Monody is a poem form inspired by the old Greek odes, and more specifically elegies. It is a poem of grieving, meant to be recited by a single person. As such, monodies do have a tendency to be more personal than other elegies, referencing the feelings of the individual rather than the general opinions of a group.
Allegorical poetry refers to any poem in which allegory is a major element, but when calling an entire poem an “allegorical poem” we would usually understand it to mean that the entire poem is an allegory. Specifically, this means it is a poem with a specific moral, political, or spiritual message as its main purpose.
Slam poetry is a type of competitive poetry that emerged after Marc Kelly Smith started holding competitions in the 1980s, coining the term “poetry slam” for these events. Slam poems are prepared with an emphasis on vocal delivery and audience engagement. They’re as much about the performance as the poem.
Gwawdodyn Byr is a Welsh meter based on quatrains that is nearly, but not quite, isosyllabic. It features two nine-syllable lines followed by two ten-syllable lines, with a single rhyme sound that appears on all four lines. The sound appears at the end of lines one, two, and four, but in the middle of line three.
The Gwawdodyn verse form is the 20th of the codified Welsh meters. This form is made up of quatrains comprised of distinct couplet forms that are, themselves, other members of the codified meters. More specifically, a Gwawdodyn verse will be a Cyhydedd Naw Ban couplet followed by either a Toddaid or a Cyhydedd Hir.
Jintishi, or regulated verse, is a group of Chinese poem forms that rely heavily on tonality and rhyme, traditionally written in couplets. This particular form is so entrenched in tonality that there is no true English equivalent, since the English language has a limited relationship with tone compared to Chinese.
While you might hear that the gogyohka is a short Japanese poem form and mistakenly conflate it with the extremely popular haiku, the two are not related. The gogyohka is a modern invention of the Japanese poet Enta Kusakabe (born 1938) and only has two simple rules. It is five lines long. Each line is one phrase.
Masnavi (or mathnawi) are a poem form that emerged from the middle east, and most likely the Persian empire, sometime between the 4th and 10th century. The form is entirely comprised of couplets, though triplet variants exist, with isosyllabic lines of either ten or eleven syllables and varies from region to region.