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Let’s take one of the basic shapes of geometry – the circle. What can we do with it? We can draw a line from the center towards the edge. That’s radius. We can also dissect circle in two equal parts through the center. That gives us diameter. Diameter equals two radiuses.

What if line is not merely a geometrical abstraction but a physical string? Diameter then represents a sound. Radius will be the same sound but octave higher. If we double the length of diameter it should give us octave lower. By doubling down the string we should soon or a later reach infrasound spectrum. By doubling up – ultrasound.

Every division other than a half will give us a note.

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Line that is string that is sound can be folded into shape. For example I have string that is 651mm long. By dividing it by half I get roughly 325mm which is octave. If I divide 651mm into three equal parts I get 217mm. I can build a triangle that has 217mm on each side and sounds accordingly. Tetrahedron has 6 edges. So one side of the tetrahedron is 651/6=108,5.

651mm is the length of guitar string.

I am sure that what has been written above is not new. Definitely someone somewhere already discovered and researched this kind of geometry. Any ideas, speculations, links to sources or software would be much appreciated.