An analysis of a poem begins with determining the meaning of the poem. For "Asides on the Oboe," this is a bit of a difficult task because of the sometimes obscure allusions to other literature that Stevens builds his meaning through.
allusion: a word or phrase capturing a broad, complex idea or emotional reaction in a quick image born of a phrase or word pointing to or taken from a well known and widely understood idea related to a person, place or thing in literature, history, music, popular culture or Classical mythology. [Allusion, an indirect mention of something, is different from reference even though the word "reference" is often used in definitions of "allusion"; reference is a direct mention of a well known person place or thing from history etc.; e.g., indirect allusion, "His ambition is his weak heel" (allusion to Achilles from Greek mythology); direct reference, "Their fraud will make them the next Enron" (reference to the Enron scandal).]
The first allusion in "Asides" is to the conventional structure of books, with the Prologue heading up the introductory pages setting the stage for the discussion comprising the body of the book. Stevens is alluding to the idea that, after having read the prologue, the reader then delves into the serious questions discussed within the text. He states that the question to consider is "final belief," or one's belief in the final reality of life and death. He assumes agreement, "So, say that ...," that our final belief in reality must be a belief in a "fiction," in other words, a myth or superstition. "It is time to choose," means to Stevens that answering the question at hand requires choosing between possible fictions. These opening lines set a despairing existential, absurdist framework for the examination of "fictions" that follows and that are revealed through further allusions.
The next allusion is to T. S. Eliot's post-World War I masterpiece The Waste land (1922). The allusion lies in the words "wide river" and "empty land": "That obsolete fiction of the wide river in / An empty land; ...." Though this seems obscure, those who have read and studied Waste Land immediately recognize the allusion to Eliot's Section III, The Fire Sermon on England's River Thames that runs through a now (post-World War I) empty land:
The river’s tent is broken: ...
... The nymphs are departed.
Sweet Thames, run softly, till I end my song.
The river bears no empty bottles, sandwich papers,
Silk handkerchiefs, cardboard boxes, cigarette ends
Or other testimony of summer nights. The nymphs are departed.
And their friends, the loitering heirs of city directors;
Departed, have left no addresses.
By the waters of Leman I sat down and wept ...
It is interesting to note as an aside that Eliot employs his own allusions in this passage, as in to the Biblical allusion to Psalm 137:1-6 that says in part: "By the waters of Babylon we sat down and wept ...." A second way to see the above "wide river in / An empty land" allusion is to understand it as the river Jordan in the land of the Christian gods, "the gods that Boucher killed," the archaeologist Boucher de Perthes, whose work unearthed the "fiction" of the gods of past eras and revealed the "fiction" of the mythical "metal heroes" (e.g., Menelaus, Achilles) with their images cast in bronze that "time granulates," turning them into "waste" men.
The most difficult allusion is to the "philosophers' man" who "by the sea-side mutters ... immaculate imagery," the "central man, the human globe," who is
As a mirror with a voice, the man of glass,
Who in a million diamonds sums us up.
This allusion of "philosophers' man" is accepted as alluding to Shakespeare, thought to be the greatest poet and seer of humanity of all ages. Paul Murray, writing for Communio in 2000, identifies Stevens' line as an allusion to Shakespeare in "God's Spy: Shakespeare & Religious Vision":
Is it possible that Shakespeare, the man who is arguably the greatest poet of all time, "the man of glass who in a million diamonds sums us up," has failed, in fact, to explore that one fundamental dimension of human life which we call religion .... (Murray)
Two other allusions helpful to identify for the purpose of analysis are "hautboy" and "jasmine scent / And the jasmine islands were bloody martyrdoms." The hautboy is an archaic (ancient) form of oboe, thus central to the title of the poem (a satirical painting by Hogarth shows the hautboy being played and badly received). During Shakespeare's time (1564-1616) Queen Elizabeth I, whom Edmund Spenser styled as the allegorical Queen Gloriana, gave a royal charter (i.e., royal grant to do business) in 1600 to found the East India Company to enter into spice trade in the areas of South Africa, Malaysia (part of the spice islands) and then India. The tropical flowering plant, jasmine, with its intoxicating heavenly scent, is indigenous (i.e., native) to South Africa and the South China Sea islands, like Malaysia.
The East India Company had strong competitors in the Dutch East India Company and in a similar trading concern in Portugal. In the 1612 Battle of Swally against Portugal, the East India Company was victorious though the hostilities between the warring parties slowed the importation of spices, symbolized by the allusion to "the jasmine scent" of the native flowering plant. It is most logical, though critics have no firm consensus on the root of this allusion, that the brief interruption of "one year" during Shakespeare's lifetime of the spice trade, "the jasmine scent," provided the impetus for rethinking the "sum of man."
How was it then with the central man? Did we
Find peace? We found the sum of men. We found,
If we found the central evil, the central good.
We buried the fallen without jasmine crowns.
Now that you have the foundation for unraveling the meaning of the poem through its undergirding allusions, you can proceed with the standard analysis procedure of discussing the elements of theme, structure, point of view (which gives voice), tone and mood. You can then proceed to analyzing the other techniques employed, besides allusion, such as symbolism, imagery, irony, metaphor, personification and other figures of speech (phrasing that means other than its literal meaning).