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Music by Numbers :
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Most people perceive a clear distinction between art and science. Science has connotations of rational, structured, going by rules, following the logic. Art is associated with expression, emotion, freedom, following the heart. Nonetheless, Pythagoras, a Greek philosopher who lived some 2500 years ago, described some of the scientific, in casu mathematical, foundations of music. In short, and relevant to this essay : he showed that music is a form of mathematics.
Before we get in to the mathematics, let us point out that it's clear that music and physics are related as well. Music is about sounds, and musical instruments produce sound (vibration of air), coused by vibrations of an air column (trumpets, saxofones, organs, ...), vibrations of strings (guitar, violin, ...) etc. There's plenty of physics theory on strings, frequencies (tones), overtones, harmonics, etc. (see links below : The Physics Classroom : Musical Instruments). In brief : the pitch of a tone is related to the the length of the string. Devide a string in 2, and the frequency will double : you'll hear a sound 'twice' as high : an octave.
An additional easpect of technology in music came with the development of 'artificial' musical instruments : synthetic sound produced by electronical devices : so-called synthezisers. They allowed to change not only the frequency of the sound waves, but also their shape, creating new sounds
Quantum physics seem to have bearing on music as well. Anyone who's ever played in a blues band will confirm that, while you know where the drummer is (in the pub), there's no way of knowing what time he will show up for rehearsal (or sound check, or whatever). This is knwon in quantum mechanics as Heisenberg's Uncertainty Principle : "The more precisely the POSITION is determined, the less precisely the MOMENTUM is known".
Also, there's something with a string theory there, a candidate for the grand unifying theory of physics. So guitar players and theoretical physicists share a common concern : their strings.
In western classical music : the following intervals are known :
freq ratio name 1:1 unison 21:20 [semitone] 16:15 [semitone] / minor second 10:9 major second 9:8 major second 6:5 minor third 5:4 major third 4:3 perfect fourth 7:5 tritone / augmented fourth / diminished fifth 3:2 perfect fifth 8:5 minor sixth 5:3 major sixth 9:5 minor seventh 7:9 major seventh 2:1 octave
The typical form of a blues song is the '12 bar' blues, build around 3 chords. There's a relation between those 3 chords - for the sake of argument : E - A - B. If we look only at the tonica of the chord (the 'ground note', the note that the chord is build on), a 12-bar / 3 chord blues will consist of
The same ratios will appear wether you play the blues in E, or in A, or even in C, and so on. Also other songs, in their simpliest form, can often be reduced to a 3 chord pattern with exactly the same ratio between the frequencies. A typical country song will often be build around C - F - G or G - C - D, and those chords relate to eachother exactly the same way as the E-A-B from our 12 bar blues.
Chords are multiple tones played together or in sequence. In its basic form, a chord consists of 3 notes, and between those 3, the following ratio of frequencies can be found :
In blues, one often adds 1 additional note to the 3th chord, the so-called minor 7th, with a frequency of 9/5 of the frequency of the tonica of the chord.
This all goes for a blues in the Key of E, i.e. all frequencies can be derived from the 330 Hz of the natural E. Blues in any other key will show the same frequency ratios ('intervals'), based on the freqyency of the key note. So, a computer can play the blues ?
Blues has a typical 'sound' or 'feel' about it. We've seen how our 12 bar blues was build around 3 chords / 9 or 10 notes with a given interval (a given ratio between the respective frequencies). The melody that is sung or played against these chords would, in other music, use notes that fit in, based on their freguencies (they 'belong to the scale'). In blues music, however, the melody is often based on a minor scale, accompanied by major chords (see links to music theory below for the difference between minor and major scales : it has to do with using different intervals). This results in a certain discrepancy between the frequencies of the chords and the frequencies used in the melody (the voice, the guitar solo, the harp), which creates the 'typical' blues sound.
So, one can argue that blues melodies are not 'in tune'. Apart from the tension between minor and major scale, the musician might throw in additional notes, notes that, according to the theory of scales and intervals (in classical western music), would not fit in. But they do, somehow, sometimes. These are called the 'blue notes'. They 're the 'magic numbers' - according to their frequency, one would not expect them to work, but they do, and they add to the 'blues feel' or 'blues sound' of the song. On a guitar, these notes can be played by bending the strings while you play a note. Notes can also be played at a slightly higher frequency than would be 'correct', or you can 'bend' or 'slide' from one tone to another, producing an infinite number of tones inbetween. A human voice and musical instruments such as the guitar, the harp, the slide trombone, allow for such 'blue notes' and are therefore very popular in blues music. You can make them wail.
And with the introduction of magic, we leave the realm of exact science. A true blues musician will play the blues, and apply blue notes without having to think about it. He'll play them when it's right to play them. Like the Zen archer who releases the arrow when the moment is right, not when his eyes / brain / training tells him to. As in martial arts, where the master becomes unaware of the technique he uses.
... you can not sing the blues if you own a computer.
This was but an over-simplified approach to music and mathematics applied to it. There's much more to music as such, and th the mathematics behind it. As I am not a musician nor a mathematician - although I have been known to have the blues occasionally - this is just a first introduction, a proof-of-concept that there is numbers behind the music.
There's a lot more theory (and numbers, and relations between numbers) in the wide variety of scales and chords applicable to western music. Then there are also thee aspects of rhythm, modulation, the structure of a musical piece, the problems related to tuning and tempperament, and so on, all of which can be described bu numbers and relations between them.
More information can be found here :
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