Experiments

For the following experiments we use a collection of 230 pieces of music, ranging from classical music, such as Mozart's ``Kleine Nachtmusik'', via some hits from the 1960's such as Cat Steven's ``Father and Son'' or Queen's ``I want to break free'', to modern titles, e.g. Tom Jones' ``Sexbomb''.

These songs were segmented into 5-second-intervals, of which every second segment was used for further processing with a total of 17 frequency bands being selected. Following the Lagrange interpolations and FFT we thus end up with 5022 feature vectors representing the 5022 5-second segments of the 230 songs in a 4352-dimensional feature space. These feature vectors were further used to train a $22 \times 22$ dimensional SOM. Due to space restrictions we cannot provide a representation of the resulting map, yet we will use some examples for more detailed discussion.

For most songs the individual segments are mapped onto a rather small number of neighboring units. For example, we find most segments from classical titles mapped onto the lower right corner of the segment SOM. Some titles, such as ``Ironic'' by Alanis Morissette contain both rather soft and very dynamic passages and thus have their segments spread across several clusters co-located with segments from other songs of similar characteristics. However, the characteristics of some songs are too fuzzy to allow precise mapping of their segments and are thus spread across larger areas on the map.

In order to obtain a more compact representation of the musical archive, we create new feature vectors for each song based on the location of its segments. This results in a $22 \times 22$, i.e. 484-dimensional feature vector for each of the 230 songs. These vectors were used to train the $10 \times 10$ SOM presented in Figure 2.

Each song is now mapped onto one single position according to its musical characteristics. For example, we find a rather large cluster of classical music in the lower left corner of this map, including, amongst others, Mozart's ``Kleine Nachtmusik'', Bach's ``Air'' as well as the Andante of his ``Brandenburg Concerto No. 2'' on unit $(0/8)$, next to the ``Moonlight Sonata'' by Beethoven. It is important to note, that the SOM does not organize the songs according to their melody, but rather according to their musical genre, i.e. their sound characteristics. We thus find mapped onto the same unit both Tchaikovsky's ``Schwanensee'' as well as Bette Midler's ``The Rose'', a very soft love song with mostly Piano and Violin passages. Another example for this co-location of Pop and classic titles is Madonna's ``Frozen'', located on the same unit as Bach's ``Fuge in D-Moll'' and the Overture of Rossini's ``Willhelm Tell''.

To pick just one further example, we find Cher's ``Believe'', Robbie Williams' ``Rock DJ'', The Pet Shop Boys' ``Go West'' mapped together on unit $(4/0)$ next to Lou Bega's ``Mambo No. 5'' and Tom Jones' ``Sexbomb'' on units $(3/0)$ and $(5/0)$, respectively.

Figure 2: SOM representing 230 pieces of music