Quantifying Melodic Similarities

I read a science fiction short story many years ago where the plot involved someone composing the last possible piece of music. Every combination of musical notes had been created. I don’t recall the author (it sounds like something Bradbury or Lieber or Ellison would come up with), or even the rest of the plot and how it was resolved, but I do remember thinking how sad it would be – and that this was not an impossible scenario. There are a finite number of note combinations. That number is, of course, staggeringly large (someone has made a pretty convincing attempt to compute it) but given enough time, we could run out of melodies.

This came to mind as I continued to think about this post about the obvious (to me, anyway) similarities between songs by Joe Ely and Toby Keith. Rob left a comment linking to another comparison of two similar songs; that comparison involved an analysis that went well beyond simply hearing a tune and thinking it sounded very familiar.

And then I began to wonder what the criteria are for determining whether a melody is so similar to another that it can be deemed a violation of copyright. I suspect it’s a pretty subjective judgment – but is it unnecessarily so? Music and mathematics have much in common, more so than I understand, and surely there’s a way to perform an objective computation that would spit out a “percentage match” between two songs. And, indeed, a Google search for “mathematical comparison of two melodies” turns up a number of scholarly articles on the subject.

Then there’s this article with the enchanting title of Statistical Comparison Measures for Searching in Melody Databases (PDF format). Such research has undoubtedly informed the technology behind such music identification software as Shazam and SoundHound, which are so scarily effective as to be, as they say, indistinguishable from magic. In fact, Slate described in layman’s terms the approach employed by Shazam:

Obviously, it’s much more complicated than that, and Shazam’s co-founder, Avery Li-Chun Wang, published a scholarly paper (PDF) describing the technology in more detail. And as good as Shazam is, some think SoundHound works even better (it will also identify melodies that are simply sung into a microphone). Unfortunately, SoundHound’s explanation of its technology laps over into the magical realm with its references to “Target Crystals,” and the company is obviously protecting intellectual property.

In any event, I wonder if these math-based, objective comparisons of melodies have ever been used in a court of law to determine copyright infringement, and if there are any quantified guidelines to be used by judges and juries in making such calls. Gee, if there was only some way of searching a database…