This is not an easy question to answer. Each song would be judged on an individual basis as to whether it meets the burdon of a fair use defense to copyright infringement as a "parody." You should consult with an entertainment attorney.
Oh boy, does this scream "sue me!"
As my colleague noted, each work would need to be considered and you already alluded to your answer: "All the songs are parodies, but none of them really have much to do with the songs they're set to." If that is the case, then these are more than likely NOT true parodies, which would require that they comment in some way either on the work itself, the message or the artist.
If it is feasible, I would seek a license (permission) to do any of this. At a min, you should have an IP lawyer review all the content to get an opinion before you put it out there. Keep in mind as well that even if a lawyer concludes that in her opinion this would be a parody, if the copyright owner disagrees, which happens all the time, you will still get sued and forced to present your defense in court, which can be a very expensive proposition even if you are legally correct.
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I agree with the other 2 attorneys who have posted. Have someone listen to the songs and make sure they're really parodies. They may actually be commentaries on the Tumbler site, which may or may not be something you can do without asking them. Your title reminds me of an "unofficial biography." The fact that the real name of the site "Tumblr" is in your title may be the tip of the iceberg in taking this out of the realm of parody. (For a good example of parody, go to Bad LipReading's YouTube page and watch "Magic Man" which is a parody of a Ludacris song.) Still, you may be able to do this as long as you get good legal advice and follow it.
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Although Tumblr is mostly known as a place to display and exchange illegal porn, it is also widely used for copyright infringement of other materials, as well. If you want to get sued, that is a good place to put stuff. What you describe does not sound like parodies, but rather simply illegal copyright infringement ripping off the artists involved. Disclaimers don't work in bank robbery ("Disclaimer - The transfer of the bank's assets from you to me is not a bank robbery, but rather a charitable redistribution of wealth to persons more in need.") and a disclaimer calling copyright infringement "parody" won't excuse copyright infringement, either. In fact, in your situation disclaimers and attribution are likely counterproductive as they show you had access to the original and knew that copying was illegal but attempted to call it "parody". Yes, I think you need explicit permission from the creators of both works if you don't want to have serious legal problems. Think about it, you were worried enough to get on this site and ask - why was that? Likely, because you crossed the line from legal to illegal and were worried.
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I agree with the other lawyers' comments that if your use of a song does not parody the song itself, you will probably not be protected by Fair Use or the Parody Exception.
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While I agree with my colleagues here that you probably don't meet the tests for 'parody," it's not impossible that with some guidance from a knowledgeable attorney and some changes to your concept and content, you MIGHT meet the test for parody... What I would advise is that you make sure to ask any attorney you approach this: even if you do properly change your content so that it is considered a social commentary and properly combines the elements of the parodied song with Tumblr content, how much will it cost you to defend that position in court against the copyright owners? That is the problem with creating something that is or should be considered legal based on a fair use theory- it costs quite a bit of money to prove it in court. Often times, if the original creator has money and the parody-creator doesn't, that is what predicates the outcome... not the question of whether or not the parody truly is a "legal" parody.
Sometimes in situations in which a new version of a song doesn't qualify as a "parody," the person creating the new version will enter into a co-publishing agreement with the owner of the original song. But the owner of the original song can refuse permission and refuse to enter into such a co-publishing agreement.
Also, in some instances the owner of the original song will allow the new version to be released, but will require 100% copyright ownership in the new version of the underlying musical composition., and an advance to boot.
Btw, if you Google this case: Campbell v. Acuff-Rose Music, Inc., it lays out the requirements that apply in order for a song to be considered a legal "parody."
If it's not a legal parody, a disclaimer will do nothing for you.
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