As in does it use a qualitative or quantitative metre, and does it include any rhyme/alliteration/something else with a similar role? I’ve been fascinated with its narrative and characterization ever since I first read an English translation forever ago, but it somehow never even occurred to me until right now to wonder about its specifically poetic qualities.
The really unsatisfying answer is that we don't know for sure. What makes Akkadian poetry poetic is one of the longest-standing problems in Assyriology, and as far as we can tell, there's no overarching definition that works for all texts we consider poetic. At the same time, it's abundantly clear that there's some kind of difference between prose texts and something like the Epic of Gilgamesh, so really the question is what these characteristics are and how they are used in Akkadian texts. I'll just outline the main ones here, based mostly on the introductory notes in Foster (2005), Before the Muses. A good collection of more in-depth essays, on various aspects of poetry in Mesopotamia, is Vogelzang & Vanstiphout (1996), Mesopotamian Poetic Language.
Parallelism
The most obvious characteristic of poetry is parallelism, for which the best example is Ishtar's Descent. Look at the opening lines:
1. To Kurnugi’a, domain of Ereškigal,
2. did Ištar, daughter of Sîn, her ear direct;
3. indeed did direct the daughter of Sîn her ear
4. to the house of darkness, the dwelling of Irkalla...
The structure of these lines is chiastic - lines 1 and 4 contain four names for the underworld, and lines 2 and 3 are almost identical, so you have a nice classic ABBA structure. (For the geeks, ln 2-3 are even internally chiastic: [daughter of Sîn, her ear] [directed] / [directed] [daughter of Sîn her ear]).
In Gilgamesh, we find plenty of examples, such as in Tablet XI (the famous 'flood tablet'):
142. On Mt Nimush the boat ran aground,
143. Mt Nimush held the boat fast and did not let it move.
and
161. The gods smelled the savour,
162. the gods smelled the sweet savour.
Doublets/triplets
I'm putting this as a separate category although there's some overlap with the previous one, because you'll often find similar, but not identical, concepts in doublets. Ishtar's Descent is a full of these, but another good one for variety is Enuma elish:
1. When above was not [yet] called 'heaven',
2. below, the earth not [yet] called by name...
These two lines don't describe the exact same thing in different words, but two separate things in similar words. We find these all throughout Gilgamesh too (again Tablet XI):
244. The Thief [i.e., death] has taken hold of my flesh
245. In my bed-chamber Death abides,
246. and wherever I might turn my face, there too will be Death.
Language use
An important feature of Gilgamesh is that, in its most famous incarnation, it's written in a dialect of Akkadian called Standard Babylonian. This dialect was never actually spoken as vernacular, but was a literary dialect only - think modern fantasy writers trying to write Elizabethan English and getting their thous and thines mixed up, and finishing random verbs with -eth to make it sound older. SB is effectively this, and it does a couple things (not specific to SB, but used frequently in it) that broadly fall under 'language use' to make it clear we're reading (or listening to) poetry:
Word order is different: vernacular Akkadian is verb-final, while SB often puts the verb in the penultimate position.
Words are written differently: vernacular Akkadian had lost its grammatical cases at this point, and SB randomly brings them back. SB also spells many words with Old Akkadian case endings (e.g. mutum instead of mutu for 'death' in our last example). Anecdotally, I recall reading Gilgamesh in class and coming across sentences with no nominative-case nouns but several separate genitives, and our professor just saying "it's Standard Babylonian, just pretend one of them is nominative".
Use of unusual or uncommon words: e.g. ammatum instead of ersu for 'earth' (in the Enuma elish example above).
Simile/metaphor: e.g. when Marduk kills Tiamtu in Enuma elish, he 'hangs her up like a fish for drying'.
Writing layout and metre
A very common feature of ancient writing is a complete lack of punctuation, and Akkadian is no different in this regard. What is notable, however, is that Akkadian poetic texts very strictly conform to keeping coherent parts of sentences on a single line. Sentences will often continue across various lines, but you'll never see a full sentence end at the start of a line, and then a new sentence start on that same line. You'll even see examples of scribes having laid out the tablet structure and then running out of space (on the middle of the tablet here, past the dividing middle line).
There were also certainly metric considerations in some poetic texts, although as Foster (2005: 16) puts it,
Though Akkadian poetry has meter, the same metrical pattern is seldom found many lines in succession. There is uncertainty as to whether metrics were based on syllables, ideas or thought units, some type of quantitative stress, or combinations of these possibilities.
So Akkadian poetry doesn't conform to any strict metric rules, like the ones we find in Graeco-Roman poetry - or perhaps it did, and we just haven't figured out yet what the actual rules were!
In conclusion, Gilgamesh didn't have a poetic 'form' as such, although it can easily be identified as a poetic text. What makes it poetic is slightly nebulous, although there are many aspects of the writing in the Epic that identify it as not prose.
Is there any commentary on characteristics of this poetry being attributed to its originating in being recited aloud rather than read?
I'm thinking of a doc I saw a long time ago about Syrian bards who recite poetic accounts of the battles between Christians and Muslims during the Crusades...also, of course, Homer and his fellow bards reciting.
While these tales were eventually written down, they were/are still being recited and can take hours. I'm wondering whether many of the peculiarities you mention become more cohesive if they are thought of as aids to keeping listeners alert with unusual usages that signal the story belongs out of normal time and discourse. (And perhaps reflect a long period of oral transmission where errors in declension and tense crept in.) And of course, they aid the bard to fill out the story and help listeners keep characters and their attributes straight, eg. Ox-eyed Hera.
u/SirVentricle has given a good summary of what we know (there are lines, and often groups of 2, 4, 6, or 8 lines; often we can break those lines into halves and break each half into halves of a word or certain types of phrase; rhyme is not important; any kind of rule people can think of seems to have exceptions). So I'll link to two modern performances of Babylonian literary works:
- the coming of the Flood from the Standard Babylonian Epic of Gilgameš by Lorna Govier of the Southwest Harp Project and Dr. Anne Kilmer of University of California Berkeley. I'm not sure about her pronunciation but at best most of us speak Akkadian with a strong German accent.
- The Poor Man of Nippur by some people at Cambridge
How close either is to anything someone might have listened to in antiquity I can't say, but can take what we know, try out different theories and different living traditions (traditions of singing the psalms are one common inspiration) and then go back to the texts with new ideas.
