The most popular poetry patterns are rhyming schemes. Before we go on let's first define a stanza. A stanza is a poetic paragraph. Often, when using a rhyming pattern, it is a set of lines whose rhyming scheme is repeated through out the poem. Here's an example of a few couplet stanzas written by a friend, Draegar Bloodknife:

The horse and mule live thirty years
And never knows of wines and beers.

The goat and sheep at twenty die
Without a taste of scotch or rye.

The modest, sober, bone-dry hen
Lays eggs for noggs and dies at ten.

But sinful, ginful, rum-soaked men
Survive three-score years and ten.

And some of us...though mighty few
Stay pickled 'til we're ninety-two!

The tercetis an Italian rhyming form. In a tercet, the first and third lines rhyme, while the second is 'blank', meaning it doesn't rhyme. In rhyming notation it is represented as A-B-A. Dante's Divine Comedy was written in this pattern. Though most of it is lost in translation, there are still a few stanzas in which it is still present in English. The following stanza is from the second canto of Inferno:

And I have come to you just as she wished,
and I have freed you from the beast that stood
blocking the quick way up the mount of bliss.

The quatrain, or the four lined stanza, is probably the most popular rhyming form used. The quatrain uses a variety of rhyming schemes. Anywhere from simply putting two couplets together (A-A-B-B) to the A-B-B-A. Have a look at some other types of quatrain patterns:

A-B-A-B

When their eyes upon Cereberus glanced,
Their silenced hearts all filled with dread.
Hades' fires in all six eyes danced,
As he guarded the gates of the dead.

A-B-C-B

She stood at the bar of justice,
A creature wan and wild,
In form too small for a woman,
In feature too old for a child.

("Guilty or Not Guilty?" - Author Unknown)

A-A-A-B

The maenads came with fierce eyes,
And wrapped their hands around their prize,
Lightning flashed and lit the skies-
The earth with thunder shook!

A-B-A-C

And as her last song wailed into the night
Oh, have you heard the Centaur Harper?
The Dear Harper Steed took heed of her plight.
Oh, the Centaur Harper with eyes of frost.

One of the most famous of poetry forms is the sonnet. Sonnets have two parts: the octave, or setup, and the sestet, or conclusion. There are actually more than one type of sonnets, here is a diagram of  the rhyming scheme of one of the more popular styles of sonnet, used by Shakespeare:

Octave - A-B-A-B-C-D-C-D (introduces situation or problem)

Sestet - E-F-E-F-G-G (suggests a conclusion or solution)

Sonnet #147 by William Shakespeare

My love is as a fever longing still,
For that which longer nurseth the disease,
Feeding on that which doth preserve the ill,
Th' uncertain sickly appetite to please:
My reason the physician to my love,
Angry that his prescriptions are not kept
Hath left me, and I desperate now approve,
Desire is death, which physic did except.

Past cure I am, now reason is past care,
And frantic-mad with evermore unrest,
My thoughts and my discourse as mad men's are,
At random fron the truth vainly expressed.
For I have sworn thee fair, and thought thee bright,
Who art as black as hell, as dark as night.

The ballade (pronounced "bah-LAYD" not "BAH-led") is a French poetry form (literally "a dancing song"). It is a four stanza poem in which the last line of all is the same.

The first three stanzas have the following rhyming scheme:
a-b-a-b-b-c-b-C

The last stanza is shorter:
b-c-b-C

Here is a poem that is an example of word play, a little poem I wrote called "Westly's Escape"

Walking one day through the bestial wilds was Westly, a hero true
Every beast he came upon without a glance would let him simply walk through
Smirking to himself he walked up to a giant timberwolf and spat
The timberwolf glanced at him and said, "Boy, I wouldn't do that"
Looking for a way to escape, Westly began to back away from the beast
Yet the wolf began to advance and Westly soon found himself deceased
Startled his soul awoke amongst the howls and screams of the underworld.

Easily he leapt to his feet and ran through bridges and fire and gates
Stopped only to jump past lava swept rocks and dodge a couple of fates
Coming finally to a large gate of bronze he paused to look at the sky
Alas it was still blocked by earth, not a hint of the sun could he spy
Pushing himself on he finally managed to slip from Hades fiery grasp
Evening had come, no hint of the sun, "It took me 2 minutes!" he gasped.

If you write down the first letter of each line, in order, you find that they spell out the name of the poem "Westly's Escape". This is an example of an acrostic, which means literally, "outermost line of poetry". As a literary form, the basic acrostic is a poem in which the first letters of the lines, read downwards, forms a word, phrase or sentence. Another variation of this is the "double acrostic", where the first and the LAST letters of the line are used, this of course makes rhyming nearly impossible, but who says you always have to rhyme?  Nonrhyming poetry is refered to as a blank verse.
Even though "grasp" and "gasped" in the last two lines of the second stanza do not make a true rhyming combination, they sound similar enough to create the same effect. When you use an unlike, yet very similar sounding, word to complete a rhyme it is called assonance.

Here is an example of blank verse, or nonrhyming poetry, by Milton...

Abhorred Styx, the flood of deadly hate,
Sad Acheron of sorrow black and deep ;
Cocytus named of lamentation loud
Heard on the rueful stream ; fierce Phlegethon
Whose waves of torrent fire inflame with rage.
Far off from these, a slow and silent stream,
Lethe, the river of Oblivion, rolls
Her watery labyrinth, whereof who drinks
Forthwith his former state and being forgets,
Forgets both joy and grief, pleasure and pain.

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