Music is not so multidimensional, it is a mixture of different signals (from different sources of signals - instruments, signers). So,  first step is so called segmentation of signal in small parts. Then you can take one of these parts and compare it with your database of parts of  already known songs.  Actually you can imagine approach, in which you can scale up or scale down each of these parts and change speed of music - slow or fast speed https://en.wikipedia.org/wiki/Speech_recognition#Dynamic_time_warping_.28DTW.29-based_speech_recognition . An example is https://en.wikipedia.org/wiki/Shazam_%28service%29

Makarand, there is a very large volume of research on matching similarity for music. I suggest you start with ISMIR (International Society for Music Information Retrieval) conferences and proceedings, and you should find some here http://www.ismir.net

Thanks for the reply. About multidimensional , I was referring to different features such as tune, timbre, rhythm etc. and music similarity on the basis of these different features present. 

Yes, those are the elements that I understood you to mean, and you will find a lot of information on it in the ISMIR conference proceedings. You will also find information in the International Computer Music Conference (ICMC) proceedings - http://quod.lib.umich.edu/i/icmc/ - although it is less focussed on what you want than ISMIR.