional motion; to set into purposeful motion; to establish deliberate change; to establish [place or set ][for] the purpose [of, for, or by] emotions; + (rd) = to move or motivate the substantial possibilities of the Holy Spirit; the different possibilities; to be moved or motivated by the Holy Spirit; ® (erd) = to will for different possibilities; for the purpose of change or difference to be possible; + (do) = the third being, the Holy Spirit of infinite substantial possibilities to become (revealed); to proclaim or reveal the possibilities to be-becoming; + (oi) = "this", this is; to-be-being-becoming is energized or enabled; to become (by) "this" energy; "this" comes to be enabled, "this" "is" becoming enabled; to become energized or enabled; to come to be able; to become by ability; this is energized or enabled; to become (by) "this" energy, "this" comes to be enabled or energized; ® (doi) = the substance of Being energized, or the aspect of a Being of Energy; to reveal or proclaim the possibilities that are being-becoming enabled or energized; the Holy Spirit reveals possibilities to become energized or enabled; the possibility for "this" to come is enabled; to reveal or proclaim this.

PARAMA:
To fix or establish to remain a motivation as source of beginnings emerging from divine mind

PAR = "in them": to fix or establish to remain that emotion or motivation; "in them" there remains that emotion or motivation; + (ara) = Significant Triad showing the source-waves of beginning arising from the Root of Motion; all beginnings arise from motion, change; that which moves or motivates anew; that which renews or refreshes (eg., as through the emotions). that which changes, that which awakens, that which motivates anew; + (ram) = to move to refresh or renew the knowledge; emotion which triggers the memory; to be taught or reminded of; + (ama) = the mind (and what it knows) as the source of all beginnings, the Mind that began all, to renew or refresh the memory of all.

PARAZAM:
To establish that motivation alike as a memory in separated (but similarly begun) minds.

PAR = "in them": to fix or establish to remain that emotion or motivation; "in them" there remains that emotion or motivation; + (ara) = Significant Triad showing the source-waves of beginning arising from the Root of Motion; all beginnings arise from motion, change; that which moves or motivates anew; that which renews or refreshes (eg., as through the emotions); that which changes, that which awakens, that which motivates anew; + (ra) = to move to begin; to move at the beginning; to move again or anew, to refresh or renew; to dawn or to awaken, as of a new day; to be reborn; to move or motivate a new beginning; emotional renewal, refreshment; + (az) = the source or origin of parts; the original division; the source divided; a time of separation; to begin to divide or separate; to begin by division: thus, separated but similar by virtue of being parts of the original whole; to begin similarly, all to begin alike as parts, all otherness; the beginning of division, separation; the beginning of otherness (i.e. other than the self); ® (raz) = to move or motivate to begin similarly [but] separately; + (za) = to divide the origin or source, to divide or separate from the source; by division all began; to divide or separate at the beginning; by division to begin; separately to begin; others to begin, ® (aza) = Significant Triad showing the source-wave of time, of begining, arising out of the Root of Division; all beginnings arise from division, separation. The concept of "Division" mandates a preexistent Unity or Wholeness as the source that was divided. All of the parts are begun similarly; all begin alike out of division of what was whole. All new beginnings represent a separation from what was; + (am) = the Source of Mind, the Original Mind; to begin mind, or to begin in the mind: as an idea, awareness, consciousness; to begin to learn, to begin to know; to begin to think; the beginning of knowledge; again to know, to refresh or renew the memory, the beginning of memory; ® (zam) = to separate from the source mind, separate new minds.

PARAKETI:
To establish that motivation as source of beginnings causing willed balancing of energies

PAR = "in them": to fix or establish to remain that emotion or motivation; "in them" there remains that emotion or motivation; + (ara) = Significant Triad showing the source-waves of beginning arising from the Root of Motion; all beginnings arise from motion, change; that which moves or motivates anew; that which renews or refreshes (eg., as through the emotions); that which changes, that which awakens, that which motivates anew; (ra) = to move to begin; to move at the beginning; to move again or anew, to refresh or renew; to dawn or to awaken, as of a new day; to be reborn; to move or motivate a new beginning; emotional renewal, refreshment, + (ac) = the source or original cause; to begin to make or cause; to begin because; ® (rac) = to move to begin to cause or create; to motivate the source of creation; to be renewed or refreshed from the source of creation; to awaken creation; motive or emotion is the source of causation; + (ace) = the source or origin of creation or causality is the will; to begin to cause or make by will, to begin because of will; to begin to cause for the purpose of; it began because it was willed, it was begun intentionally; + (ce) = to make or cause by will; because (I) willed it; to make for a purpose; + (et) = to will for (or for the purpose of) adjustment or balance, ® (cet) = to make or cause for the purpose of balance or adjustment; + TI = "it is", to balance or adjust energy or ability; to judge the ability of; balance to enable; ® (eti) = to willfully or purposely adjust the energy or ability; [for] the purpose of balance of energy or ability.

PARASEG:
to establish that motivation as a source of beginnings possessing the will to negate (ie destroy)

PAR = "in them": to fix or establish to remain that emotion or motivation; "in them" there remains that emotion or motivation; + (ara) = Significant Triad showing the source-waves of beginning arising from the Root of Motion; all beginnings arise from motion, change; that which moves or motivates anew; that which renews or refreshes (eg., as through the emotions); that which changes, that which awakens, that which motivates anew; + (ras) = to be motivated to begin again; to awaken or refresh the fourth to gather; to be awakened, renewed or refreshed all together; + (as) = the time presently possessed: today, now; the source or origin of possession; to begin to have, gather, possess, or acquire; the beginning of gathering; to begin together, to begin sharing together; whatever begins or is begun together; to begin the fourth together; to refresh or renew all together; to be refreshed by sharing together; until all are gathered together; + (se) = to have will or purpose; to possess or gather by will; to acquire what is willed; the fourth together to will; ® (ase) = to begin (the fourth, together) to have or acquire the will or purpose; + (seg) = to have will-not, to have purpose-not, to have willfully negated what was possessed (?), to obtain or acquire by willing for what was not; to have willed without a purpose; to have what was willed-not, to have willed-not; perhaps, to acquire unwillingly.

Read also the interpretation of the sigils of the EM