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I was wondering if someone knew the word that describes a poem where each word begins with the letters of a previous word, of if such a word even exists.

An example of such a poem is this: http://crosswords.net23.net/poems/Joshua.html (I wrote it)

Someone told me there was a word for this kind of thing, but he couldn't remember it, either.

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Here's a neat way to find out things like this yourself: OneLook.com on the title of this question – Mitch Sep 5 '12 at 0:03
up vote 13 down vote accepted

You started with an acrostic of 'JOSHUA':

An acrostic is a poem or other form of writing in which the first letter, syllable or word of each line, paragraph or other recurring feature in the text spells out a word or a message.

Each instance after that is new acrostic of the word made from each letter in the original.

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Maybe you could call that recursively acrostic? – J.R. Sep 5 '12 at 0:35
I considered it. :) – cornbread ninja 麵包忍者 Sep 5 '12 at 1:16
As a programmer, I like this description. – lowerkey Sep 5 '12 at 18:49

The scholarly term technopaegnia encompasses all kinds of interplay between the words of a poem and its structure, including (but not limited to) picture poems, acrostics, and other such puzzles. For facts about the term and links to many interesting examples of such poetry – ancient and modern – see my answer to another question.

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+1, Would it be pronounced with a hard 'g' as in "go" or the soft 'g' in "bridge"? – Zairja Sep 4 '12 at 22:12
The usual rule for borrowed Greek is not to pronounce the "g" at all, so "tech-no-PAIN-yah", IPA:/ˌtɛk noʊ ˈpeɪn jə/, US:/ˌtĕk nō ˈpān yə/. See: en.wikipedia.org/wiki/… – MετάEd Sep 4 '12 at 22:54

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