Mathematical Tools in Music

Is this Music ? Some people are of the opinion that, this type of music (e.g. Xenakis' music) it is NOT MUSIC since:

  1. this music/art does not appeal to the public
  2. it does not seem to express emotions and it seems to be just an intellectual game
  3. it does not have melody
  4. some times a computer makes the final decisions as to what sounds are going to be part of the composition; creativity implies control over the final product, including its details

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First of all, this music does not need to be defended: it is the music of our century (some of it more than 40 years old), written by composers of the same caliber as the ones with more familiar names who died long time ago. The question is not if Xenakis or Cage have done something valid but how could one better understand their thinking. If someone decides that reading Shakespeare or Joyce requires too much effort and throws their books away, the loss is not Joyce's or Shakespeare's.

Here are some answers to the statements listed above:

  1. The major problem in understanding this issue is the misconception that music and art in general are dedicated to entertainment. Although sometimes a major work of art might also have an entertainment value, that is not its main objective. (See our first discussions). Some of the most important musical achievements of Western musical culture such as Beethoven's last String Quartets, Bach's works or Schubert's music are only some striking examples of pieces initially received with indiferrence or even contempt. Popularity has nothing or very little to do with value. McDonalds has a much larger volume of business than your sophisticated French restaurant and it's easier to understand what Gillette, the inventor of the disposable blade, did than Eistein's theory of relativity. They all affect our lives but at different levels.

    Approaching unfamiliar music should be done with an open mind. If one has precise, well defined expectations based on previous experiences, he/she will be disappointed since any worthwhile new piece will contain original elements, sounds or combinations of sounds never imagined before.

  2. Another misconception is that if music does not expresses emotions, it is not music. True, most of the works we hear today in concerts or on the radio were produced in the 19th century when this was the norm. However, both older or newer music are not based on the same assumption. Most medieval or early Renaissance composers did not even sign their compositions let alone try to describe their personal feelings. Igor Stravinsky, one of the most wildly recognized artists of this century declared that music is incapable of conveying emotions or ideas . According to him, when a listener thinks that he can detect such things in music, he is only deluding himself. Even in the midst of the 19th century, a famous polemic took place with Eduard Hanslik, taking the same stand as Stravinsky.

    For Stravinsky, composing was a "problem solving activity" and Xenakis defines music as "expressing human intelligence through sonic means". Writing a fugue like Bach did or inventing chord progressions as complex and elaborate as Wagner or Chopin did is certainly an involved intellectual activity.

    An even more radical point of view comes from John Cage who thinks that even non intended sounds and/or noises could be music if we decide to accept them as such (if we would only have ears). One could easily dismiss such statements as ridiculous but a more enlightened person would rather try to see if there is any truth to them. Or why obviously intelligent and creative people would make them in the first place.

  3. Most music has melody in the sense that it presents sequences of pitches in a certan rhythmic arrangement. Many times, such sequences of sounds are related to speech patterns and the constrains of the human breath. However, in some cultures, traditional music may contain only the rhythmic element (African drumming) and other cultures may emphasize timbral color at the expense of pitch (classical Chinese music). Contemporary Western music has experimented with both alternatives and, among other things, with textures like the clouds of sound, imagined by Xenakis. To say that music without melody is not music is to exclude such possibilities and adopt a rather narrow definition. Moreover, for some people, a melody means not only a string of pitches and durations but also implies a tonal organization. That makes their understanding of what music is a very parochial one (Western Europe) and limited to a, historically speaking, short period of time (1600-1900).

  4. Allowing a chance (random) procedure to determine certain aspects of a work, especially the details does not necessarily mean that the composer is not creative enough or does not care enough to put the final touches on the piece. Xenakis, Cage and others have done this for philosophical and/or aesthetical reasons. In their case, the creative process takes place on a different level and the author wants to remove himself from it as much as possible so less of his own biases would show up in the final product.

    This is connected to the first point of our discussion: such a composer is not trying to convey personal emotions or experiences but to deal with more abstract concepts. In the middle ages artists viewed themselves as people who have the ability to reflect a higher reality as they received it from above. In a different context, some composers today are trying to articulate their understanding of what the world is all about. And, for example, science tells us that, at a certain (sub-atomic) level, all matter is made out of fleeting particles which are created and destroyed millions of times every second, according to probabilistic, random processes.

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