Assonance is the repetition of similar vowel sounds. 

From A Poet’s Glossary

The following definition of the term assonance is reprinted from A Poet’s Glossary by Edward Hirsch.

The audible repetition of vowel sounds within words encountered near each other. Robert Latham defines assonance as the “resemblance of proximal vowel sounds.” The word derives from the Latin assonare, meaning “to answer with the same sound.” Listen to the interplay of vowels in these lines from Alfred, Lord Tennyson’s “The Lotos–Eaters” (1833):

       And round about the keel with faces pale,
       Dark faces pale against that rosy flame,
       The mild-eyed melancholy Lotos-eaters came.

Notice the repetition of the letters ou in the words round about; the recurrence of the vowels a and e in “faces pale,” which is repeated twice; how the soft a reverberates from the words and to about to dark to against; how the hard a is picked up again in the words flame and came; how the letter o moves as a hard sound from the word rosy to the first syllable of the word Lotos and as a soft sound from the word melancholy to the second syllable of the word Lotos; and how the letter e echoes from mild-eyed to Lotos-eaters. This is “vocalic rhyme.”

John Keats was especially compelled by technical problems of assonance, of vowel music. “One of his favorite topics of discourse was the principle of melody in Verse,” his friend Benjamin Bailey remembered in 1849: “Keats’s theory was, that the vowels should be so managed as not to clash one with another so as to mar the melody, –– & yet that they should be interchanged, like differing notes of music.” Keats’s verbal tactics of repetition and variation, his subtle way of mixing long and short vowels, enabled him to fashion a sonorous music, and his vowels dilate the line into a numinous presence, creating a feeling both of intensity and spiritual easefulness. One notices, for example, how he grasps and modulates the pitch of a nightingale across several lines of “Ode to a Nightingale” (1819), how suggestively he invokes “a light-winged Dryad of the trees” who

             In some melodious plot
       Of beechen green, and shadows numberless,
            Singest of summer in full-throated ease.

One hears the letter i in the words In, singest, and in again; the hard e repeating in beechen green and coming back in the word ease; the soft e echoing softly in the words numberless and Singest; the letter o vibrating from melodious plot to shadows and full-throated; and the letter u echoing from numberless to summer and then taking on a different valence in full-throated. All this imitates the effect of a nightingale singing melodiously in the trees.

Assonance preceded rhyme in the early verse of the Romance languages, Old French, Provençal, and in Spanish, where it was a characteristic coordinating element. For example, each strophe or laisse closes with the same vowel sound in the epic Chanson de Roland (The Song of Roland, ca. 1090), the oldest surviving major work of French literature. As a binding element, assonance was later replaced by rhyme in European poetry. Nonetheless, poets have continued to experiment with assonance as an echo chamber within a poem. Assonance remains a key aural device, subtle and unsystematic, a form of internal vowel play that pleases the ear.

See also alliteration, rhyme.

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