ORIGINAL: Roflcopter
In the US (and I think in most countries) you can only copyright entire songs, not individual melodies nor phrases.
The first 9 notes of Fur Elise (Beethoven) have been a trademark since 2003.
http://www.furelise.com/
To clarify some important points:
1. This does not affect the public right to use this public domain composition
2. Those notes are not copyrighted, they are trademarked (there is a
big difference)
3. Anyone can still play, record, perform, and/or release an original recording of Fur Elise in part or in its entirety
4. Anyone can still use those notes in a musical composition or performance
5. Anyone who uses the composition does not owe any sort of royalties to the trademark holder.
It's important to understand that the "trademark" on those nine notes does NOT mean that the company that owns the trademark has exclusive ownership of them, anymore than Apple has exclusive ownership of the word "apple" or Monster has exclusive ownership of the word monster or McDonald's has exclusive ownership of the name McDonald.
If someone owned the *copyright* to that melody then nobody else could use it without permission (which neither the EU nor the US will recognize). The case cited is one where some company or whatever uses those nine notes as their jingle. Another company could use the whole thing in any other capacity, but cannot (in the EU) use that melody in a way that would infringe on the trademark (which does not even strictly mean that they cannot use those notes, just that the use is restricted to ways that do not infringe upon the trademark).
The decision to allow a company to trademark a portion of a public domain composition may or may not be stupid (I'm not sure it is, personally), but the composition is still in the public domain and the public is in no way prevented from using it.
Let me use a silly example as an analogy of how trademarks work:
Suppose Calvin Klein comes up with a perfume called "Be." They make weird black and white commercials of people staring at a beach with a voiceover that says: "To be or not to be... just Be. By Calvin Klein." They register the quote and the ad campaign as a trademark, NOT in any way that gives them full or even partial ownership of Hamlet, but merely so that you or I cannot create a perfume or some other product called "To Be" or whatever and use the same quote to try and confuse people into buying our competing product.
The critical difference between this and a COPYRIGHT is that anyone can still use the phrase "to be or not to be" in literature or everyday parlance or in corporate communications or journalism or even in certain kinds of advertizing capacities so long as it doesn't infringe on Calvin Klein's trademarked ad campaign. Excatly how "infringement* is established is a *little* gray, but it basically comes down to whether you are creating confusion in the marketplace or using the tagline in such a way that people will think your product is somehow affiliated with the Calvin Klein one.
All of the above is perfectly legitimate and reasonable use and protection of trademarks, both legal and common-sense. What would NOT be legitimate would be if Calvin Klein were to then go out and sue anyone who quoted Hamlet or staged, filmed, or published the play, i.e. if Calvin Klein tried to assert exclusive ownership of the line as though they had a copyright on it. Monster has basically been doing an even more egregious version of this by trying to effectively assert complete ownership of the word "Monster."
People sometimes tend to conflate copyright with trademark and they are not the same thing. A copyright gives you the complete rights to something and generally means that anyone who wants to use it has to get your permission or at least pay you certain prescribed royalties. A trademark refers to some kind of mark (such as a company name, logo, jingle or slogan) that you use to identify your company or product in the marketplace. You do not necessarily have any exclusive rights to that image or text or whatever, but other people or organizations are not allowed to use it to capitalize on your name or reputation. If it is a totally original word such as "Texaco" then you pretty much have exclusive rights only because it would be pretty hard to demonstrate any legitimate use of the word other than to refer to your trademark.
If you trademark a commonplace term such as "apple" then people are only prohibited from using it in ways that would cause confusion. E.g. they can still sell apple pie or candy-apple lip gloss or hard apple cider or write songs about apples but they could not make an apple mp3 player or computer and they'd probably run into trouble if they tried to make apple office furniture.
Cheers.