General terms:
* Elegy: This is the most common and specific term for a poem lamenting the death of a person or thing.
* Lament: A broader term that encompasses any poem expressing sorrow, grief, or regret.
* Dirge: A somber song or poem, often used for funerals or mourning.
* Threnody: Similar to an elegy, but often with a more intense and passionate expression of grief.
More specific terms:
* Mourning song: A song or poem expressing grief, particularly for a deceased loved one.
* Wailing song: A lament that emphasizes the emotional intensity of sorrow.
* Complaint: A poem that expresses a specific grievance or complaint, often with a melancholic tone.
* Sonnet of grief: A sonnet that focuses on the theme of sorrow.
Ultimately, the best term for a sorrowful poem depends on its specific content and style.