Following Tolkien's bugle-cry in the thirties, the most general trend in Beowulf studies has doubtless been the approach to the poem itself as a successful artistic product. Subsequent critics have found one element of the poem after another to be significant in ways unsuspected by Ker.  I propose to contribute to this well-advanced trend not by demonstrating a new system of significance operating throughout the text, but by the detailed examination of a few lines with reference to their semantic and phonetic content. 
In general I think the relation between the two in poetry is similar to that between signifier and signified in language as a whole: that is, their association may be originally arbitrary, but it becomes meaningful once the correspondence is established, though the relation is always more aptly characterized as a pursuit of one by the other than as an equivalence. In an aesthetic text, moreover, such relations are legitimately read as highly determined and determining without any necessary implications regarding the intentions or the powers of the author. Indeed, an intentional effect unperceived by a given reader does not exist for that reader, and what seems to the reader to be designed functions for that reader as meaningful, whatever the writer’s intention.
In fact the significant relation between signifier and signified is constitutive of literature, and thus analysis of any sample of an accomplished poetic text will reveal what I find in the case of Beowulf, namely that most of the sound-sense ratios are indeed direct or inverse. In either case one may be said to reinforce the other.  (Those which do not serve such a relation may be considered unassimilated data with an unknown meaning or simply the random noise which inevitably accompanies any expression. )
I choose to examine the last sentence of the poem, lines 3178-3182, not because I expect any greater degree of artfulness in a rhetorical conclusion. Rather, I would claim that the same operation I undertake here might be done with equally good results in any other portion of the text. However this is not to say that the lines are uninfluenced by their placement within the poem as a whole. Even if the passage is found to declare itself the conclusion; indeed, even if it were known to be dense and more carefully “worked over” for that reason; it would not necessarily be more highly determined. 
The semantic content of the lines is clear and straightforward, more so in fact than much of the poem. Beowulf is dead, the poem that bears his name is in a sense already over. Lines 3178-3182 simply tell us that his people mourned for him as the best king on earth. The structure of the expression of this simple statement is not itself, however, simple. The semantic content may be described as doubly symmetrical in its presentation. The first hemistichs as a group have a unity balanced by that of the second hemistichs. Further, lines 3178-3179 are a group while 3181-3182 are another with 3180 as a transition.
The first half-lines possess a certain obvious continuity in that they may be read with no reference whatever to the second half-lines and the basic sense of the passage (indeed, its grammatical integrity, too) does not suffer. The second half-lines do reinforce and enrich that sense, but in no simple pattern of echoing what has just been said. 3178b and 3179b are largely synonymous as are 3181b and 3182b. The first pair names the mourners, the second names the qualities of their king, and the central one names their linkage in the institution of monarchy. Thus the second half-lines restate in their periodic way the same idea stated in the first. The right side of the page may also be independently read though grammar and syntax suffer in the version of the story given there.
Turning to the other symmetrical axis, one notes that the first half of the passage contains the essential message “the people mourned for their king” while the second half explains his qualities which make clear why they mourned and what they said while mourning. The middle line 3180 is abstract, cleansed of specificity, saying only that people spoke of a king. It stands between the particulars concerning the people's mood and those of the king's nature. The first half of this pivotal line restates the content of the previous two lines and the second half foreshadows the last two.
The five lines as a whole might be thought to represent the entire poem in miniature, for surely Beowulf may be accurately described as a verbal memorial offered up to the dead leader. Thus the linguistic activity that concludes the poem is identical with the poem as a whole. In fact the very last word is an even more condensed epitome: lofgeornost. This is the only occurrence of the word in the entire text, almost as though it were reserved for this capping location. It suggests not only the nature of the poem itself (praise invested with emotion) but also recalls the whole pattern of behavior that might elicit such praise and the centrality of the relation between lord and warriors which provides such a great share of the thematic meat throughout the text. 
Analysis of sound patterns is notoriously liable to slip over into super-subtlety, but I will here have space only to consider the most apparent of effects, those which will be most likely accepted as genuinely operative. The available data are set forth in these arrays:
3178 a e o o o ea a eo e
3179 a o e y e eo e ea a
3180 ae o ae e ae e y u y i a
3181 a a i u o o ae u
3182 eo u i o o o eo o
3178 sw b gn rn d n g t l d
3179 hl f d shr r h rthg e t s
3180 cw d nth t h w r w r ldc n ng
3181 m n m ld st ndm nthw r st
3182 l d ml th st nd 1 fg rn st
The following observations seem most important for these data:
1) Alliteration is stronger in 3181-3182 than in the other lines.
2) The open vowel sounds of the first hemistich are similar to those of the last.
3) 3178b provides a vowel pattern repeated in 3179b and then carried over and expanded in 3180a.
4) 3180 contains an abundance of sounds not found elsewhere, both vowels and consonant clusters
5) The superlative -st which ends each of the last four hemistichs had not occurred before.
6) The m's and n's of the last two lines are prefigured in the three n sounds of begnornodon.
Certain reinforcement of semantic patterns is obvious. The structure of the alliterative line insists that the second hemistichs are redundant of the first in a broad sense. A number of characteristics bind the last two lines and set apart the middle line. The semantic equivalence of 3178b and 3179b is underlined by their similar vowel patterns which then provide a transition into the turn of the central line. Not having analyzed sound patterns in the whole poem I have no evidence that the function of the end in epitomizing the whole is phonetically reproduced. The only really new element produced by the phonetic survey is the added impression of unity one gains in seeing the reminiscence of 3178a in 3182b. Much information remains in the arrays which might be called the “narrative” (because non-recurring) sound pattern.
This brief survey of sound and sense relation in a five line passage should emphasize yet again the sophistication and complexity of the poem's texture, though it does not imply any conclusion about the literacy or training of the poet. Indeed, conventions of style and of sentiment make density of signification at once more easily realized and more easily neglected. A poet working in a prescribed and artificial tradition may either flat-footedly supply his readers' expectations (and thus signify less) or, by a very minute distortion of those same expectations, he may signify more efficiently. In Beowulf the divided line, the alliterative pattern, the storehouse of phrases that belong to the heroic ethos are efficiently used to convey more, I think, in shorter compass than one would find to be the case with most contemporary poets not supplied with a closed tradition.
1. The implications of this for literary historical reconstruction may go in either direction. One might see in his artistry proof either of book-learning or of the oral tradition.
2. If I were to seek a more modern bugle-cry than Tolkiens, I might find it in Eco’s advocacy of the “semiotic civil rights” of ever smaller elements in the stuff of the work. (p. 268, A Theory of Semiotics [Bloomington: 1979]).
3. In the case of an inverse relationship the stakes would be raised a bit, and one would be justified in speaking of ambiguity, irony, and the metaphoric “lie.”
4. Alternatively, one might call this "meaningless" component the constitutive bearer of that desirable residue of mystery which allows the work to retain after interpretation its original quantum of aesthetic mana.
5. My opinion is the opposite, that more is likely to be encoded in a passage if the “purpose” of the passage is not apparent, though sometimes a high degree of motivation can allow the writer to deceive himself and the reader. I am thinking of such instances as Pound’s translations where he felt justified in doing as he pleased since he had an original as his excuse.
6. Normally in French romance the second half line will be more likely wholly conventional just as the rhyming line of a couplet (the second) will. The poet has license at first, but must obey his formal imperative after.
7. Lof by itself occurs only once also. It is applied in a sense similar to this in line 1536 (very nearly the midpoint of the poem) just before Beowulf fights Grendel's mother.