Thanks to my new scanner, here's the whole enchilada. The lyrics are by Howard Dietz, who also wrote standards like "Dancing in the Dark," "That's Entertainment," "By Myself," "You and the Night and the Music," and one called "Smokin' Reefers."

"Triplets" from Between the Devil is a curious kind of comedy song, a narrative ballad in which Dietz has employed somewhat made-up names for cities and people. What is curious is that these names might easily have been created for rhyming purposes but such is not the case. The use of Baden Baden Baden and Walla Walla Walla, of course, suggests that each of the triplets says one of the words.
The proper names are matched syllabically as to length but are in no way meant to rhyme: Mrs. Whiffenpoofer. Mrs. Hildendorfer, Mrs. Hassencooper, and Mrs. Goldenwasser, plus later, Doctor Heimerdinger.
The layout is also somewhat unusual. There are a verse, chorus, interlude, and two choruses. At the same point in the three choruses (eighth and ninth line ends) we have words ending with 'les' or 'els,' which make the same sound:
measles (twice), vittels (sic), bottles, battles, rattles. There is a curious a rhyme in the interlude: day. major. Lane, day.
(Lehman Engel, Their Words Are Music, 1975)

The song was written for the 1937 musical Between the Devil, and revised for the 1953 film version of The Band Wagon. Personally, I think the song is obnoxious, but I have to admit is made one of the most memorable scenes ever filmed - Fred Astaire, Nanette Fabray, and Jack Buchanan, all in baby clothes.
-Joe Offer-

TRIPLETS
(lyrics by Howard Dietz, music by Arthur Schwartz, 1937)

Three little unexpected children simultaneously.
The doctor brought us and you can see
That we'll be three forever and aye-e-i---Oo.
You wouldn't know how agonizing being triple can be;
Each one is individually
The victim of the clinical day-e--i---oo.
Every summer we go away to Baden Baden Baden,
Every winter we come back home to Walla Walla Walla.
We do everything alike,
We look alike, we dress alike,
We walk alike, we talk alike,
And what is more
We hate each other very much.
We hate our folks. We're sick ofjokes.
Oh what an art it is to tell us apart.
If one of us gets the measles,
Then all of us get the measles,
And mumps and croup.
How I wish I had a gun,
A little gun - it would be fun
To shoot the other two
And be only one.

Mrs. Whiffenpoofer loves to talk to Mrs. Hildendorfer
Of the day she went to Sloan's and had her silly Willie.
Mrs. Hassencooper loves to talk to Mrs. Goldenwasser
Of her major operation when she had her twins.
But when mother comes along she silences the others,
She accomplished something that is very rare in mothers.
For example just to prove that she was more than ample
She admits Lane Bryant thought they were measuring a giant.
Doctor Heimerdinger almost broke his middle finger
On the day that he first looked upon us three.

We do everything alike,
We look alike, we dress alike,
We walk alike, we talk alike,
And what is more,
We hate each other very much. We hate our folks.
We're sick of jokes.
Oh what an art it is to tell us apart.
We eat the same kind of vittels,
We drink the same kind of bottles,
We sit in the same kind of highchair (highchair, highchair).
How I wish I had a gun - a little gun.
It would be fun to shoot the other two
And be only one.

We do everything alike,
We look alike, we dress alike,
We walk alike, we talk alike.
And what is more,
We hate each other very much.
We hate our folks. We're sick of jokes.
Oh what an art it is to tell us apart.
We play the same kind of soldiers,
We fight the same kind of battles,
We shake the same kind of rattles.
How I wish I had a gun - a little gun.
It would be fun to shoot them other two
And be only one.

JRO