I haven't watched this show, but I used to be a linguistics nerd, and I'm highly skeptical of the claim that these chants are written in actual Sumerian. I think they're just a mishmash of English and English-looking nonsense.
First, the case against the Sumerian theory. Disclaimer 1: I'm assuming that these passages are appearing as the creators intended and we don't have a case like the disaster in the Del Rey release of Negima Volume 6, where we had appendices full of complete nonsense being passed off as Greek because the translators had tried to transliterate the Greek into the Roman alphabet based on Akamatsu's transliteration of the Greek into katakana. Disclaimer 2: I'm no expert on Sumerian. But these passages don't pass the sniff test.
The phonology doesn't match the postulated Sumerian phonology
Let's look at a passage of transliterated Sumerian:
An adab to Bau for Luma (Luma A)
1. dumu an-na an gal ki gal-ta šag4 kug-ga-ni im-mi-in-pad3-de3
2. nam-nin kalam-ma-kam bi2-in-tum2-en
3. dba-u2 dumu an-na an gal ki gal-ta
4. šag4 kug-ga-ni im-mi-in-pad3-de3
5. nam-nin kalam-ma-kam bi2-in-tum2-en
6. den-lil2-le e2-kur za-gin3-ta
7. ki-sikil ama dba-u2 igi zid mu-un-ši-in-bar
8. /en\ dnin-ĝir2-su gal-bi mu-un-na-an-du7
9. kur gal den-lil2-le e2-kur za-gin3-ta
10. ki-sikil ama dba-u2 igi zid mu-un-ši-in-bar
(From http://etcsl.orinst.ox.ac.uk/cgi-bin/etcsl.cgi?text=c.2.3.1&display=Crit&charenc=gcirc# at Oxford University's Electronic Text Corpus of Sumerian Literature. The transliteration is described here)
Notice what's missing? There are no initial clusters, like we see in granzizel and tron. There are no dipththongs, as we see in seilien and raizen. There is no f, as we see in bilfen and coffin, or v, as we see in various, or o, as we see in zeios and shou, or w or y, as we see in balwisyall. There seem to be no doubled l's, like we see in kellter, or c, as in nescell.
[...] syllable initial consonant
clusters were prohibited by Sumerian phonotactics [...]
— Aleksi Sahala, "Sumero-Indo-European Language Contacts", page 11.
(There is some argument on this point. Cuneiform is a mixed logographic/syllabic writing system—a little like Japanese, actually. Most sources state there were no initial consonant clusters, but Encyclopedia of Linguistics says that although the cuneiform system "precludes the writing of initial and final consonantal clusters, it is quite likely that Sumerian did have them." We know this is true of Mycenaean Greek written in Linear B, for instance—like English written in the Japanese system, a Greek word like khrusos is written in Linear B as kuruso.)
The vocalic system is quite simple: /a/, /e/, /i/, /u/. The possible existence of an /o/ vowel remains unsubstantiated.
— Encyclopedia of Linguistics, page 1046
And
To the
best of today’s mainstream science, Sumerian consists of the following consonants:
{ b , d , g , p , t , k , m , n , ĝ , l , r , h , s , z , š , () }
— Ioannis Kenanidis, "Yet Another Suggestion about the Origins of the Sumerian Language", page 31
Because Sumerian is incredibly ancient—it's the first known written language—and so much of it has come down to us through Akkadian scribes, who kept using it after it was dead because they thought it was cool, and because of the difficulties with the writing system that I alluded to above, there's a ton we don't know about it. No one believes the reconstructed phonology is 100% correct, or even 90% correct. But what we see here is too far off base to be taken seriously as an attempt to write Sumerian according to a reconstructed phonology.
You can see where they cribbed from
Whatever language this is, it includes the English words various and coffin, as well as killter, which looks a lot like kilter, as in "off kilter". The word baral in the swan song looks like it comes from Hebrew בלל (balal), which means "to confuse" or "to mix" and is apparently the source of the word "Babel". It uses the English form of ziggurat; the Akkadian form is ziqqurat, while "ziggurat" comes from the Hebrew form זיגוראט (zygwrʼt).
That doesn't automatically disqualify it as a real language; after all, in the Australian language Mbabaram, dog means "dog". But, combined with the widespread use of English for mysterious and exotic things in anime, this makes me highly suspicious of any claim that the sentences are Sumerian or any other language.
Aside from that, the sentences conform remarkably well to English phonology. Almost all of these words are easily pronounceable to an English speaker. The ones that look a little weird, like zeios and rei, show some pretty clear Japanese influence.
Machine systems can't make heads or tails of it
I fed all the activation chants and the swan song to Google Translate and Translated.net Labs's language detector, both together and individually. I wasn't expecting it to translate them, but I was hoping it would detect what language they were.
As a side note, machine translation still sucks, but this kind of language detection is supposed to be pretty good; Russel and Norvig claim in Artificial Intelligence: A Modern Approach that computer systems can identify languages, even based on short texts like "Hello world" and "Wie geht es dir", with greater than 99% accuracy (AIMA 3ed., page 862).
None of these systems can detect Sumerian or Akkadian, but they can detect most modern languages, even some quite obscure ones. The general consensus was that the activation chants have a Germanic flavor (Google Translate pegged them as English, even after I deleted the words various and coffin, while another service took them as Frisian, a Germanic language closely related to English), while the swan song was taken as Indonesian. Google Translate insisted that both texts together were English, while Translated.net took both texts together as Sundanese.
For comparison, I took a passage from Shakespeare's Titus Andronicus and a few lines from The Who's "Call Me Lighting", shoved them together, and fed them to Translated.net:
so, so; now sit: and look you eat no more
than will preserve just so much strength in us
as will revenge these bitter woes of ours.
marcus, unknit that sorrow-wreathen knot:
thy niece and i, poor creatures, want our hands,
and cannot passionate our tenfold grief
with folded arms. this poor right hand of mine
is left to tyrannize upon my breast;
who, when my heart, all mad with misery,
beats in this hollow prison of my flesh,
then thus i thump it down.
hey little girl who's dancing so lightly, my xke is shining so brightly, the noose around us is slowly tightening, i'm gonna show you why they call me lightning
English, English, and more English. It defies my suspension of disbelief to think that if these passages were all the same language, there would be so much confusion about what language that was.
I have no idea what algorithm Google Translate uses; Translated.net seems to use some kind of nearest neighbors algorithm.
The "translations" are absurd
The translation of Ichaival's chant seems to have been removed from the wikia sometime between when this question was asked and now, which probably doesn't say much for its authenticity. But let's take a look at the one in the OP:
Killter ichaival tron -> Evening draws in the awakened Ichaival
Since all the chants end with tron, that has to be something that makes sense in every chant. Based on the context, I'm going to say that has to be "awakened"; it is an activation song, so it makes sense that they would all be "awakened". So Ichaival tron means "awakened Ichaival". So we can postulate that this language puts modifiers after nouns, like Spanish and Irish.
Then what does killter mean? It has to mean evening draws in. But this is linguistically absurd; it violates constituent structure. draws in is a verb, while evening is a noun. killter can't literally mean evening draws in in a real language (if it does, we've got the makings of a real whopper of a paper in theoretical syntax here—it'll be almost to theoretical syntax what those particles that traveled faster than light would have been to relativity).
killter therefore must mean either evening or draws in, with the other element implied or indicated in some way by the morphology. So we have a language where you can just say draws in, and everyone automatically assumes you meant evening draws in, or a language where you can just say evening, and everyone assumes you meant evening draws in. Some languages, at least in their poetry, do allow you to get incredibly terse like this. Still...I'm not buying it. It reminds me too much of Helge K Fauskanger's analysis of Auld Elvish from Bored of the Rings.
Conclusion
I'm not convinced these are passages from a real language, or even from a somewhat sensible conlang like the Hymnos language from the Ar Tonelico series. All my instincts are telling me they're just gibberish courtesy of the people who gave us a determination to fist. I wish I knew where the "translations" came from or why they spread around the online anime community, a community generally obsessed with the minutiae of dead languages, which surprised the Japanese production staff of Madoka with its determination to translate the runes.
