Assonance occurs in Frost but not as effectively and deliberately as in Swinburne, Tennyson and others who used it as part of their poetic theory. Actually assonance was a poetic device that Frost was trying to avoid. He wrote this in a letter dated July 4, 1913 to John Bartlett:

"I am probably the only person going who works on any but a worn out theory (principle I had better say) of versification. You see the great successes in recent poetry have been made on the assumption that the music of words was a matter of harmonized vowels and consonants. Both Swinburne and Tennyson arrived largely at effects in assonation. But they were on the wrong track or at any rate on a short track. They went the length of it. Any one else who goes that way must go after them. And that's where most are going. I alone of English writers have consciously set out to make music out of what I may call the sound of sense."

 
Review the definition of assonance:
Assonance The relatively close juxtaposition of the same or similar vowel sounds, but with different end consonants in a line or passage, thus a vowel rhyme, as in the words, "same day." Assonance does not occur simply by having the same vowel spelling, eg. lost and most.
 
Tennyson uses assonance in its definitive way. See his poem, "The Lady of Shalott." Now, where does this leave Frost? Assonance and consonance can be found in Frost, but more incidentally. Frost's idea of sound culminates in his own theory which he called "the sound of sense." This is a tricky thing to understand, but it is important to understand definitive assonance and see that Frost is not practicing it. This is not to say you will never find it in his poems. Frost was after the sound of sense - putting word sounds together poetically which result in meaning and most importantly TONE. He makes you say certain lines a certain way - with a tone of voice we all seem to recognize and adhere to. This is what "SOUND" means to Frost.
Lord Alfred Tennyson,   1809–1892 
   
 "The Lady of Shalott" 
   
PART  I                                Assonance - say the lines and hear it

ON either side the river lie                                                  side....lie  (long i's -  si and li )
Long fields of barley and of rye,   
That clothe the wold and meet the sky;                             clothe...wold (long o's  -  clo and wo) 
And thro' the field the road runs by   
          To many-tower'd Camelot;          5 
And up and down the people go,   
Gazing where the lilies blow   
Round an island there below,   
          The island of Shalott.   
  
Willows whiten, aspens quiver,   10 
Little breezes dusk and shiver   
Thro' the wave that runs for ever   
By the island in the river   
          Flowing down to Camelot.   
Four gray walls, and four gray towers,   15 
Overlook a space of flowers,   
And the silent isle imbowers                                               silent isle  (long i's)
          The Lady of Shalott.   
  
By the margin, willow-veil'd,   
Slide the heavy barges trail'd   20 
By slow horses; and unhail'd   
The shallop flitteth silken-sail'd                                          silken....
          Skimming down to Camelot:                                      Skimming   (short i's  - il and im)
But who hath seen her wave her hand?   
Or at the casement seen her stand?   25 
Or is she known in all the land,   
          The Lady of Shalott?   
  
Only reapers, reaping early   
In among the bearded barley,   
Hear a song that echoes cheerly   30 
From the river winding clearly,   
          Down to tower'd Camelot:   
And by the moon the reaper weary,   
Piling sheaves in uplands airy,   
Listening, whispers ''Tis the fairy   35                        listening whispers "Tis  (short i's, lis, whis and tis)
          Lady of Shalott.'   
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