One of the oldest forms of art, music is natural to man. After all we are born with the ability to produce with our vocal chords a wide range of sounds. It’s like being born with an attached musical instrument. Being able to communicate with sound is obvioulsy an evolutionary advantage.
Music can be defined as the structured production of sound, with the purpose of transmitting though and emotion. In a non-trivial process, sound is received by our ears and decoded, estimulating certain regions in the human brain. It involves both acoustics and psychology.
Music has four major components: Melody, the set of sounds executed in succession; Harmony, the set of sounds executed simultaneously; Counterpoint is a subtle concept, perhaps best experienced; And there is Rhythm, the proportion of the sounds in melody and harmony.
Surprisingly enough, all the myriad sounds of music can be represented by only seven musical notes (and accidents). This has more to do with the fact that music as a subset of sound that is pleasant to hear, so it ends up having this pattern. Physically, every note has a specific frequence, and from one A to the next, the frequency is doubled.
Music is produced today in an industrial scale (it became mass art), with musical producers working side by side with performers and lyric writers. As Adorno and Horkheimer so brilliantly stated, we are tricked into believing we have a choice for music.
Formally, in Music Theory, a composition is written in modern musical notation. This is a rich creation, with somewhat simple rules, in which music is organized into a sheet composed of staffs.
Music Theory has many points of connection with Mathematics.
Since the music of an instrument is a sucession of frequencies, one can assign numbers to each note and obtain integer sequences. For example, by applying the number 1 to the the lowest pitch in the following sheet an integer sequence is obtained:
This entire song can be heard here.
Then one can, for example study the frequence of notes, or try to find a recurrency relation for the music. I’m sure that from all the possible sequences in the universe, only a handful are considered beautiful songs to us. Is there a pattern to those sequences?
If we understood better how some sequences are more pleasing than others we could improve the quality of our music.
The process described above doesn’t work if more than one note is played at the same time unless you separate it into different sequences. This is unfortunately quite common in music.
The other way around, taking a mathematical table or relation and turning it into music is also possible (although it’s kind of useless).
For example, the astronomer Johannes Kepler, studying the movement of the planets considered each planet as emmiting a note proportional to the orbital velocity, that changes during a revolution around the Sun. There would be a celestial music to each planet. Something similar is done beatifully in an app here – complements to the designer.
A personal selection of songs, divided into pop and classical can be found in this page.
[IMAGE: Vinyl store. image source]