What an excellent question, and it has three parts:
- Tennyson borrows from Edmund Spenser
- phonetics contribute significantly to the tempo and tone
- repetition contributes significantly to the tempo and mood
- language contributes to the tempo
Tone is the narrator's or rather the poetic speaker or persona's emotion toward the subject. Mood is the emotion within the literary work. Sometimes these might be the same, i.e., the persona and the characters might have the same emotions, while sometimes these might be different, i.e., the persona and characters might have different emotions. One example of the possible differences is that the persona (or narrator in prose) might feel scorn for the characters while the characters feel fear.
Starting with repetition, the coda of stanza one repeats at the end of each stanza with a profound variation in the last. The coda,
She only said, 'My life is dreary,
He cometh not,' she said;
She said, 'I am aweary, aweary,
I would that I were dead!'
with its internal rhyme and repetition, slows down the tempo of the four stanzas and emphasizes the sad, slow tempo of the final three stanzas. Thus repetition helps makes the lines from "And ever when the moon was low," to "'O God, that I were dead!'" so sad.
Now we'll go to Edmund Spenser. Spenser is renowned for constructing poetry from individual letters upward. He doesn't start with the right word or the right image; he starts with the right sounds. The Epithalamion is an exquisite example of this as is The Faerie Queene. Space doesn't permit a digression to Spenser's poetry, so suffice it to say that Tennyson employs the same structural approach, which leads us to phonetics, i.e., simply put, the sound of each individual letter or letter group.
Briefly, the first four stanzas emphasize consonants that have "snap" to them; they are voiced and unvoiced plosives [d-t, b-p] and fricatives [v-f] and other short consonant sounds like /n/ /k/ /s/ /sh/. These consonant sounds are quickly pronounced and brisk to the ear. Thus they move the tempo along rapidly until the coda, which slows down because of more slowly pronounced [m, r,w, l, th].
The first line of interest, "And ever when the moon was low," has more sonorous and slowly pronounced consonants [n, v, r, m, z (s), l]. The result is that immediately when you read this line, the tempo changes gears to a long, low mournful, sad slowness. This consonant pattern remains throughout the next stanzas. We didn't talk about vowels earlier but they also play a role. Here, there are many "open" vowel sounds, like [aw, ow, ay], whereas in the first stanzas there were many "close" vowel sounds , like [ee, ere, i, ange]. These also slow down or speed up the tempo adding to or holding back (respectively) a tone and mood of sadness.
Finally, the language of the last coda, which is a variation on the other codas, puts the crowning touch on the sadness while adding a sharp pain with it.
She wept, 'I am aweary, aweary,
O God, that I were dead!'
She wept; she didn't say. She cries out in an apostrophe "O God." The language shows anguish and the letters return to plosives, with [p, t, d]. The shock of the variation to the coda, the reentry of sharp phonetic sounds, and re-energized tempo all add to the intensified sadness that finalizes the poem.