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Geometry and Music

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As part of the new Digital Arts program I'm part of in university I have to come up with an idea thats completely avant garde to use in my ensemble class.  The whole point of this class is to fuse acoustic and digital music together.  Anything I record I'm supposed to screw with in the computer.

In any case my first assignment is to find a website with an interesting idea for us to explore musically and my inkling is to look at the relationship between music and geometry.  and I'm talking about all sorts of math.  There are correlations between quantum mechanics and music all over the place, and you can usually put some aspect of music into things like the golden mean, and the fibbonaci spiral, as well as things like mobius strips and sacred geometry.

I'm posting about this because I'm looking for a good website to show off all this crap, and I"m having difficulty finding a really good one.

I also thought I'd pick your brains for anything you have to say on the subject.
 
Cant think of anything in particular at the moment, but have a look into Fractals.

Complex repeating patterns which form interesting geometric 'art'

http://en.wikipedia.org/wiki/Fractal

http://www.fractal-recursions.com/

:dontknow:
:icon_thumright:
 
Try searching:  mathematics + music instead - a bunch comes up:

http://www.google.com/search?client=firefox-a&rls=org.mozilla%3Aen-US%3Aofficial&channel=s&hl=en&source=hp&q=mathematics+music&btnG=Google+Search

Add Bach:

http://www.google.com/search?hl=en&client=firefox-a&channel=s&rls=org.mozilla%3Aen-US%3Aofficial&hs=gjb&q=mathematics+music+bach&btnG=Search&aq=f&oq=&aqi=
 
The whole point of the project is to fuse acoustic and digital music, and you have to do something with a computer?

Record "Blowin in the Wind" using your laptops built in mic.
 
A lot of research has been done on this, reaching all the way back to Pythagoras (anyone have a comma?).  The latest stuff that I'm familiar with all been AI composition programs that will create a song for you, then adjust it based on your tastes.  The idea is that the program 'learns' what you like and don't like by your response to the music that it creates.

Check out AI papers on musical composition.  U of A has done a bunch of work on this type of stuff (at least when I was there).

 
what really interests me is how it relates to so many different facets of mathematics.

I'm kind of playing around with the idea that music relates to string theory.  Now I'm no mathematician but this is my rudimentary understanding of string theory:

We work in 2 scales in physics.  the super huge.. like size of the universe super huge. and quantum mechanics which is the super small. like sub atomic particles.  the problem is that physicists can't get them to relate directly to each other, like the formulas dont work with each other when they should.  So they developed string theory which is basically the theoretical realm of physics that would have to be real in order for the super huge and the super small to work together.  Nobody has proved that string theory is real, it just shows that a bunch of formulas and such will work *IF* it did in fact exist.  And if it did exist than from what I understand is that technically the universe exists in 11 dimensions instead of 3 (or something like that) which is why it is so difficult to prove that string theory is real because nobody can see outside the 3 dimensions we live in and can interact with (assuming the other 8 are real)

So what I'm thinking is why not make my music project in my ensemble class a way to "show" how music and string theory are interrelated, by using the mathematics of music and relating it to the mathematics of physics, and geometry (pythagoras mayfly?)

Example.  what if music itself is one of those other dimensions? What if on a different plane that we can't interact with in string theory is a place where music is a physical and observable thing? and if so what would it look like?

what do you think? am I pretentious or what?
 
Well, here's my take on string theory...

There's 6 of them. they are tuned EADGBE. If you push down on a fret, the sound goes up by 1 semitone per fret. Harmonics are possible. Chords can be done.
 
I like Jim's idea with the fractal geometry.  The idea being the more you zoom in or out, visually it looks the same.  For example, an atom with oribiting to electrons, to a planet with moons, to a solar system with planets, to a galaxy with solar systems.

With music, you could overdub at 1/2 or double time and the sound would go up or down an octave.  For instance, The Beatles' "In My Life" with George Martin on the Harpsichord.  It's not a Harpsichord.  It's a piano, but George couldn't play it that fast, so they recorded it with the music slowed down to 1/2 the speed.  When they sped the recording up, it sped up his solo and raised it one octave, and made it sound like a Harpsichord.

You could do something similar with an acoustic guitar.
 
this probably won't help - but I find it interesting:

http://www.riprense.com/Zappanotes.htm

mainly this part:

Second, Zappa often employed what he called a "weights and measures" approach to symphonic composing:

"In my compositions," he wrote in The Real Frank Zappa Book, "I employ a system of weights, balances, measured tensions and releases---in some ways similar to Varese's aesthetic. The similarities are best illustrated by comparison to a Calder mobile: a multicolored whatchamacallit dangling in space, that has big blobs of metal connected to pieces of wire, balanced ingeniously against little metal dingleberries on the other end. Varese knew Calder, and was fascinated by these creations.

"So, in my case, I say: A large mass of any material will 'balance' a smaller, denser mass of any material, according to the length of the gizmo it's dangling on, and the 'balance point' chosen to facilitate the danglement."

This extremely architectural approach to his music is characteristic. Zappa's aesthetics favored the physics of organizing and realizing sound. His descriptive language bears this out. A group of notes ("the recipe," as he termed it in The Real Frank Zappa Book), does not "become a 'musical experience' in normal terms" until "it has been converted into wiggling air molecules." What's more:

"Music, in performance, is a type of sculpture. The air in the performance space is sculpted into something. This 'molecule-sculpture-over-time' is then 'looked at' by the ears of the listeners---or a microphone."
 
Keep us posted on this project.  I have been thinking about it all week.  Especially the part about the other dimensions, and the thought that music can exist as a physical entity in another dimension.  It might not be truly the way things work, but its a cool concept today dream about.  Also, the Frank Zappa idea of music as a temporary "air sculpture."  Very cool ways of thinking about music.

I don't know that I have anything to add.  But its cool to think about it.

If I were inclined to drop acid again, this would be a great topic to explore.

I'm interested in hearing how this project turns out, and how it might change as you work on it.
 
really in a practical application it would be far less fantastical.  When i think of using a mobius strip... thats where you twist a piece of paper around and tape the ends together so that you draw a line on both sides in one motion... its kind of like back in the day playing mario brothers, when you jump off one end of the screen you appear at the other end.  anyway. people have done things like arrange notes a certain way on the mobius strip. which flattened out just looks like a square.  and when you play as the notes are highlighted it kind of draws a picture, which can be a pretty complex and cool looking geometrical shape.  I just find it interesting that there really is a correlation, its not just contrived but certain note patterna actually look like a septacle or a dodecahedron or similar kinds of shapes.
 
Really, anything that follows a repeating pattern is mathematical.  Music has the chromatic scale repeating AND the added bonus of being made up of sound waves, which follow laws of physics and can be observed doing all kinds of interesting things when you study acoustics.  So there is a lot of mathematical material there. 

I personally tend to relate music to painting more easily because I'm a painter and not a mathematician.  Though, painting is oddly scientific once you get into color theory and the study of optics. 

Music reminds me of these shapes we used to draw in school (I can't remember if we did them in math class or in art class, they're a little of both).  I can't remember what they were called, but you would take any standard geometric shape and put a specified number of equidistant dots along the outside lines of it.  Then you would number them with the numbers starting over at each side, then you would take a rule and draw straight lines from 1 on one side to 1 on another side and so on until you had lines connecting the dots throughout.  You didn't have to neccessarily go from 1 to 1.  You could go from 1 to 5 if you wanted, provided that the next on was from 2 to 6.  The pattern had to remain constant.  Anyways, differences in the pattern you chose would create differences in the picture you came up with when you were all done.  Intervals and scales make me think of that sometimes. 
 
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