It is safe to say that the film was shot and mastered, just like Antichrist, with 25fps. It was then printed on 35mm film and distributed (-> 24fps) as needed for the projectors. The official website states a runtime of 130min and a framerate of 25 http://www.melancholiathemovie.com/#_technicalinfo
. In most countries all over the world the Blu-Ray was released with 1080/24p due to no support of 25p in the Blu-Ray specifications and incompatibility with many American hardware devices due to hardware limitations. In Finland and Switzerland, possibly also Sweden, Norway, Denmark and other countries, the Blu-Ray was released with 1080/50i.
I own both the 1080/24p and the 1080/50i transfer and, after some testing, I can tell you that the American/International transfer release is slowed down and the pitch is different. The American/International transfer has a runtime of 136min. The Nordic transfer has a runtime of 130min, like the runtime stated on the official website.
There is an easy way to find out which version is the correct one: By comparing the music of the "Prologue" audio. If you compare the 24p transfer version with the Music CD Version of the Prologue track on the OST and then with the 50i transfer version, you will notice that the Music CD has exactly the same pitch and speed like the 1080/50i transfer.
Another myth that needs to be cleared is the interlacing. Both Antichrist and Melancholia are stored progressively with 25p on the Blu-Ray Disc not 50i. The 50i is just a "container" to trick the Blu-Ray Player and make it take 25p. This is done with some cheating, or probably PsF (Progressive segmented Frame or Progressive Frame segmenting) a way to store progressive video in an interlaced format with 2:2 pulldown. It is even more likely that the film is stored 25p and just flagged 50i with a 2:2 pulldown, much like 60i DVD's contain 23,976 footage flagged with an 2:3 pulldown. Not sure how it is achieved in the case of Melancholia, but the film is in any case progressively stored and recognized as 25fps by for example mediainfo.
But yeah, anyway, it's basically a shame how this film was released, since most of the world watches a slowed down version with the wrong framerate, much like in PAL/NTSC times were people had to watch films in 25/30p instead of the original 24p. But here we are in 2014 with the same problem. Disgusting isn't it? It also baffles me that this topic is not much talked about and just condoned. I'm a purist and I'd like to own a movie in its original representation and not some compromised version. I get the same twitching when I see studios release movies on 25GB single layer Blu-Rays instead of 50GB.
Another thing I am certain of: Lars von Trier doesn't give a crap about all this, let alone framerate.