HBO [Home Box Office] - "Different Music!" (Sign-Off, 1976) 

Though this has been uploaded many times by various users, here is the earliest yet known representation (albeit with different music) of the animated sign-off of HBO (or as it was fully referred to in those days, Home Box Office from Time-Life) as used from about 1975 to the point they went to a 24-hour-a-day, 7-day-a-week schedule in 1981.
Includes:
Last few seconds of ending credits for special, Folies Bergere (which originated from the Tropicana in Las Vegas)
Slide with HBO logo and cartoon drawing of dove and baby chicks in nest, with something resembling an actual sign-off accompanied by musical background (voiceover by ??):
"This concludes our schedule of events for today. If you've missed a program, or would like to see one a second time, Feature Presentations are repeated throughout the month on Home Box Office. Consult your Program Guide for exact dates and times."
And finally, the animated sign-off sequence itself, with completely different music from what all other videos show - reminiscent of an MTM sitcom theme (the horn punctuations at the ending HBO logo do match each letter disappearing)
(The later version of this animated sign-off, featuring the more familiar music with heavy emphasis on tom-toms and conga drums, and as aired in 1979 [though its earliest airing in that form may have been 1977], can be seen here - • HBO Sign-Off (1979) )
11 seconds of black, before either recording ends or carrier is cut
This aired on local Texas TV (via cable) early Sunday, April 25th 1976 at about 12:30am.
About The Museum of Classic Chicago Television:
The MCCTv (FuzzyMemoriesTV) is a 501(c)(3) non-profit whose primary mission is the preservation and display of off-air, early home videotape recordings (70s to early 80s, mostly) recorded off of TV (in Chicago or other cities now too); things which would likely be lost if not sought out and preserved digitally. If you have any old 1970s videotapes recorded off of TV please email: tapes@fuzzy.tv Even though (mostly) short clips are displayed here, we preserve the entire broadcasts in our archives - the complete programs with breaks (or however much is present on the tape), for historical preservation. For information on how to help in our mission, to donate or lend tapes to be converted to digital, please e-mail tapes@fuzzy.tv Thank you for your help!