I'm preparing a seminar for my math degree, and I'd really like to cover a topic that includes my fascination with geometry, music, and some physics. I stumbled upon one of those 'wooden books' coffee table books that covered an interesting device called a harmonograph. It covered exactly what I wanted to look into.
The harmonograph is a device that uses 2 or 3 pendulums with weights at differing ratios, two swinging perpendicular, and sometimes one rotating for another degree of movement. this movement in turn manipulates a surface where a pen or marker is touching, drawing out a pattern based on the oscillations and decay of the pendulums. essentially, it's the grandfather of the spirograph.
the wooden book approaches the ratios of the weights in relation to the ratios that musical intervals operate on, discovered way back by pythagoras. ratios such as 3:2 (the fifth) produce beautiful geometric images on the harmonograph.
If anyone here has experiences or knowledge of harmonographs, or has any websites to further research and understand these devices I'd appreciate it. They seem fairly straight forward in graphing with parametric equations (Lissajous curves with some modifying elements), but I haven't tried my hand at much yet.
A simple google search has yielded some valuable resources already, such as equations to mess around with and try in graphing software (at which I will need to learn in a hurry) and a really great java emulation that lets you play with many variables, or just randomly produce images. mathworld has a very short article as well. I don't know of any math journal search sites, if any exist I can access let me know!
the site with the physics help is
http://members.tip.net.au/~apurdam/harm ... ysics.html
and the java emulator is
http://members.tip.net.au/~apurdam/harm ... graph.html
any help or info would be great!
The harmonograph is a device that uses 2 or 3 pendulums with weights at differing ratios, two swinging perpendicular, and sometimes one rotating for another degree of movement. this movement in turn manipulates a surface where a pen or marker is touching, drawing out a pattern based on the oscillations and decay of the pendulums. essentially, it's the grandfather of the spirograph.
the wooden book approaches the ratios of the weights in relation to the ratios that musical intervals operate on, discovered way back by pythagoras. ratios such as 3:2 (the fifth) produce beautiful geometric images on the harmonograph.
If anyone here has experiences or knowledge of harmonographs, or has any websites to further research and understand these devices I'd appreciate it. They seem fairly straight forward in graphing with parametric equations (Lissajous curves with some modifying elements), but I haven't tried my hand at much yet.
A simple google search has yielded some valuable resources already, such as equations to mess around with and try in graphing software (at which I will need to learn in a hurry) and a really great java emulation that lets you play with many variables, or just randomly produce images. mathworld has a very short article as well. I don't know of any math journal search sites, if any exist I can access let me know!
the site with the physics help is
http://members.tip.net.au/~apurdam/harm ... ysics.html
and the java emulator is
http://members.tip.net.au/~apurdam/harm ... graph.html
any help or info would be great!