Frater Barrabbas’s Hierarchy of Elemental Emperors & Grand Dukes from the Ars Theurgia Goetia (with sigils)
“As we have seen, the sixteen elementals are associated with the tarot’s sixtteen court cards, representing a kind of feudal hierarchy. Yet there is another hierarchy that we can associate with the elemental spirits, one that comes from the early Renaissance grimoire, the Theurgua-Goetia. I have incorporated this lore to provide a spirit name for focus and as a way of bringing the elemental correspondences together…The spirits of the Theurgua-Goetia…are reputed to be wind demons arrayed in a hierarchical structure…believed to consist of both good and evil entities…it must be assumed such a power is actually neutral…Thus, it is up to the Witch who unleashes this spirit whether it will do good or evil…Therefore, in examining the qualities of the sixteen elementals, we will merge the lore of the Spirits of the Theurgua-Goetia with that of the sixteen court cards and the sixteen elemental energy fields.”
~Fratar Barrabbas
Honestly it sounds 
to me, but it is interesting, and the text / sigils from the Ars Theurgia Goetia itself are certainly worth looking at. As are the invocations from The Stenographia (via The Goetia of Dr. Rudd).
The Four Elemental Emperors
“…to work this system of magic using these spirits, you should always invoke the four Emperors as part of the ritual structure and then the established spiritual hierarchy below them.”
~Fratar Barrabbas
Caramasiel: Emperor of Air 
Summary
Carnesiell [Carnesiel] is the most great and Cheefe Emporor Ruling in The East who hath, 1000 great Dukes and a 100 lesser Dukes under him, besides 50000000000000 of ministering spirits which is more Inferior then the Dukes, whereof [wherefore] we shall make no mention [of these], but only 12, of the Cheefe Dukes and their seals, because they are sufficient for practise.
The Supplementary Conjurations from the Steganographia, Book 1, Chapter XVII:
Carnesiel aphroys chemeryn mear aposyn. Layr pean noema ovear rna sere cralty calevo thorteam chameron ianoar pelyn Layr, baduson iesty melros ionatiel delassar rodivial meron savean fabelron clumarsy preos throen benarys favean demosynon laernoty chamedonton.
Carnesiel aproysi chameron to pemalroyn phroys Cadur mearmol benadron Vioniel saviron army pean arnotiel fabelronthusyn throe chabelron savenear medaloys year olmenadab cralty sayr
Caspiel: Emperor of Fire 
Summary
Caspiel is the Great and Cheefe Emperor Ruling in the South who hath 200 great Dukes and 400 lesser Dukes under him, besides 1000200000000 ministering spirits, which are much Inferiour &c. whereof wee (Salomon saith) shall make noe mention, but only of 12 of the Cheefe Dukes and their seales, for they are sufficient for practise.
The Supplementary Conjurations from the Steganographia, Book 1, Chapter XVIII: 3
CaspieJ aloyr chameron noeres padyr diviel prolsyn year maduson cralnoti fruon phorsy larsonthon thiano pemarson theor. Caveos adeveos friato briosi panyeldrubon madiel sayr fabelrusyn gonear pean noty nabusran. (conjuratio spiritus)
CaspieJ asbyr Chameronty churto freveon dayr fabelron Cathurmy meresyn elso peano tailtran Caspio fuar Medon clibarsy Caberosyn ulty pean Vearches pemasy natolbyr meldary noe Cardenopen men for diviel adro.
Ameradiel: Emperor of Water 
Summary
Amenadiel is the Great Emperor of the west, who hath 300 great Dukes, and 500 lesser Dukes, besides 40000030000100000 other ministering spirits more Inferiour to attend him, wheof [whereof] we shall not make any mention but only of 12, of the cheefe Dukes and their seales which is sufficient for practice.
The Supplementary Conjurations from the Steganographia, Book 1, Chapter XIX:
Amenadiel aprolsy chameronta nosroy throen mesro salayr chemaros noe pean larsy freveon ionatiel pelroyn rathroy Caser malusan pedon Cranochyran daboy seor marchosyn lavo pedar venoti gesroy phemotiel Cabron.
Amenadiel bulurym chameroty eriscoha pedarrnon flusro pean truarbiel fabelron greos belor malgoty nabarym stilco melros fuar pelaryso chitron amanacason. (coniuratio)
Demoriel: Emperor of Earth 
Summary
Demoriel is the Great and Mighty Emperor of the North, who hath 400 great Dukes and 600 lesser Dukes with 70000080000900000 [700,000,800,000,900,000] servants under his Command to attend him, whereof we shall make mention but of 12 of the cheefe Dukes and their seales, which will be sufficient for practice.
The Supplementary Conjuration’s from the Steganographia, Book 1, Chapter XX:
Demoriel onear dabursoy Cohyne chamerson ymeor pean olayr chelrusys noeles schemlaryn venodru patron myselro chadarbon vevaon maferos ratigiel personay lodiol camedon nasiel fabelmerusin sosiel chamarchoysyn. (carmen conjurationis)
Demoriel osayr chameron chulty save porean lusin dayr pean cathurmo fomarson ersoty lamedon iothar busraym fuar menadroy chilarso fabelmerusyn. (carmen conjurationis)
The Sixteen Elemental Grand Dukes
Note that all correspondences and associations come from Fratar Barrabbas, and all seals come from The Ars Theurgia Goetia, or The Goetia of Dr. Rudd. The “Sixteen Elemental Grand Dukes” of Barrabbas do NOT share equal status in The Ars Theurgia Goetia! Nearly all are Princes (indicated by a circle around their sigil), while one (Godiel) is a Servant Duke.
Air of Fire: Godiel (Learning)
Summary
(Night Duke of Usiel)
Earth of Fire: Maseriel (Organization)
Summary
The eighth spirit in order But the fourth under the Emperour of the South is called Maseriel, Who Rulleth as king in the Dominion of ye West, and by South, and hath a great number of princes & servants under him, to attend him, whereof we shall make mention of 12 of the cheefe [Dukes] thatt attend him in the day time, and 12 that attend him to doe his will in the night time, which is sufficient for practice, they are all good by nature & willingly will doe your will in all things.
The Supplementary Conjurations from the Steganographia, Book 1, Chapter VIII:
Maseriel bulan lamodyn chamoty Carmephin iabrun caresathroyn asulroy bevesy Cadumyn turiel busan Sevear: almos ly cadufel emoty panier iethar care pheory bulan thorty paron Venio Fabelronthusy. (conjuratio)
Maseriel onear Camersin, Cohodor messary lymo balnaon greal, lamedon odiel, pedamoy nador ianoz auy chamyrin. (conjuratio)
Fire of Fire: Barmiel (Insight)
Summary
The fift [fifth] spirit in order is called Barmiel; he is the first and cheefe spirit under Caspiel, The Emperour of the South [He ruleth] as king [of the South] under Caspiel, and hath 10 Dukes for the day: And 20 for the night to attend him to doe his will, the which is all very good, and willing to obey the Exorcist, whereof wee shall make mention but of 8 that belongs to the day, and as many for the night, with their seals for they are sufficient for practice.
The Supplementary Conjurations from the Steganographia, Book 1, Chapter V:
*Barmiel buras melo charnotiel malapos veno masphian albryon, chasmia pelvo morophon apluer charmya noty Mesron alraco caspiel hoalno chorben ovear ascrea cralnoty carephon elcsor bumely nesitan army tufaron. *
Barmiel any casleon archoi bulesan eris, Casray molaer pessaro duys anale goemo mesrue greaJ cusere drelnoz, parle cufureti basriel afly maraphe neaslo, camos emeo, damerosenotis any carprodyn.
Water of Fire: Asyriel (Intuition)
Summary
The seventh spirit in order, but the third under the great Emperour of the South is called Asyriel, he is a mighty kinge, Ruling in the South West part of the world and hath 20 great Dukes to attend him, in the day time, and as many for the nights…
The Supplementary Conjurations from the Steganographia, Book 1, Chapter VII:
Asiriel aphorsy Lamodyn to Carmephyn drubal asutroy Sody baruchon, usefer palormy thulmear asmeron chomemadusyn coleny busarethon duys marphelithubra nasaron venear fabeironty. (conjuratio)
Asiriel onear Camor Laveviel gamer sothin ianoz alnay bulumer pal orson, irgiel lamedon, ludiel Casparosyn navy asparlon nadiel bulephor ianos pesonty tresloty Camon elyr, mearsu nosy thamerosyn. (conjuratio)
Air of Water: Cabariel (Regeneration)
Summary
The twelfth spirit in order, But the fourth under the Emperour of the West is called Cabariel; [Sl2731 adds: who is a mighty prince Ruling in the west & by North] he hath 50 Dukes to attend on him in ye day and as many in the night, under whom are many servants to attend on them, whereof wee shall make mention but of 10 of the cheefe Dukes that belongs to the day, And as many for the night, & every of them hath 50 servants to give attendance when their masters is Invocated, &c. Note Those Dukes that belongs to the day is very good and willing to obey their Master, and is ^are to be called in the day time, And they of the night is ^are by nature Evill & Disobedient, and will deceive you if They can &c they are to be called in the night.
The Supplementary Conjurations from the Steganographia, Book 1, Chapter XII:
Cabariel onear chameron fruani, pamaton fosiel bryosi nagreal fabelrontyn adiel thortay nofruav pena afesiel chusy.
Cabariel asiar paremon chiltan amedyn sayr pemadon chulty movayr savepor peatha mal frimaston dayr pean cothumo fabelrusyn elsoty chelmodyn.
Earth of Water: Dorochiel (Lust)
Summary
The tenth spirit in order, But the second under the Emperour of the West is called Dorochiel, who is a mighty prince bearing Rule in the West, and by North, and hath 40 Dukes to attend [on] him in the day time, and as many for the night, with an Innumerable company of servants spirits, whereof wee shall make mention of 24 Cheefe dukes that belongs to the day, and as many for the night.
The Supplementary Conjurations from the Steganographia, Book 1, Chapter X:
Dorothiel cusi feor madylon busar pamersy chear ianothym baony Camersy ulymeor peathan adial cadumyr renear thubra Cohagier maslon Lodiemo fabelrusyn.
Dorothiel onear chameron ulyfeor madusyn peony oriel nayr druse movayr pamerson etro dumeson, davor caho. Casmiel haymo, fabelrunthon.
Fire of Water: Usiel (Compassion)
Summary
The eleventh spirit in order, But the third under the Emperour Amenadiel is called Usiel, who is a mighty prince Ruleing as king in the North West. he hath 40 Dyurnall [diurnal], and 40 nocturnall Dukes to attend on him in the day and the night…And the first 8 that belongs to ye night hath forty Servants a piece to attend on them…and they are very obedient and doth willingly appeare when they are called, they have more power to hide or discover Treausures [treasures] then any other spirits (saith Salomon) that is contained in this Booke…
The Supplementary Conjurations from tbe Steganographia, Book 1, Chapter XI:
Usiel parnothiel chameron briosy sthrubal brionear Caron sotronthi egypia odiel Chelorsy mear Cbadusy notiel omycb turbelsi paneras tbortbay pean adresmo boma amotiel Cbelmodyn drusarloy sodiviel Carson, eltrae myre notiel mesraym Venea dublearsy mavear melusyron cbartulneas fabelmerusyn.
Usiel asoyr paremon cruato madusyn sauepe mavayr realdo chameron ileo paneras tburmo pean elsoty fabelrusyn iltras cbarson frymasto chelmodyn.
Water of Water: Malgaras (Empathy)
Summary
The ninth spirit in order, but the first under the Emperour of the West is called Malgaras – he Rulleth as king in the Dominion of the West, and hath 30 Dukes under him to attend him, in the day, and as many for the night, and several under them againe;…They are all very courteous and will appear willingly to due your will, they Appear 2 & 2 at a time wth their servants…
The Supplementary Conjurations from the Steganographia, Book 1, Chapter IX:
Malgaras ador ehameso bulueriny mareso bodyr Cadumir aviel easmyo redy pleoryn viordi eare viorba, ehameron very thuriel ulnavy, bevesy mevo ehasrnironty naor emyso, ehony barmo ealevodyn barso thubra sol.
Malgaras apro ehameron asoty mesary throes Zameda sogreal paredon adre Caphoron onatyr timo beosy. Chameron phorsy mellon tedrumarsy dumaso duise Casmiel elthumy pes on alproys fabelronty Sturno panalmo nador. (carmen spiritus)
Air of Air: Pamersiel (Decision)
Summary
Pamersiel is the First and Cheefe spirit in the East, under Carnesiel, who hath 1000 spirits under him which are to be called in the day time, but with great care for they are very Lofty and stuborne…note these Spirits are by nature evil and very false, and not to be trusted in
[with] secrets, but are excellent in driving away Spirits of darkness from any
that is haunted as houses.
The Supplementary Conjurations from the Steganographia, Book 1, Chapter 1:
Pamersiel, anoyr madriel through the service ebra sothean abrulges itrasbiel. And nadres ormenuitules rablion hamorphiel.
Pamersiel oshurmy delmuson Thafloin peano charustea melany, lyaminto colchan, paroys, madyn, moerlay, bulre + atloor don melcove peloin, ibutsyl meon mysbreath alini driaco person. Crisolnay, lemon asosle mydar, icoriel pean thalmon, asophiel il notreon banyel ocrimos estevor naelma befrona thulaomor fronian beldodrayn bon otalmesgo mero fas elnathyn boframoth.
[PamersielJ Lamarton anoyr bulon madriel traschon ebra sothea panthenon nabrulges Camery itrasbier rubanthy nadres Calmosy ormenulan, ytules demy rabion hamorphyn.
Earth of Air: Camuel (Discipline)
Summary
The Third Spirit placed and Ranked In order under the Cheefe Mighty great and potent King of the East is called Camuel who Regneth Ruleth and governeth as King in the South East part of the world & hath many & severall spirits under his Goverment & command…They appear all in A verry Beautifull forme,& verry Courteously…
The Supplementary Conjurations from the Steganographia, Book 1, Chapter Ill:
Camuel aperoys, melym mevomanial, casmoyn cralty bufaco aeli lumar photirion theor besamys, aneal Cabelonyr thiamo vesonthy.
Camuel Busarcha, menaton enatiel, meran sayr abasremon, naculi pesarum nadru lasmon enoti chamubet usear lesponty abrulmy pen sayr thubarym, gonayr asmon friacha rynon otry hamerson buccurmy pedavellon.
Fire of Air: Padiel (Realization)
Summary
The Second Spiritt in order under the Emperor of the East is called Padiel, he Ruleth in the East and by South as King, and governeth 10000 spirits by day and 20000, by night, besides severall Thousands under them, They are all good by nature and may be trusted. Salomon sayeth that these spirits have noe power of them selves but [only] what is given unto them by their prince Padiel.
The Supplementary Conjurations from the Steganographia, Book 1, Chapter II:
Padiel aporsy mesarpon omevas peludyn malpreaxo. Condusen, ulearo thersephi bayl merphon, paroys gebuly mailthomyon ilthear tamarson acrimy Ion peatha Casmy Chertiel, medony reabdo, lasonti iaciel mal atri bulomeon abry pathulmon theoma pathormyn.
Padiel ariel vanerhon chic tharson phymarto merphon amprisco ledabarym, elsophroy mesarphon ameorsy, paneryn atle pachumgel thearsan utrul ut solubito beslonty las gomadyn triamy mefarnothy.
Padiel melion, parme, carniel, busayr, ilnoma, venoga, pamelochyn.
Water of Air: Aschiel (Imagination)
Summary
The Fourth Spirit in order is called Aseliel he governeth as King under Carnesiel, in the South and by East he hath 10 cheefe spirits belonging to ye day, and 20 to the night, under whome are 30 principall spirits…they are all very courtious and Loving, and beautifull to behold…
The Supplementary Conjurations from the Steganographia, Book 1, Chapter IV:
Aseliel aproysy, melym, thulnear casmoyn, mavear burson, charny demorphaon, Theoma asmeryn diviel, casponti yearly basamys, emoti chava lorson.
Aseliel mumea casmodym bularcha vadusynaty belron diviel arsephonti si panormys orlevo cadon Venoti basramyn.
Air of Earth: Armadiel (Work)
Summary
The fiveteenth [sic] spirit in order, But the third under the Emperour of the North is called Armadiel, who rulleth as king in the North East part, and haue many dukes under him besides other servants…these spirits are good by nature and willing to doe your will in all things.
The Supplementary Conjurations from the Steganographia, Book 1, Chapter XV:
Armadiel marbevo pelrusan neor chamyn aldron pemarson Cathomaor pean lybunny Caveron Thorty abesmeron year larso chamoty theor Caveos myat drupas Camedortys ly paruffes emoty mesoryn elthy chaor atiel; lamesayn rovemu fabelrusin, friato chasalon pheor thamomy mesardiel pelusy madiel baferoty sarreon prolsoyr asenosy cameltruson. (conjuratio)
Armadiel afran meson Casayr pelodyn, Cavoti Chameron thersorvy marbevon pheor Casoyn myrvosy lyburmy deor fabelronton. Chubis archmarson. (conjuratio)
Earth of Earth: Rasiel (Healing)
Summary
The 13[th] Spirit in order (but the first under Demoriel the Emperor of the North) is called Rasiel, he ruleth as King in the North, and hath 150 Dukes for the day and as many for the night to attend him and they have many servants under them again for to do their will &c, whereof we shall mention
16 Chief Dukes that belong to the day because they are by nature good and willing to obey, and but only 14 belong to the night because they are by nature evil and stubborn & disobedient & will not obey.
The Supplementary Conjurations from the Steganographia, Book 1, Chapter XIII:
Raysiel afruano chameron fofiel onear Vemabi parnothon fruano Caspiel fufre bedarym bulifeor pean Curmaby Layr Vaymeor pesarym adorcus odiel Vernabi peatha darsum laspheno deuior Camedonton phorsy lasbenay to charmon druson olnays, Venouym lulefin, peorso fabelrontos thumo. Calephoy Vern, nabelron bural thorasyn charnoty Capelron. (carmen conjuration is)
Raysiel myltran, fruano fiar charmy clymarso pean Sayr pultho chultusa medon vepursandly tusan axeyr aIDon. (carmen conjurationis)
Fire of Earth: Baruchas (Responsibility)
Summary
The 16th spirit in order, But the fourth under the Emperour of the North is called Baruchas – who rulleth as [a] king in the East and by North and hath many Dukes and other several spirits to attend him whereof we shall make mention of 15 of the cheefe Dukes that belong to the day and night who have 7040 servants to attend on them: they are all by nature good and are willing to obey [you,]…
The Supplementary Conjurations from the Steganographia, Book 1, Chapter XVI:
Baruchas malvear chemorsyn chamotiel bason ianocri medusyn aprilty casmyron sayr pean cavoty medason peroel chamyrsyn cherdiel avenos nos ear penaon sayr chavelonti genayr pamelron frilcha madyrion onetiel fabelronthos. (conjuratio)
Baruchas Mularchas chameron notiel pedarsy phroys lamasay myar chalemon phorsy fabelrontho theras capean Vear almonym liemo medusan thersiel peatha thumar nerosyn cralnothiel peson segalry madon scoha bulayr. (conjuratio spiritus)
Water of Earth: Symiel (Fertility)
Summary
The 14th spirit in order, But the second under the Emperour of the North is called Symiel. who ruleth as King in the North & by Easte who hath 10 dukes to attend him in the day & a 1000 for the night & every one of these have a certaine number of sarvants…
The Supplementary Conjurations from the Steganographia, Book 1, Chapter XN:
Symiel myrno chamerony theor pasron adiveal fanerosthi sofear Carmedon Charnothiel peasor sositran fabelrusy thyrno pamerosy trelno chabelron chymo churmabon, asiel, peasor carmes nabeyros toys Camalthonty. (carmen ad spiritus)
Symiel marlos chameron pyrcohi pean fruary fabelronti gaelto siargoti melafsor hialbra penor olesy Aiulbrany ordu Casmeron orner vemabon. (conjuratio).
