Final answer:
The type of poetry based on the medieval Nibelungenlied that Wagner devised and which uses alliterative consonant repetition is called an epic.
Step-by-step explanation:
The kind of poetry Wagner devised, based on the medieval Nibelungenlied, which employs frequent alliterative repetition of consonants is known as an epic. Epics are long narrative poems that are usually about heroic deeds and events that are significant to the culture of the poet. This form of poetry often employs a formal and elevated style, as seen in the ancient works of Homer, such as the Iliad and the Odyssey. These poems can be quite extensive and often include measures like the heroic measure, which has been proven effective for narratives due to its stateliness and massiveness, allowing for the use of rare words and metaphors. Richard Wagner's Ring cycle, for example, is a famous modern adaptation of the epic form inspired by the Nibelungenlied, which itself is an epic poem from Germanic oral tradition.