Friday, July 07, 2006

Principal Components Analysis

There is nothing more interesting than merging two different fields of knowledge and discovering that what you know about something can also be applied to another completely different area. Sometimes you might not get tangible results, but changing you point of view can open your mind and help you gain a better understanding on the subject you are dealing with. Two disciplines apparently so different as music and image analysis (both of which I'm keen on) can be linked in several ways. Wonder how? Keep on reading...

Quoting Wikipedia, “principal components analysis (PCA) is a technique for simplifying a dataset. It is a linear transformation that transforms the data to a new coordinate system such that the greatest variance by any projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on. PCA can be used for dimensionality reduction in a dataset while retaining those characteristics of the dataset that contribute most to its variance, by keeping lower-order principal components and ignoring higher-order ones. Such low-order components often contain the 'most important' aspects of the data. But this is not necessarily the case, depending on the application."

Although PCA is a technique than can be applied to any type of data, one of its most prominent uses is in the field of image analysis, reducing the number of bands of an image and thus simplyfing it.

And now, let’s see what all this has to do with music:

I've taken a little break from my recording routine (which, by the way, will not be resumed until the beginning of september, since I'm leaving twomorrow for China and won't be back in two months...), and I have spent sometime trying to find new songs I can cover. When doing it, I have listened to a few tunes with very simple arrangements, but most of them had more complex ones involving several instruments with different sounds and textures, each of them playing a different role in the song.

When you mix piano, guitar, voice, bass guitar and, let's say, horns, into a song, each instrument does not only plays its particular phrases, but also adds its characteristic colour to the mix, and for this reason their roles are different and their lines are not interchangeable. Trying to arrange a song for a set of guitars, all of them having exactly the same sound and tone (this is exactly what I have been doing when recording songs for my raw guitar project), is not as simple as playing all the parts of a tune, each of them with a separate guitar. That will simply not work. One has to analyze the song and "guess" the signature of each instrument, which is made upon what it plays and the characteristics of the instrument itself, and then try to recreate this with the guitar. In other words, if we have n instruments in a tune, we have to play that tune with just one single instrument, trying to capture it essence and preserve wichever elements define it (it might be a matter of rhythm, texture, feeling, sound...or many of this "variables" at the same time). And this is exactly what the analysis of principal components is all about!

While in the field of image analysis principal components are analyzed using mathematical expressions in a purely scientifical way, in music it is more art than science what is needed to perform such an analysis. And that art is something that a musician, as the artist he is (or pretends to be...), should not overlook.

During this months of adapting and arranging songs, I have discovered that I'm getting better at doing this each time, and somehow I'm slowly developing this ability to extract the most importants elements of a tune and "translate" a song from its original format to one that includes just guitars. A good musician should be able to take a simple line and arrange it for a trio, a quartet or a whole orchestra, but also to do just the opposite and simplify (at least in terms of number of different instruments used) any tune. This is not only good for covering songs, but your whole playing is affected, and when it comes to improvise over a complex tune it is easier to dissect the tune into the elements that comprise the backgorund and therefore have a better knowledge of what’s going on (which, rather logically, leads to a better improvisation...)

I do not have the key to show other people how to do this (assuming that more or less I know a bit about it, which might not even be true...), but I can say that it is really fun to do it, so I will for sure keep on doing it and recording new songs. But that, I'm sorry to say, will be after the summer, for now China awaits for me.

See y'all in a couple of months!

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