Alliteration is the repetition of a consonant sound, within a line of poetry. Similarly, assonance is also when a sound is repeated within a line of poetry, but it is the repetition of a vowel sound.
In William Blake's "The Tyger," the alliteration and assonance serve to make specific lines of the poem stand out. For example, the first line is alliterative in two places: "Tyger! Tyger! Burning bright." Here both the "t" and the "b" sound are repeated. Essentially, the "t" and "b"are rather harsh sounds. The accompaniment of the exclamation point adds to the intensity of the first line. It is not only seen as yelling, it is seen as speaking down at the tiger as well.
Assonance, given the repetition of a vowel is heard, is much softer. It seems that the speaker of the poem wanted to get the tiger's attention, and then, once received, decided to change his (assumed given the gender of the poet) tone (as if the tiger turned and glared at the speaker).
The speaker's questions come from pure lack of knowledge. The speaker is questioning how the tiger, a creature of God, could be constructed by the same hands which made the lamb. This, too, adds to the back and forth nature of the alliteration and assonance (it seems the speaker is speaking loudly about the tiger and softly about the lamb).
The overall effect of the alliteration and assonance allow certain lines to stand out based upon how one reads the poem. At times, when the line is filled with assonance, the lines come out softer and more musical). When the lines are filled with alliteration, the lines are harsher and more demanding.
Blake relies primarily on alliteration rather than assonance to create an internal rhythmic tension in his poem. Very few of the words begin with vowels, though there is assonance in the line "And what shoulder, & what art," which later connects the "a" in the word "art" to the "a" in "anvil."
The pounding of the consonants in the poem echoes the pounding Blake must have imagined as he pictured God as a smith at his fiery forge. God uses a hammer to beat out the fearful form of the tiger he is creating.
Alliteration brings emphasis to certain moments in the poem that Blake hopes the reader will remember. For example, the most pointed use of alliteration, outside of the refrain "Tyger, Tyger, burning bright," comes at this pivotal moment (we know it is pivotal because it ends in the poem's one exclamation point): "what dread grasp/dare its deadly terrors clasp!" Here, the "d" sound beginning the words "dread," "dare," and "deadly" draws our attention to those three words. They are simple, pounding words, all with a fearsome meaning, and are connected as well by the internal rhyme of "dread" and "deadly." Blake wants to reinforce in our minds that the creation of the tiger is no gentle waltz through a flower garden, but a powerful, aggressive act by a God not afraid of a tiger—a God who is creating a dangerous predator. Blake wants us to ponder the mystery of why—and what kind of—God would create such a creature.