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There are many types of palindromes, though I havent seen one that reads forward and backward letter by letter while rhyming, nor one set to note-palindromic music.
Ive heard symmetric music (the last half being the same as the first backwards) that sounded satisfactory, and believable palindrome
lyrics can be fashioned or found.
A word by word palindrome like the one below set to symmetric music might make a pleasantly balanced tune, though keeping the listener forever wondering if it was the forward or backward version that was sung:
Love is This and This is Love
Darling, my love
Is great, so great;
Recalling Heavens calm above.
Fate is sweet this--
All after Fall!
Fall? After all,
This, sweet, is fate--
Above calm Heavens recalling.
Great, so great is
Love, my darling!
I palendrome I
Has a bit of palindrome in it (starting with "son I am able"), though I don't thing the tune is palindromic. [Worldgineer, Apr 25 2005]
The Inverted Crab Canon (scroll to bottom of page)
This is music which reads the same when you turn the page upside down - very clever. [hippo, Apr 25 2005]
Lyrics to Weird Al's "Bob"
[krelnik, Apr 25 2005]
[Ian Tindale, Apr 25 2005]
||"I, man, am regal - a German am I
Never odd or even
If I had a hi-fi
Madam, I'm Adam
Too hot to hoot
No lemons, no melon
Too bad I hid a boot
Lisa Bonet ate no basil
Warsaw was raw
Was it a car or a cat I saw?"
Weird Al Yankovic
||I'm really tempted to bake this.
||Just reading this over, I feel oddly baked as it is.
||So if I held it upside down in front of a mirror, and sang it to the tune of "Oh My Darling", everything would be ok? (+ For the description alone.)
||Hippo, that's my favorite song on Weird Al's most recent album.
||I have a ginger cat called
||Go hang a salami, I'm a lasagna hog.
||Linked inverted canon: Why does it seem that notes 3 and 4 on the upper treble clef don't match the inverted music (ditto for notes 6 and 7 on the lower clef)?
||My choir actually performed a piece written for us a few years ago. It was titled simply "Palindrome", and it was a word-for-word palindromic poem set to a palindromic melody. It was pretty funny, actually, if a little dissonant, and exaordinarily difficult to sing.