Using sound as a medium of translation for these 4D shapes?

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Using sound as a medium of translation for these 4D shapes?

Postby Nate » Tue Jul 22, 2014 4:58 pm


I was super fascinated by the posts that user ICN5D had made on Reddit, and decided to try to learn how to explore these shapes myself. I would like to explore them using a different medium, however. I am a computer programmer and music producer in my 20s looking for new and exciting ways to combine both of these passions. I was hoping that this forum could help me start my journey exploring these shapes with sound :D.

I guess my first question is kind of broad, but does anyone have any ideas on where I could start? I know of a program called MAX ( which is a visual programming language that has built in sound generation modules. I was thinking I would probably end up using that for the sound synthesis, but I'm not entirely sure how to approach it.

Has anyone worked with these shapes and sound before?
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Re: Using sound as a medium of translation for these 4D shap

Postby ICN5D » Wed Jul 23, 2014 5:14 pm

Now that you mention it, one of my friends put something up on FB that references a band called Tesseract. I'm not sure how much high-D geometry they apply to the music, but probably some.
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Re: Using sound as a medium of translation for these 4D shap

Postby student91 » Wed Jul 23, 2014 11:10 pm

I was just thinking about a video of vi harts which used sound to "visualize" a braid. here. Mayhe a similar thing can be done to visualize the toratopes. There is a small problem though, because the "visualization" would be 1+1-dimensional (1 static dimension and 1 time dimension). The original pictures of ICD5Ns were 3+1-dimensional (ofc. it was actually 2 dimensional which gave a 3-dimensional expression, but let's just ignore that). This means quite a big loss of information, because you can only have 1-dimensional cutting planes that are rotating/translating through these shapes.

A sound for a circle would then start with a single note, which will split in two notes that are quickly moving away from each other in pitch, then stabilizing around some value, and then coming together again. You could also make a formula for this, and then change that in a sound-file. I don't think that to be too hard. The formula would look something like
sin(440*(r+sqrt(r^2-t^2))t) + sin(440*(r-sqrt(r^2-t^2))t). the parts (r+sqrt(r^2-t^2)) and (r-sqrt(r^2-t^2)) give a circle that touches the 0-line at t=0, and the pich is then dependend on these. For the full thing the soundwave has to start at -r, which is not desirable. We could thus translate the function, so that we get sin(440*(r+sqrt(r^2-(t-r)^2))t) + sin(440*(r-sqrt(r^2-(t-r)^2))t). this would give a circle in a pitch-time kind of world, and an error at t>2r.
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